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1
Abebe, Amare, and Maye Elmardi. "Irrotational-fluid cosmologies in fourth-order gravity." International Journal of Geometric Methods in Modern Physics 12, no. 10 (October 25, 2015): 1550118. http://dx.doi.org/10.1142/s0219887815501182.
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In this paper, we explore classes of irrotational-fluid cosmological models in the context of f(R)-gravity in an attempt to put some theoretical and mathematical restrictions on the form of the f(R) gravitational Lagrangian. In particular, we investigate the consistency of linearized dust models for shear-free cases as well as in the limiting cases when either the gravito-magnetic or gravito-elecric components of the Weyl tensor vanish. We also discuss the existence and consistency of classes of non-expanding irrotational spacetimes in f(R)-gravity.
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PATEL, L. K., and LAKSHMI S. DESAI. "PLANE SYMMETRIC VISCOUS-FLUID COSMOLOGICAL MODELS WITH HEAT FLUX." International Journal of Modern Physics D 03, no. 03 (September 1994): 639–45. http://dx.doi.org/10.1142/s0218271894000770.
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A class of nonstatic inhomogeneous plane-symmetric solutions of Einstein field equations is obtained. The source for these solutions is a viscous fluid with heat flow. The fluid flow is irrotational and it has nonzero expansion, shear and acceleration. All these solutions have a big-bang singularity. The matter-free limit of the solutions is the well-known Kasner vacuum solution. Some physical features of the solutions are briefly discussed.
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CHIMENTO, LUIS P., and WINFRIED ZIMDAHL. "DUALITY INVARIANCE AND COSMOLOGICAL DYNAMICS." International Journal of Modern Physics D 17, no. 12 (November 2008): 2229–54. http://dx.doi.org/10.1142/s0218271808013820.
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A duality transformation that interrelates expanding and contracting cosmological models is shown to single out a duality invariant, interacting two-component description of any irrotational, geodesic and shear-free cosmic medium with vanishing three-curvature scalar. We have applied this feature to a system of matter and radiation, to a mixture of dark matter and dark energy, to minimal and conformal scalar fields, and to an enlarged Chaplygin gas model of the cosmic substratum. We have extended the concept of duality transformations to cosmological perturbations and demonstrated the invariance of adiabatic pressure perturbations under these transformations.
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Chase, D. M. "Fluctuations in wall-shear stress and pressure at low streamwise wavenumbers in turbulent boundary-layer flow." Journal of Fluid Mechanics 225 (April 1991): 545–55. http://dx.doi.org/10.1017/s0022112091002161.
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Turbulent boundary-layer fluctuations in the incompressive domain are expressed in terms of fluctuating velocity-product 'sources’ in order to elucidate relative characteristics of fluctuating wall-shear stress and pressure in the subconvective range of streamwise wavenumbers. Appropriate viscous wall conditions are applied, and results are obtained to lowest order in this Strouhal-scaled wavenumber which serves as the expansion parameter. The spectral amplitudes of pressure and of the shear stress component directed along the wavevector both contain additive terms proportional to source integrals with exponential wall-distance weighting characteristic respectively of the irrotational and the rotational fields. At low wavenumbers, barring unexpected relative smallness of the pertinent boundary-layer source term, the rotational terms become dominant. There the wall pressure and shear-stress component have spectra that approach the same non-vanishing, wavevector-white but generally viscous-scale-dependent level and are totally coherent with phase difference ½π. The other, irrotational contributions to the shear-stress and pressure amplitudes likewise bear a simple and previously known, generally wavevector– and frequency-dependent, ratio to one another. In an inviscid limit this contribution to the pressure amplitude reduces to the one obtained previously from inviscid treatments. A representative class of models is introduced for the source spectrum, and the resulting rotational contribution to the spectral density of wall pressure and K-aligned shear stress at low (but incompressive) wavenumbers is estimated. It is suggested that this contribution may predominate and account for measured low-wavenumber levels of wall pressure.
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Kojima, Yasufumi, Shota Kisaka, and Kotaro Fujisawa. "Magneto-elastic equilibrium of a neutron star crust." Monthly Notices of the Royal Astronomical Society 506, no. 3 (July 19, 2021): 3936–45. http://dx.doi.org/10.1093/mnras/stab1848.
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ABSTRACT We examine the equilibrium of a magnetized neutron star crust. We calculate axially symmetric models in which an elastic force balances solenoidal motion driven by a Lorentz force. A large variety of equilibrium models are allowed by incorporating the elastic shear deformation; in addition, toroidal-magnetic-field-dominated models are available. These results remarkably differ from those in barotropic fluid stars. We demonstrate some models wherein the magnetic energy exceeds the elastic energy. The excess comes from the fact that a large amount of magnetic energy is associated with the irrotational part of the magnetic force, which is balanced with gravity and pressure. It is sufficient for equilibrium models that the minor solenoidal part is balanced by a weak elastic force. We find that the elasticity in the crust plays an important role on the magnetic field confinement. Further, we present the spatial distribution of the shear stress at the elastic limit, by which the crust-fracture location can be identified. The result has useful implications for realistic crust-quake models.
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Compelli, A., R. Ivanov, and M. Todorov. "Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2111 (December 11, 2017): 20170091. http://dx.doi.org/10.1098/rsta.2017.0091.
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A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet–Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to approximations of Boussinesq and Korteweg–de Vries (KdV) types, taking into account the effect of the slowly varying bottom. The arising KdV equation with variable coefficients is studied numerically when the initial condition is in the form of the one-soliton solution for the initial depth. This article is part of the theme issue ‘Nonlinear water waves’.
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Ilin, Konstantin. "Shallow-water models for a vibrating fluid." Journal of Fluid Mechanics 833 (November 2, 2017): 1–28. http://dx.doi.org/10.1017/jfm.2017.687.
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We consider a layer of an inviscid fluid with a free surface which is subject to vertical high-frequency vibrations. We derive three asymptotic systems of equations that describe slowly evolving (in comparison with the vibration frequency) free-surface waves. The first set of equations is obtained without assuming that the waves are long. These equations are as difficult to solve as the exact equations for irrotational water waves in a non-vibrating fluid. The other two models describe long waves. These models are obtained under two different assumptions about the amplitude of the vibration. Surprisingly, the governing equations have exactly the same form in both cases (up to the interpretation of some constants). These equations reduce to the standard dispersionless shallow-water equations if the vibration is absent, and the vibration manifests itself via an additional term which makes the equations dispersive and, for small-amplitude waves, is similar to the term that would appear if surface tension were taken into account. We show that our dispersive shallow-water equations have both solitary and periodic travelling wave solutions and discuss an analogy between these solutions and travelling capillary–gravity waves in a non-vibrating fluid.
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LABERTEAUX, K. R., and S. L. CECCIO. "Partial cavity flows. Part 1. Cavities forming on models without spanwise variation." Journal of Fluid Mechanics 431 (March 25, 2001): 1–41. http://dx.doi.org/10.1017/s0022112000002925.
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Partial cavities that formed on the vertices of wedges and on the leading edge of stationary hydrofoils were examined experimentally. The geometry of these test objects did not vary in the spanwise direction (i.e. two-dimensional). Open partial cavities formed on a series of two-dimensional wedges and on a plano-convex hydrofoil. These cavities terminated near the point of maximum cavity thickness, and small vapour-filled vortices were shed in the turbulent cavity wake. The turbulent flow in the wake of the open cavity was similar to the turbulent shear flow downstream of a rearward-facing step. Re-entrant flow was not observed in the cavity closure of open cavities, although recirculating flow associated with a region of flow separation was detected for some cases. Predictions of a two-dimensional free-streamline model of the cavitating wedge flows were compared to the experimentally observed cavities. The model predicted the profile of the open cavity only to the point of maximum cavity thickness. Examination of the flow field near the closure of the open cavities revealed adverse pressure gradients near the cavity closure. The pressure gradients around the open cavities were sufficient to cause large-scale condensation of the cavity. Unsteady re-entrant partial cavities formed on a two-dimensional NACA0009 hydrofoil. The interface of the unsteady closed cavities smoothly curved to form a re-entrant jet at the cavity terminus, and the re-entrant flow was directed upstream. The re-entrant flow impinged on the cavity interface and led to the periodic production of cloud cavitation. These cavities exhibited a laminar flow reattachment. The flow around the closed cavity was largely irrotational, while vorticity was created when the cloud cavitation collapsed downstream of the cavity. Examination of the flow field near closure of these cavities also revealed adverse pressure gradients near the partial cavity closure, but the rise in pressure did not lead to the premature condensation of the cavity.
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Sami, Heba, and Amare Abebe. "Perturbations of quasi-Newtonian universes in scalar–tensor gravity." International Journal of Geometric Methods in Modern Physics 18, no. 10 (June 29, 2021): 2150158. http://dx.doi.org/10.1142/s0219887821501589.
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In this contribution, we consider the well-known equivalence between [Formula: see text] gravity and Brans–Dicke-type scalar–tensor theories to study the evolution of scalar cosmological perturbations for a class of shear-free cosmological dust models with irrotational fluid flows. We use the [Formula: see text] covariant formalism to present the covariant linearized evolution and constraint equations. We then derive the integrability conditions describing a consistent evolution of the linearized field equations of quasi-Newtonian universes in the modified (scalar–tensor) theory of gravity. Finally, we derive the evolution equations for the density and velocity perturbations of the quasi-Newtonian universe. We apply the harmonic decomposition and explore the behavior of the matter density contrast by considering [Formula: see text] toy models. The growth of the matter density contrast for both short- and long-wavelength modes has been examined by applying certain assumptions of the initial conditions. We then apply the so-called quasi-static approximation to obtain exact solutions on small scales, but the results show that this approximation is not applicable here. Moreover, any small deviation from general relativity and any small change in the initial conditions of the perturbations causes huge orders-of-magnitude deviations from limiting general relativistic results, potentially putting constraints on the modified theory in the quasi-Newtonian cosmologies treatment. Our current work differs from other works in the literature, in that it is the first such work to show quasi-Newtonian cosmologies are unstable to linearized perturbations in modified gravity.
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COLEMAN, G. N., D. FEDOROV, P. R. SPALART, and J. KIM. "A numerical study of laterally strained wall-bounded turbulence." Journal of Fluid Mechanics 639 (August 28, 2009): 443–78. http://dx.doi.org/10.1017/s0022112009991042.
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Direct numerical simulation (DNS) is used to study the effects of mean lateral divergence and convergence on wall-bounded turbulence, by applying uniform irrotational temporal deformations to a plane-channel domain. This extends a series of studies of similar deformations. Fast and slow straining fields are considered, leading to a matrix of four cases, all corresponding to zero-pressure-gradient (ZPG) flows along the centreplane in ducts with constant rectangular cross-sectional area but varying aspect ratio. The results are used to address basic physical and modelling questions, and create a database that allows detailed yet straightforward testing of turbulence models. Initial tests of three representative one-point models reveal meaningful differences. The extra-strain effects introduced by the matrix of fast and slow divergence and convergence are documented, separating the direct effects of the strain from the indirect ones that alter the shear rate and change the distance from the wall. Some findings are predictable, and none contradict experimental findings. Others require more thought, notably an asymmetry between the effect of convergence and divergence on the peak turbulence kinetic energy.
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Skehill, Ronan J., and Sean McGrath. "The Application of Fluid Mobility Modelling in Wireless Cellular Networks." Mobile Information Systems 3, no. 2 (2007): 89–106. http://dx.doi.org/10.1155/2007/380671.
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Mobility models, synthetic or trace, try to accurately model the movement of a single user or a group of users. Models can be used in simulators and emulators to investigate the consequences of mobility on new protocols or network management techniques. A limitation with current trace mobility models is they are based on empirical data which are limited to specific network types and environments. Limitations with synthetic models are that they are complex, computationally heavy, and lack realism. To address these issue a new approach needs to be taken. One such approach is the use of fluid mechanics and transport theory to represent user mobility. A model based on viscous free irrotational fluid mechanics with empirical data from pedestrian and vehicular studies provide a means of creating realistic group movement characteristics with smooth non random trajectories and smooth continuous velocity. The model is used in an example to provide boundary crossing rates for users in a cellular network and optimising the size of cellular location areas.
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DeLano, Kevin, Jeffrey Lee, Rachelle Roper, and Andrew Calvert. "Dextral, normal, and sinistral faulting across the eastern California shear zone–Mina deflection transition, California-Nevada, USA." Geosphere 15, no. 4 (June 24, 2019): 1206–39. http://dx.doi.org/10.1130/ges01636.1.
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Abstract Strike-slip faults commonly include extensional and contractional bends and stepovers, whereas rotational stepovers are less common. The Volcanic Tableland, Black Mountain, and River Spring areas (California and Nevada, USA) (hereafter referred to as the VBR region) straddle the transition from the dominantly NW-striking dextral faults that define the northwestern part of the eastern California shear zone into a rotational stepover characterized by dominantly NE-striking sinistral faults that define the southwestern Mina deflection. New detailed geologic mapping, structural studies, and 40Ar/39Ar geochronology across the VBR region allow us to calculate Pliocene to Pleistocene fault slip rates and test predictions for the kinematics of fault slip transfer into this rotational stepover. In the VBR, Mesozoic basement is nonconformably overlain by a Miocene sequence of rhyolite, dacite, and andesite volcanic rocks that yield 40Ar/39Ar ages between 22.878 ± 0.051 Ma and 11.399 ± 0.041 Ma. Miocene rocks are unconformably overlain by an extensive sequence of Pliocene basalt and andesite lava flows and cinder cones that yield 40Ar/39Ar ages between 3.606 ± 0.060 Ma and 2.996 ± 0.027 Ma. The Pliocene sequence is, in turn, unconformably overlain by Quaternary tuffs and sedimentary rocks. This sequence of rocks is cut by NS- to NW-striking normal faults across the Volcanic Tableland that transition northward into NS-striking normal faults across the Black Mountain area and that, in turn, transition northward into NW-striking dextral and NE-striking sinistral faults in the River Spring area. A range of geologic markers were used to measure offset across the faults in the VBR, and combined with the age of the markers, yield minimum ∼EW-extension rates of ∼0.5 mm/yr across the Volcanic Tableland and Black Mountain regions, and minimum NW-dextral slip and NE-sinistral slip rates of ∼0.7 and ∼0.3 mm/yr, respectively, across the River Spring region. In the River Spring area, our preferred minimum dextral slip and sinistral slip rates are 0.8–0.9 mm/yr and 0.7–0.9 mm/yr, respectively. We propose three kinematic fault slip models, two irrotational and one rotational, whereby the VBR region transfers a portion of dextral Owens Valley fault slip northwestward into the Mina deflection. In irrotational model 1, Owens Valley fault slip is partitioned into two components, one northeastward onto the White Mountain fault zone and one northwestward into the Volcanic Tableland. Slip from the two zones is then transferred northward into the southwestern Mina deflection. In irrotational model 2, Owens Valley fault slip is partitioned into three components, with the third component partitioned west-northwest onto the Sierra Nevada frontal fault zone. In the rotational model, predicted sinistral slip rates across the southwestern Mina deflection are at least 115% greater than our observed minimum slip rates, implying our minimum observed rates underestimate true sinistral slip rates. A comparison of summed geologic fault slip rates, parallel to motion of the Sierra Nevada block relative to the central Great Basin, from the Sierra Nevada northeastward across the VBR region and into western Nevada are the same as geodetic rates, if our assumptions about the geologic slip rate across the dextral White Mountain fault zone is correct.
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Jiménez, Javier. "Optimal fluxes and Reynolds stresses." Journal of Fluid Mechanics 809 (November 15, 2016): 585–600. http://dx.doi.org/10.1017/jfm.2016.692.
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It is remarked that fluxes in conservation laws, such as the Reynolds stresses in the momentum equation of turbulent shear flows, or the spectral energy flux in anisotropic turbulence, are only defined up to an arbitrary solenoidal field. While this is not usually significant for long-time averages, it becomes important when fluxes are modelled locally in large-eddy simulations, or in the analysis of intermittency and cascades. As an example, a numerical procedure is introduced to compute fluxes in scalar conservation equations in such a way that their total integrated magnitude is minimised. The result is an irrotational vector field that derives from a potential, thus minimising sterile flux ‘circuits’. The algorithm is generalised to tensor fluxes and applied to the transfer of momentum in a turbulent channel. The resulting instantaneous Reynolds stresses are compared with their traditional expressions, and found to be substantially different. This suggests that some of the alleged shortcomings of simple subgrid models may be representational artefacts, and that the same may be true of the intermittency properties of the turbulent stresses.
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Johansson, Arne V., and Magnus Hallbäck. "Modelling of rapid pressure—strain in Reynolds-stress closures." Journal of Fluid Mechanics 269 (June 25, 1994): 143–68. http://dx.doi.org/10.1017/s0022112094001515.
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The most general form for the rapid pressure—strain rate, within the context of classical Reynolds-stress transport (RST) closures for homogeneous flows, is derived, and truncated forms are obtained with the aid of rapid distortion theory. By a classical RST-closure we here denote a model with transport equations for the Reynolds stress tensor and the total dissipation rate. It is demonstrated that all earlier models for the rapid pressure—strain rate within the class of classical Reynolds-stress closures can be formulated as subsets of the general form derived here. Direct numerical simulations were used to show that the dependence on flow parameters, such as the turbulent Reynolds number, is small, allowing rapid distortion theory to be used for the determination of model parameters. It was shown that such a nonlinear description, of fourth order in the Reynolds-stress anisotropy tensor, is quite sufficient to very accurately model the rapid pressure—strain in all cases of irrotational mean flows, but also to get reasonable predictions in, for example, a rapid homogeneous shear flow. Also, the response of a sudden change in the orientation of the principal axes of a plane strain is investigated for the present model and models proposed in the literature. Inherent restrictions on the predictive capability of Reynolds-stress closures for rotational effects are identified.
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McManus, Des J., and Alan A. Coley. "Shear-free, irrotational, geodesic, anisotropic fluid cosmologies." Classical and Quantum Gravity 11, no. 8 (August 1, 1994): 2045–58. http://dx.doi.org/10.1088/0264-9381/11/8/011.
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Belcher, S. E., J. A. Harris, and R. L. Street. "Linear dynamics of wind waves in coupled turbulent air—water flow. Part 1. Theory." Journal of Fluid Mechanics 271 (July 25, 1994): 119–51. http://dx.doi.org/10.1017/s0022112094001710.
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When air blows over water the wind exerts a stress at the interface thereby inducing in the water a sheared turbulent drift current. We present scaling arguments showing that, if a wind suddenly starts blowing, then the sheared drift current grows in depth on a timescale that is larger than the wave period, but smaller than a timescale for wave growth. This argument suggests that the drift current can influence growth of waves of wavelength λ that travel parallel to the wind at speed c.In narrow ‘inner’ regions either side of the interface, turbulence in the air and water flows is close to local equilibrium; whereas above and below, in ‘outer’ regions, the wave alters the turbulence through rapid distortion. The depth scale, la, of the inner region in the air flow increases with c/u*a (u*a is the unperturbed friction velocity in the wind). And so we classify the flow into different regimes according to the ratio la/λ. We show that different turbulence models are appropriate for the different flow regimes.When (u*a + c)/UB(λ) [Lt ] 1 (UB(z) is the unperturbed wind speed) la is much smaller than λ. In this limit, asymptotic solutions are constructed for the fully coupled turbulent flows in the air and water, thereby extending previous analyses of flow over irrotational water waves. The solutions show that, as in calculations of flow over irrotational waves, the air flow is asymmetrically displaced around the wave by a non-separated sheltering effect, which tends to make the waves grow. But coupling the air flow perturbations to the turbulent flow in the water reduces the growth rate of the waves by a factor of about two. This reduction is caused by two distinct mechanisms. Firstly, wave growth is inhibited because the turbulent water flow is also asymmetrically displaced around the wave by non-separated sheltering. According to our model, this first effect is numerically small, but much larger erroneous values can be obtained if the rapid-distortion mechanism is not accounted for in the outer region of the water flow. (For example, we show that if the mixing-length model is used in the outer region all waves decay!) Secondly, non-separated sheltering in the air flow (and hence the wave growth rate) is reduced by the additional perturbations needed to satisfy the boundary condition that shear stress is continuous across the interface.
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Chazel, F., M. Benoit, A. Ern, and S. Piperno. "A double-layer Boussinesq-type model for highly nonlinear and dispersive waves." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2108 (May 27, 2009): 2319–46. http://dx.doi.org/10.1098/rspa.2008.0508.
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We derive and analyse, in the framework of the mild-slope approximation, a new double-layer Boussinesq-type model that is linearly and nonlinearly accurate up to deep water. Assuming the flow to be irrotational, we formulate the problem in terms of the velocity potential, thereby lowering the number of unknowns. The model derivation combines two approaches, namely the method proposed by Agnon et al. ( Agnon et al. 1999 J. Fluid Mech. 399 , 319–333) and enhanced by Madsen et al. ( Madsen et al. 2003 Proc. R. Soc. Lond. A 459 , 1075–1104), which consists of constructing infinite-series Taylor solutions to the Laplace equation, to truncate them at a finite order and to use Padé approximants, and the double-layer approach of Lynett & Liu ( Lynett & Liu 2004 a Proc. R. Soc. Lond. A 460 , 2637–2669), which allows lowering the order of derivatives. We formulate the model in terms of a static Dirichlet–Neumann operator translated from the free surface to the still-water level, and we derive an approximate inverse of this operator that can be built once and for all. The final model consists of only four equations both in one and two horizontal dimensions, and includes only second-order derivatives, which is a major improvement in comparison with so-called high-order Boussinesq models. A linear analysis of the model is performed, and its properties are optimized using a free parameter determining the position of the interface between the two layers. Excellent dispersion and shoaling properties are obtained, allowing the model to be applied up to the deep-water value k h =10. Finally, numerical simulations are performed to quantify the nonlinear behaviour of the model, and the results exhibit a nonlinear range of validity reaching at least k h =3π.
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Coley, Alan A., and Des J. McManus. "On spacetimes admitting shear-free, irrotational, geodesic time-like congruences." Classical and Quantum Gravity 11, no. 5 (May 1, 1994): 1261–82. http://dx.doi.org/10.1088/0264-9381/11/5/013.
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Krasiński, Andrzej. "Shear‐free normal cosmological models." Journal of Mathematical Physics 30, no. 2 (February 1989): 433–41. http://dx.doi.org/10.1063/1.528462.
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Mimoso, J. P., and P. Crawford. "Shear-free anisotropic cosmological models." Classical and Quantum Gravity 10, no. 2 (February 1, 1993): 315–26. http://dx.doi.org/10.1088/0264-9381/10/2/013.
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Komori, Satoru, and Hiromasa Ueda. "The large-scale coherent structure in the intermittent region of the self-preserving round free jet." Journal of Fluid Mechanics 152 (March 1985): 337–59. http://dx.doi.org/10.1017/s0022112085000726.
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Large-scale coherent structure in a round free jet injected into a low-speed, co-flowing stream was experimentally investigated using laser-Doppler and cold-wire techniques. Particular attention was paid to the coherent structures in the outer intermittent region of the jet in an almost self-preserving state. Velocity fluctuations u (axial) and v (radial) and temperature fluctuations θ were measured simultaneously at two positions: a reference position and a moving position. In order to clarify the pattern of coherent motion, a pattern-averaging technique was adopted and the characteristics of the turbulent fluctuations were conditionally averaged. The results show that a large-scale coherent structure exists even in the self-preserving region of a round free jet, as well as in the near field. It has a vortical structure which consists of strong outward turbulent motion from inside the jet, turbulent reverse flow and inflow in the irrotational ambient region (entrainment). In the coherent structure, the negative pattern-averaged Reynolds stress occurs at two locations: one in the irrotational ambient region outside the turbulent/irrotational interface and the other in the turbulent jet inside the interface. The former is instantaneously produced in the irrotational inflow outside the interface when the vortical motion is accelerated, and it changes even the sign of conventionally averaged Reynolds stress. The latter is instantaneously produced in the turbulent flow near the high-shear region when the turbulent motion is more strongly directed by the acceleration of the vortical motion towards the centre of the vortical structure than the averaged motion.
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Tsai, Wu-ting, Guan-hung Lu, Jheng-rong Chen, Albert Dai, and William R. C. Phillips. "On the Formation of Coherent Vortices beneath Nonbreaking Free-Propagating Surface Waves." Journal of Physical Oceanography 47, no. 3 (March 2017): 533–43. http://dx.doi.org/10.1175/jpo-d-16-0242.1.
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AbstractNumerical simulations of monochromatic surface waves freely propagating over an initially quiescent flow field are conducted and found to reveal an array of quasi-streamwise vortices of alternating orientation in a manner akin to that of Langmuir circulation beneath wind-driven surface waves. A linear instability analysis of the wave-averaged Craik–Leibovich (CL) equation is then conducted to determine whether the structures in the simulations can be explained by the Craik–Leibovich type 2 (CL2) instability, which requires the presence of spanwise-independent drift and mean shear of the same sign. There is no imposed shear in the simulations, but they confirm the theoretical analysis of Longuet-Higgins that an Eulerian-mean shear with a magnitude comparable to that of Lagrangian Stokes drift occurs at the edge of the surface boundary layer in the otherwise irrotational oscillatory flow. The spanwise wavelength of the least stable disturbance is found to be close to the spacing between predominant vortex pairs, which likely are excited by the CL2 instability.
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Sharif, M., and M. Zaeem Ul Haq Bhatti. "Shear-free and cavity models with plane symmetry." Astrophysics and Space Science 352, no. 2 (April 26, 2014): 883–91. http://dx.doi.org/10.1007/s10509-014-1940-9.
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Msomi, A. M., K. S. Govinder, and S. D. Maharaj. "New shear-free relativistic models with heat flow." General Relativity and Gravitation 43, no. 6 (February 3, 2011): 1685–96. http://dx.doi.org/10.1007/s10714-011-1150-5.
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Collins, C. B. "Shear-free fluids in general relativity." Canadian Journal of Physics 64, no. 2 (February 1, 1986): 191–99. http://dx.doi.org/10.1139/p86-034.
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For a large class of shear-free general-relativistic perfect fluids that obey a barotropic equation of state, either the expansion or the rotation is zero; well-known examples include the Friedmann–Robertson–Walker (FRW) models, the Gödel solution, and stationary axisymmetric systems in rigid rotation. It has been conjectured that this is necessarily the case. Several results prove that restricted versions of this conjecture are valid, although no proof is known for the general case. A survey of these special results is given, together with physical and mathematical reasons for the study of shear-free fluids.If the conjecture is true, then there are three mutually exclusive subclasses, according to whether or not the expansion and the rotation are zero separately or simultaneously. Of these, the physically most interesting subclass is that in which the expansion is not zero, since this subclass might be thought to contain space-times that are suitable for the description of collapsing stars or expanding cosmologies. All space-times of this particular subclass are given, and their global properties are investigated. It turns out that the FRW models are the only ones in which the matter is physically reasonable on a global scale. This consequently provides a global uniqueness theorem for the FRW models.
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Teixeira, M. A. C., and C. B. da Silva. "Turbulence dynamics near a turbulent/non-turbulent interface." Journal of Fluid Mechanics 695 (February 13, 2012): 257–87. http://dx.doi.org/10.1017/jfm.2012.17.
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AbstractThe characteristics of the boundary layer separating a turbulence region from an irrotational (or non-turbulent) flow region are investigated using rapid distortion theory (RDT). The turbulence region is approximated as homogeneous and isotropic far away from the bounding turbulent/non-turbulent (T/NT) interface, which is assumed to remain approximately flat. Inviscid effects resulting from the continuity of the normal velocity and pressure at the interface, in addition to viscous effects resulting from the continuity of the tangential velocity and shear stress, are taken into account by considering a sudden insertion of the T/NT interface, in the absence of mean shear. Profiles of the velocity variances, turbulent kinetic energy (TKE), viscous dissipation rate ($\varepsilon $), turbulence length scales, and pressure statistics are derived, showing an excellent agreement with results from direct numerical simulations (DNS). Interestingly, the normalized inviscid flow statistics at the T/NT interface do not depend on the form of the assumed TKE spectrum. Outside the turbulent region, where the flow is irrotational (except inside a thin viscous boundary layer),$\varepsilon $decays as${z}^{\ensuremath{-} 6} $, where$z$is the distance from the T/NT interface. The mean pressure distribution is calculated using RDT, and exhibits a decrease towards the turbulence region due to the associated velocity fluctuations, consistent with the generation of a mean entrainment velocity. The vorticity variance and$\varepsilon $display large maxima at the T/NT interface due to the inviscid discontinuities of the tangential velocity variances existing there, and these maxima are quantitatively related to the thickness$\delta $of the viscous boundary layer (VBL). For an equilibrium VBL, the RDT analysis suggests that$\delta \ensuremath{\sim} \eta $(where$\eta $is the Kolmogorov microscale), which is consistent with the scaling law identified in a very recent DNS study for shear-free T/NT interfaces.
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Pereira, Thiago S., and Davincy T. Pabon. "Extending the ΛCDM model through shear-free anisotropies." Modern Physics Letters A 31, no. 21 (July 10, 2016): 1640009. http://dx.doi.org/10.1142/s0217732316400095.
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If the spacetime metric has anisotropic spatial curvature, one can still expand the universe as if it were isotropic, provided that the energy–momentum tensor satisfies a certain constraint. This leads to the so-called shear-free (SF) metrics, which have the interesting property of violating the cosmological principle while still preserving the isotropy of the cosmic microwave background (CMB) radiation. In this work, we show that SF cosmologies correspond to an attractor solution in the space of models with anisotropic spatial curvature. Through a rigorous definition of linear perturbation theory in these spacetimes, we show that SF models represent a viable alternative to explain the large-scale evolution of the universe, leading, in particular to a kinematically equivalent Sachs–Wolfe (SW) effect. Alternatively, we discuss some specific signatures that SF models would imprint on the temperature spectrum of CMB.
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Briggs, D. A., J. H. Ferziger, J. R. Koseff, and S. G. Monismith. "Entrainment in a shear-free turbulent mixing layer." Journal of Fluid Mechanics 310 (March 10, 1996): 215–41. http://dx.doi.org/10.1017/s0022112096001784.
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Results from a direct numerical simulation of a shear-free turbulent mixing layer are presented. The mixing mechanisms associated with the turbulence are isolated. In the first set of simulations, the turbulent mixing layer decays as energy is exchanged between the layers. Energy spectra with E(k) ∼ k2 and E(k) ∼ k4 dependence at low wavenumber are used to initialize the flow to investigate the effect of initial conditions. The intermittency of the mixing layer is quantified by the skewness and kurtosis of the velocity fields: results compare well with the shearless mixing layer experiments of Veeravalli & Warhaft (1989). Eddies of size of the integral scale (k3/2/∈) penetrate the mixing layer intermittently, transporting energy and causing the layer to grow. The turbulence in the mixing layer can be characterized by eddies with relatively large vertical kinetic energy and vertical length scale. In the second set of simulations, a forced mixing layer is created by continuously supplying energy in a local region to maintain a stationary kinetic energy profile. Assuming the spatial decay of r.m.s. velocity is of the form u &∞ yn, predictions of common two-equation turbulence models yield values of n ranging from -1.25 to -2.5. An exponent of -1.35 is calculated from the forced mixing layer simulation. In comparison, oscillating grid experiments yield decay exponents between n = -1 (Hannoun et al. 1989) and n = -1.5 (Nokes 1988). Reynolds numbers of 40 and 58, based on Taylor microscale, are obtained in the decaying and forced simulations, respectively. Components of the turbulence models proposed by Mellor & Yamada (1986) and Hanjalić & Launder (1972) are analysed. Although the isotropic models underpredict the turbulence transport, more complicated anisotropic models do not represent a significant improvement. Models for the pressure-strain tensor, based on the anisotropy tensor, performed adequately.
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Bocksell, Todd L., and Eric Loth. "Random Walk Models for Particle Diffusion in Free-Shear Flows." AIAA Journal 39, no. 6 (June 2001): 1086–96. http://dx.doi.org/10.2514/2.1421.
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WEI, MINGJUN, and CLARENCE W. ROWLEY. "Low-dimensional models of a temporally evolving free shear layer." Journal of Fluid Mechanics 618 (January 10, 2009): 113–34. http://dx.doi.org/10.1017/s0022112008004539.
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We develop low-dimensional models for the evolution of a free shear layer in a periodic domain. The goal is to obtain models simple enough to be analysed using standard tools from dynamical systems theory, yet including enough of the physics to model nonlinear saturation and energy transfer between modes (e.g. pairing). In the present paper, two-dimensional direct numerical simulations of a spatially periodic, temporally developing shear layer are performed. Low-dimensional models for the dynamics are obtained using a modified version of proper orthogonal decomposition (POD)/Galerkin projection, in which the basis functions can scale in space as the shear layer spreads. Equations are obtained for the rate of change of the shear-layer thickness. A model with two complex modes can describe certain single-wavenumber features of the system, such as vortex roll-up, nonlinear saturation, and viscous damping. A model with four complex modes can describe interactions between two wavenumbers (vortex pairing) as well. At least two POD modes are required for each wavenumber in space to sufficiently describe the dynamics, though, for each wavenumber, more than 90% energy is captured by the first POD mode in the scaled space. The comparison of POD modes to stability eigenfunction modes seems to give a plausible explanation. We have also observed a relation between the phase difference of the first and second POD modes of the same wavenumber and the sudden turning point for shear-layer dynamics in both direct numerical simulations and model computations.
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Bocksell, Todd L., and Eric Loth. "Random walk models for particle diffusion in free-shear flows." AIAA Journal 39 (January 2001): 1086–96. http://dx.doi.org/10.2514/3.14843.
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IVANOV, B. V. "EVOLVING SPHERES OF SHEAR-FREE ANISOTROPIC FLUID." International Journal of Modern Physics A 25, no. 20 (August 10, 2010): 3975–91. http://dx.doi.org/10.1142/s0217751x10050202.
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The fluid models mentioned in the title are studied in a modified approach, based on two formulas for the mass function. All characteristics of the fluid are expressed through a master potential, satisfying an ordinary second-order differential equation. Different constraints are imposed on this core of relations, finding new solutions and deriving the classical results for perfect fluids as particular cases. All charged anisotropic solutions, all conformally flat and all uniform density solutions are found. A large class of solutions with linear equation among the two pressures is derived, including the case of vanishing tangential pressure. The mechanism responsible for the appearance of equation of state is elucidated.
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Princevac, Marko, Johannes Bühler, and Anton J. Schleiss. "Alternative depth-averaged models for gravity currents and free shear flows." Environmental Fluid Mechanics 10, no. 3 (January 19, 2010): 369–86. http://dx.doi.org/10.1007/s10652-009-9162-3.
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Jacobs, P. A., and D. I. Pullin. "Multiple-contour-dynamic simulation of eddy scales in the plane shear layer." Journal of Fluid Mechanics 199 (February 1989): 89–124. http://dx.doi.org/10.1017/s0022112089000303.
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The method of contour dynamics (CD) is applied to several inviscid prototype flows typical of the motions found in the transition region of the free shear layer. Examples of the interaction between the fundamental streamwise-layer perturbation and its first subharmonic are presented that illustrate the events of pairing and tearing of two rolled-up cores and also the coalescence of three rolled-up cores. The present simulations of the temporally unstable two-dimensional layer, at effectively infinite Reynolds number, support the hypothesis that the dynamics of the large-scale roll-up is only weakly dependent on Reynolds number. However, we find fine-scale structure that is not apparent in previous simulations at moderate Reynolds number. Spiral filaments of rotational fluid wrap around the rolled-up vortex cores producing ‘spiky’ vorticity distributions together with the entanglement of large quantities of irrotational fluid into the layer. Simulations proceeded only until the first such event because we were unable to resolve the fine detail generated subsequently. The inclusion of prescribed vortex stretching parallel to the vortex lines is found to accelerate the initial roll-up and to enhance the production of spiral vortex filaments. In the fundamental-subharmonic interaction, vortex stretching slows but does not prevent pairing.
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ARONSON, DAG, ARNE V. JOHANSSON, and LENNART LÖFDAHL. "Shear-free turbulence near a wall." Journal of Fluid Mechanics 338 (May 10, 1997): 363–85. http://dx.doi.org/10.1017/s0022112097005065.
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The mean shear has a major influence on near-wall turbulence but there are also other important physical processes at work in the turbulence/wall interaction. In order to isolate these, a shear-free boundary layer was studied experimentally. The desired flow conditions were realized by generating decaying grid turbulence with a uniform mean velocity and passing it over a wall moving with the stream speed. It is shown that the initial response of the turbulence field can be well described by the theory of Hunt & Graham (1978). Later, where this theory ceases to give an accurate description, terms of the Reynolds stress transport (RST) equations were measured or estimated by balancing the equations. An important finding is that two different length scales are associated with the near-wall damping of the Reynolds stresses. The wall-normal velocity component is damped over a region extending roughly one macroscale out from the wall. The pressure–strain redistribution that normally would result from the Reynolds stress anisotropy in this region was found to be completely inhibited by the near-wall influence. In a thin region close to the wall the pressure–reflection effects were found to give a pressure–strain that has an effect opposite to the normally expected isotropization. This behaviour is not captured by current models.
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Azaiez, J., and G. M. Homsy. "Linear stability of free shear flow of viscoelastic liquids." Journal of Fluid Mechanics 268 (June 10, 1994): 37–69. http://dx.doi.org/10.1017/s0022112094001254.
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The effects of viscoelasticity on the hydrodynamic stability of plane free shear flow are investigated through a linear stability analysis. Three different rheological models have been examined: the Oldroyd-B, corotational Jeffreys, and Giesekus models. We are especially interested in possible effects of viscoelasticity on the inviscid modes associated with inflexional velocity profiles. In the inviscid limit, it is found that for viscoelasticity to affect the instability of a flow described by the Oldroyd-B model, the Weissenberg number, We, has to go to infinity in such a way that its ratio to the Reynolds number, G ∞ We/Re, is finite. In this special limit we derive a modified Rayleigh equation, the solution of which shows that viscoelasticity reduces the instability of the flow but does not suppress it. The classical Orr–Sommerfeld analysis has been extended to both the Giesekus and corotational Jeffreys models. The latter model showed little variation from the Newtonian case over a wide range of Re, while the former one may have a stabilizing effect depending on the product ςWe where ς is the mobility factor appearing in the Giesekus model. We discuss the mechanisms responsible for reducing the instability of the flow and present some qualitative comparisons with experimental results reported by Hibberd et al. (1982), Scharf (1985 a, b) and Riediger (1989).
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HUNT, J. C. R., D. D. STRETCH, and S. E. BELCHER. "Viscous coupling of shear-free turbulence across nearly flat fluid interfaces." Journal of Fluid Mechanics 671 (February 24, 2011): 96–120. http://dx.doi.org/10.1017/s0022112010005525.
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The interactions between shear-free turbulence in two regions (denoted as + and − on either side of a nearly flat horizontal interface are shown here to be controlled by several mechanisms, which depend on the magnitudes of the ratios of the densities, ρ+/ρ−, and kinematic viscosities of the fluids, μ+/μ−, and the root mean square (r.m.s.) velocities of the turbulence, u0+/u0−, above and below the interface. This study focuses on gas–liquid interfaces so that ρ+/ρ− ≪ 1 and also on where turbulence is generated either above or below the interface so that u0+/u0− is either very large or very small. It is assumed that vertical buoyancy forces across the interface are much larger than internal forces so that the interface is nearly flat, and coupling between turbulence on either side of the interface is determined by viscous stresses. A formal linearized rapid-distortion analysis with viscous effects is developed by extending the previous study by Hunt & Graham (J. Fluid Mech., vol. 84, 1978, pp. 209–235) of shear-free turbulence near rigid plane boundaries. The physical processes accounted for in our model include both the blocking effect of the interface on normal components of the turbulence and the viscous coupling of the horizontal field across thin interfacial viscous boundary layers. The horizontal divergence in the perturbation velocity field in the viscous layer drives weak inviscid irrotational velocity fluctuations outside the viscous boundary layers in a mechanism analogous to Ekman pumping. The analysis shows the following. (i) The blocking effects are similar to those near rigid boundaries on each side of the interface, but through the action of the thin viscous layers above and below the interface, the horizontal and vertical velocity components differ from those near a rigid surface and are correlated or anti-correlated respectively. (ii) Because of the growth of the viscous layers on either side of the interface, the ratio uI/u0, where uI is the r.m.s. of the interfacial velocity fluctuations and u0 the r.m.s. of the homogeneous turbulence far from the interface, does not vary with time. If the turbulence is driven in the lower layer with ρ+/ρ− ≪ 1 and u0+/u0− ≪ 1, then uI/u0− ~ 1 when Re (=u0−L−/ν−) ≫ 1 and R = (ρ−/ρ+)(v−/v+)1/2 ≫ 1. If the turbulence is driven in the upper layer with ρ+/ρ− ≪ 1 and u0+/u0− ≫ 1, then uI/u0+ ~ 1/(1 + R). (iii) Nonlinear effects become significant over periods greater than Lagrangian time scales. When turbulence is generated in the lower layer, and the Reynolds number is high enough, motions in the upper viscous layer are turbulent. The horizontal vorticity tends to decrease, and the vertical vorticity of the eddies dominates their asymptotic structure. When turbulence is generated in the upper layer, and the Reynolds number is less than about 106–107, the fluctuations in the viscous layer do not become turbulent. Nonlinear processes at the interface increase the ratio uI/u0+ for sheared or shear-free turbulence in the gas above its linear value of uI/u0+ ~ 1/(1 + R) to (ρ+/ρ−)1/2 ~ 1/30 for air–water interfaces. This estimate agrees with the direct numerical simulation results from Lombardi, De Angelis & Bannerjee (Phys. Fluids, vol. 8, no. 6, 1996, pp. 1643–1665). Because the linear viscous–inertial coupling mechanism is still significant, the eddy motions on either side of the interface have a similar horizontal structure, although their vertical structure differs.
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Duggal, K. L., G. G. Asgekar, and S. M. Aherkar. "A class of shear‐free, non‐static models for anisotropic magnetofluid systems." Journal of Mathematical Physics 36, no. 6 (June 1995): 2929–40. http://dx.doi.org/10.1063/1.531070.
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Gürses, Metin, Matthias Plaue, and Mike Scherfner. "On a particular type of product manifolds and shear-free cosmological models." Classical and Quantum Gravity 28, no. 17 (August 12, 2011): 175009. http://dx.doi.org/10.1088/0264-9381/28/17/175009.
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FERNANDO, H. J. S., and J. C. R. HUNT. "Turbulence, waves and mixing at shear-free density interfaces. Part 1. A theoretical model." Journal of Fluid Mechanics 347 (September 25, 1997): 197–234. http://dx.doi.org/10.1017/s0022112097006514.
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This paper presents a theoretical model of turbulence and mixing at a shear-free stable density interface. In one case (single-sided stirring) the interface separates a layer of fluid of density ρ in turbulent motion, with r.m.s. velocity uH and lengthscale LH, from a non-turbulent layer with density ρ+Δρ, while in the second case (double-sided stirring) the lower layer is also in turbulent motion. In both cases, the external Richardson number Ri=ΔbLH/ u2H (where Δb is the buoyancy jump across the interface) is assumed to be large. Based on the hypotheses that the effect of the interface on the turbulence is as if it were suddenly imposed (which is equivalent to generating irrotational motions) and that linear waves are generated in the interface, the techniques of rapid distortion theory are used to analyse the linear aspects of the distortion of turbulence and of the interfacial motions. New physical concepts are introduced to account for the nonlinear aspects.To describe the spectra and variations of the r.m.s. fluctuations of velocity and displacements, a statistically steady linear model is used for frequencies above a critical frequency ωr/μc, where ωr(=Δb/2uH) is the maximum resonant frequency and μc<1. As in other nonlinear systems, observations below this critical frequency show the existence of long waves on the interface that can grow, break and cause mixing between the two fluid layers. A nonlinear model is constructed based on the fact that these breaking waves have steep slopes (which determines the form of the displacement spectrum) and on the physical argument that the energy of the vertical motions of these dissipative nonlinear waves should be comparable to that of the forced linear waves, which leads to an approximately constant value for the parameter μc. The model predictions of the vertical r.m.s. interfacial velocity, the interfacial wave amplitude and the velocity spectra agree closely with new and published experimental results.An exact unsteady inviscid linear analysis is used to derive the growth rate of the full spectrum, which asymptotically leads to the growth of resonant waves and to the energy transfer from the turbulent region to the wave motion of the stratified layer. Mean energy flux into the stratified layer, averaged over a typical wave cycle, is used to estimate the boundary entrainment velocity for the single-sided stirring case and the flux entrainment velocity for the double-sided stirring case, by making the assumption that the ratio of buoyancy flux to dissipation rate in forced stratified layers is constant with Ri and has the same value as in other stratified turbulent flows. The calculations are in good agreement with laboratory measurements conducted in mixing boxes and in wind tunnels. The contribution of Kelvin–Helmholtz instabilities induced by the velocity of turbulent eddies parallel to the interface is estimated to be insignificant compared to that of internal waves excited by turbulence.
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Liu, J. T. C. "Possibilities of Incorporating Coherent Structure Models in Turbulent Shear Flow Calculations." Applied Mechanics Reviews 43, no. 5S (May 1, 1990): S210—S213. http://dx.doi.org/10.1115/1.3120808.
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We discuss possibilities of using coherent structure models in turbulent shear flow description. The nonuniversality of different classes of such flows is directly attributed to the nonuniversality of hydrodynamic instability mechanisms. This is fully explored in discussions of free shear flows, where dynamical instabilities are important and in wall-bounded flows where longitudinal vorticity system and its nonlinear consequence are at play.
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Scandura, Pietro, Carla Faraci, and Enrico Foti. "A numerical investigation of acceleration-skewed oscillatory flows." Journal of Fluid Mechanics 808 (November 4, 2016): 576–613. http://dx.doi.org/10.1017/jfm.2016.641.
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Numerical simulations of wall-bounded acceleration-skewed oscillatory flows are here presented. The relevance of this type of boundary layer arises in connection with coastal hydrodynamics and sediment transport, as it is generated at the bottom of sea waves in shallow water. Because of the acceleration skewness, the bed shear stress during the onshore half-cycle is larger than in the offshore half-cycle. The asymmetry in the bed shear stress increases with increasing acceleration skewness, while an increase of the Reynolds number from the laminar regime causes the asymmetry first to decrease and then increase. Low- and high-speed streaks of fluid elongated in the streamwise direction emerge near the wall, shortly after the beginning of each half-cycle, at a phase that depends on the flow parameters. Such flow structures strengthen during the first part of the accelerating phase, without causing a significant deviation of the streamwise wall shear stress from the laminar values. Before the occurrence of the peak of the free stream velocity, the low-speed streaks break down into small turbulent structures causing a large increase in wall shear stress. The ratio of the root-mean-square (r.m.s.) of the fluctuations to the mean value (relative intensity) of the wall shear stress is approximately 0.4 throughout a relatively wide interval of the flow cycle that begins when breaking down of the streaks has occurred in the entire fluid domain. The acceleration skewness and the Reynolds number determine the phase at which this time interval begins. Both the skewness and the flatness coefficients of the streamwise wall shear stress are large when elongated streaks are present, while values of approximately 1.1 and 5.4 respectively occur just after breaking has occurred. The trend of both the relative intensity and the flatness of the spanwise wall shear stress are qualitatively similar to those of the wall shear in the streamwise direction. As a result of the acceleration skewness, the period-averaged Reynolds stress does not vanish. Consequently, an offshore directed steady streaming is generated which persists into the irrotational region.
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Thorsrud, Mikjel. "Balancing anisotropic curvature with gauge fields in a class of shear-free cosmological models." Classical and Quantum Gravity 35, no. 9 (March 28, 2018): 095011. http://dx.doi.org/10.1088/1361-6382/aab65a.
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IBOHAL, NG. "NONSTATIONARY DE SITTER COSMOLOGICAL MODELS." International Journal of Modern Physics D 18, no. 05 (May 2009): 853–63. http://dx.doi.org/10.1142/s0218271809014807.
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This paper proposes a class of nonstationary de Sitter, rotating and nonrotating, solutions to Einstein's field equations with a cosmological term of variable function Λ*(u). It is found that the space–time of the rotating nonstationary de Sitter model is algebraically special in the Petrov classification of the gravitational field with a null vector, which is a geodesic, shear-free, expanding as well as nonzero twist. However, that of the nonrotating nonstationary model is conformally flat, with nonempty space.
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Figuérez, Juan Alfonso, Álvaro Galán, and Javier González. "An Enhanced Treatment of Boundary Conditions for 2D RANS Streamwise Velocity Models in Open Channel Flow." Water 13, no. 7 (April 6, 2021): 1001. http://dx.doi.org/10.3390/w13071001.
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A 2D streamwise velocity model based on the Reynolds Averaged Navier–Stokes (RANS) is a useful approach to predict the boundary shear stress and the streamwise velocity in a free surface stream where secondary flows are not relevant. Boundary conditions treatment is a key aspect implementing these models. A low computational cost and fully predictive numerical model with a novel treatment of boundary conditions is presented. The main features of the modified model are the employment of a modified law of the wall valid for any roughness condition, the estimation of the boundary shear stress is done only focusing on the near-contour region, the use of a full-predictive physical based model for the eddy viscosity distribution and the incorporation of the free surface shear stress due to water–air interface. The validation of the proposed changes was performed with a substantial number of experimental cases available in the literature using different cross-section shapes (circular, rectangular, trapezoidal and compound section) and roughness condition with quite good agreement. Preliminary results suggest that the influence of the free surface boundary layer has a significant impact on the results for both the streamwise velocity and boundary shear stress in windy conditions. The proposed approach allows its considerations in practical applications.
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Criminale, W. O., T. L. Jackson, and D. G. Lasseigne. "Towards enhancing and delaying disturbances in free shear flows." Journal of Fluid Mechanics 294 (July 10, 1995): 283–300. http://dx.doi.org/10.1017/s0022112095002898.
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The family of shear flows comprising the jet, wake, and the mixing layer are subjected to perturbations in an inviscid incompressible fluid. By modelling the basic mean flows as parallel with piecewise linear variations for the velocities, complete and general solutions to the linearized equations of motion can be obtained in closed form as functions of all space variables and time when posed as an initial-value problem. The results show that there is a continuous spectrum as well as the discrete spectrum that is more familiar in stability theory and therefore there can be both algebraic and exponential growth of disturbances in time. These bases make it feasible to consider control of such flows. To this end, the possibility of enhancing the disturbances in the mixing layer and delaying the onset in the jet and wake is investigated. It is found that growth of perturbations can be delayed to a considerable degree for the jet and the wake but, by comparison, cannot be enhanced in the mixing layer. By using moving coordinates, a method for demonstrating the predominant early and long time behaviour of disturbances in these flows is given for continuous velocity profiles. It is shown that the early time transients are always algebraic whereas the asymptotic limit is that of an exponential normal mode. Numerical treatment of the new governing equations confirm the conclusions reached by use of the piecewise linear basic models. Although not pursued here, feedback mechanisms designed for control of the flow could be devised using the results of this work.
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Ru, C. Q. "Interfacial Thermal Stresses in Bimaterial Elastic Beams: Modified Beam Models Revisited." Journal of Electronic Packaging 124, no. 3 (July 26, 2002): 141–46. http://dx.doi.org/10.1115/1.1481037.
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A simple non-local modified beam model is presented to evaluate interfacial thermal stresses in bimaterial elastic beams. The model has its root in an earlier model (Suhir 1986) which assumes that the longitudinal interfacial displacement at a point depends on the interfacial shear stress at that point. Different than that earlier local model, however, the present non-local model assumes that the longitudinal interfacial displacement at a point also depends on the second gradient of the interfacial shear stress at that point. The present model satisfies both the zero-longitudinal force and the zero-shear stress boundary conditions at the free edges, and the interfacial peeling stress given by the present model is self-equilibrated. Remarkably, the present model leads to a fourth-order differential equation for the interfacial shear stress, and is considerably simpler than other known modified beam models satisfying the abovementioned conditions. This desirable feature of the present model is believed to be significant especially when the model is applied to multilayered materials. In particular, the interfacial shear stress given by the present model is found to be in reasonably good agreement with some known numerical results.
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SCANDURA, P., G. VITTORI, and P. BLONDEAUX. "Three-dimensional oscillatory flow over steep ripples." Journal of Fluid Mechanics 412 (June 10, 2000): 355–78. http://dx.doi.org/10.1017/s0022112000008430.
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The process which leads to the appearance of three-dimensional vortex structures in the oscillatory flow over two-dimensional ripples is investigated by means of direct numerical simulations of Navier–Stokes and continuity equations. The results by Hara & Mei (1990a), who considered ripples of small amplitude or weak fluid oscillations, are extended by considering ripples of larger amplitude and stronger flows respectively. Nonlinear effects, which were ignored in the analysis carried out by Hara & Mei (1990a), are found either to have a destabilizing effect or to delay the appearance of three-dimensional flow patterns, depending on the values of the parameters. An attempt to simulate the flow over actual ripples is made for moderate values of the Reynolds number. In this case the instability of the basic two-dimensional flow with respect to transverse perturbations makes the free shear layer generated by boundary layer separation become wavy as it leaves the ripple crest. Then the amplitude of the waviness increases and eventually complex three-dimensional vortex structures appear which are ejected in the irrotational region. Sometimes the formation of mushroom vortices is observed.
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PHILLIPS, W. R. C. "Langmuir circulations beneath growing or decaying surface waves." Journal of Fluid Mechanics 469 (October 15, 2002): 317–42. http://dx.doi.org/10.1017/s0022112002001908.
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The instability to longitudinal vortices of two-dimensional density-stratified temporally evolving wavy shear flow is considered. The problem is posited in the context of Langmuir circulations, LCs, beneath wind-driven surface waves and the instability mechanism is generalized Craik–Leibovich, either CLg or CL2. Of interest is the influence of non-stationary base flows on the instability according to linear theory. It is found that the instability is described by a family of similarity solutions and that the growth rate of the instability, in non-stationary base flows, is doubly exponential in time, although the growth rate reduces to exponential when the base flow is stationary. An example is given for weakly sheared wind-driven flow evolving in the presence of growing irrotational surface waves. Waves aligned both with the wind and counter to it are considered, as is the role of stratification. Antecedent to the example is an initial value problem posed by Leibovich & Paolucci (1981) for neutral waves in slowly evolving shear. Here, however, the waves and shear may grow (or decay) at rates comparable with the LCs. Furthermore the current here has two components: a wind-driven portion due to the wind stress applied at the free surface and a second due to the diffusion of momentum due to the wave-amplitude-squared free-surface stress condition. Using the case for neutral waves in non-stratified uniform shear for reference, it is found, in general, that growing waves are stabilizing while decaying waves are destabilizing to the formation of LCs, although the latter applies only for sufficiently large spanwise spacings and is subject to a globally stable lower bound. Decaying waves in the absence of wind can also be destabilizing to LCs. When the wind is counter to the waves, however, only decaying waves are unstable to LCs. Furthermore, while growing waves are stable to the formation of LCs in the presence of stable stratification, decaying waves are unstable in both aligned and opposed wind-wave conditions. Unstable stratification on the other hand, is destabilizing to LCs for all temporal waves in both aligned and opposed wind-wave conditions.
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Khare, Rakesh Kumar, Ajay Kumar Garg, and Tarun Kant. "Free Vibration of Sandwich Laminates with Two Higher-order Shear Deformable Facet Shell Element Models." Journal of Sandwich Structures & Materials 7, no. 3 (May 2005): 221–44. http://dx.doi.org/10.1177/1099636205048592.
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