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Journal articles on the topic 'Inviscid shear flow'
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1
Stern, Melvin E. "Blocking an inviscid shear flow." Journal of Fluid Mechanics 227 (June 1991): 449–72. http://dx.doi.org/10.1017/s0022112091000198.
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The upstream influence in an inviscid two-dimensional shear flow around a semicircular ‘cape’ (radius A) is computed using a piecewise uniform vorticity model of a boundary-layer current. The area of this layer upstream from the cape increases as the square root of time t when A is small, and increases as t for larger A. Complete blocking occurs when A is approximately three times the boundary-layer thickness, in which case all oncoming particles accumulate in a large upstream vortex. The numerical results obtained from the contour dynamical method also show the generation of large eddies downstream from the obstacle.
2
Renardy, Michael. "Short Wave Stability for Inviscid Shear Flow." SIAM Journal on Applied Mathematics 69, no. 3 (January 2008): 763–68. http://dx.doi.org/10.1137/080720905.
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Murad, Abdullah. "Inviscid Uniform Shear Flow past a Smooth Concave Body." International Journal of Engineering Mathematics 2014 (July 23, 2014): 1–7. http://dx.doi.org/10.1155/2014/426593.
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Uniform shear flow of an incompressible inviscid fluid past a two-dimensional smooth concave body is studied; a stream function for resulting flow is obtained. Results for the same flow past a circular cylinder or a circular arc or a kidney-shaped body are presented as special cases of the main result. Also, a stream function for resulting flow around the same body is presented for an oncoming flow which is the combination of a uniform stream and a uniform shear flow. Possible fields of applications of this study include water flows past river islands, the shapes of which deviate from circular or elliptical shape and have a concave region, or past circular arc-shaped river islands and air flows past concave or circular arc-shaped obstacles near the ground.
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Balsa, T. F. "On the spatial instability of piecewise linear free shear layers." Journal of Fluid Mechanics 174 (January 1987): 553–63. http://dx.doi.org/10.1017/s0022112087000247.
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The main goal of this paper is to clarify the spatial instability of a piecewise linear free shear flow. We do this by obtaining numerical solutions to the Orr–Sommerfeld equation at high Reynolds numbers. The velocity profile chosen is very much like a piecewise linear one, with the exception that the corners have been rounded so that the entire profile is infinitely differentiable. We find that the (viscous) spatial instability of this modified profile is virtually identical to the inviscid spatial instability of the piecewise linear profile and agrees qualitatively with the inviscid results for the tanh profile when the shear layers are convectively unstable. The unphysical features, previously identified for the piecewise linear velocity profile, arise only when the flow is absolutely unstable. In a nutshell, we see nothing wrong with the inviscid spatial instability of piecewise linear shear flows.
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SUGIOKA, KEN-ICHI, and SATORU KOMORI. "Drag and lift forces acting on a spherical gas bubble in homogeneous shear liquid flow." Journal of Fluid Mechanics 629 (June 15, 2009): 173–93. http://dx.doi.org/10.1017/s002211200900651x.
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Drag and lift forces acting on a spherical gas bubble in a homogeneous linear shear flow were numerically investigated by means of a three-dimensional direct numerical simulation (DNS) based on a marker and cell (MAC) method. The effects of fluid shear rate and particle Reynolds number on drag and lift forces acting on a spherical gas bubble were compared with those on a spherical inviscid bubble. The results show that the drag force acting on a spherical air bubble in a linear shear flow increases with fluid shear rate of ambient flow. The behaviour of the lift force on a spherical air bubble is quite similar to that on a spherical inviscid bubble, but the effects of fluid shear rate on the lift force acting on an air bubble in the linear shear flow become bigger than that acting on an inviscid bubble in the particle Reynolds number region of 1≤Rep≤300. The lift coefficient on a spherical gas bubble approaches the lift coefficient on a spherical water droplet in the linear shear air-flow with increase in the internal gas viscosity.
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Zangeneh, M. "Inverse Design of Centrifugal Compressor Vaned Diffusers in Inlet Shear Flows." Journal of Turbomachinery 118, no. 2 (April 1, 1996): 385–93. http://dx.doi.org/10.1115/1.2836653.
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A three-dimensional inverse design method in which the blade (or vane) geometry is designed for specified distributions of circulation and blade thickness is applied to the design of centrifugal compressor vaned diffusers. Two generic diffusers are designed, one with uniform inlet flow (equivalent to a conventional design) and the other with a sheared inlet flow. The inlet shear flow effects are modeled in the design method by using the so-called “Secondary Flow Approximation” in which the Bernoulli surfaces are convected by the tangentially mean inviscid flow field. The difference between the vane geometry of the uniform inlet flow and nonuniform inlet flow diffusers is found to be most significant from 50 percent chord to the trailing edge region. The flows through both diffusers are computed by using Denton’s three-dimensional inviscid Euler solver and Dawes’ three-dimensional Navier–Stokes solver under sheared in-flow conditions. The predictions indicate improved pressure recovery and internal flow field for the diffuser designed for shear inlet flow conditions.
7
Rizzi, Arthur, and Charles J. Purcell. "Simulation of inviscid vortex-stretched turbulent shear-layer flow." AIAA Journal 24, no. 4 (April 1986): 680–82. http://dx.doi.org/10.2514/3.9326.
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MILES, JOHN. "Stability of inviscid shear flow over a flexible boundary." Journal of Fluid Mechanics 434 (May 10, 2001): 371–78. http://dx.doi.org/10.1017/s0022112001003664.
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The stability of an inviscid flow that comprises a thin shear layer and a uniform outer flow over a flexible boundary is investigated. It is shown that the flow is temporally unstable for all wavenumbers. This instability is either Kelvin–Helmholtz-like or induced by the phase shift across the critical layer. The threshold of absolute instability is determined in the form F = F∗(1 + Cεn) for ε [Lt ] 1, where F (a Froude number) and ε are, respectively, dimensionless measures of the flow speed and the shear-layer thickness, F∗ is the limiting value of F for a uniform flow, C < 0 and n = 1 in the absence (as for a broken-line velocity profile) of a phase shift across the critical layer, and C > 0 and n = 2/3 in the presence of such a phase shift. Explicit results are determined for an elastic plate (and, in an Appendix, for a membrane) with a broken-line, parabolic, or Blasius boundary-layer profile. The predicted threshold for the broken-line profile agrees with Lingwood & Peake's (1999) result for ε [Lt ] 1, but that for the Blasius profile contradicts their conclusion that the threshold for ε ↓ 0 is a ‘singular and unattainable limit’.
9
Arratia, C., and J. M. Chomaz. "On the longitudinal optimal perturbations to inviscid plane shear flow: formal solution and asymptotic approximation." Journal of Fluid Mechanics 737 (November 26, 2013): 387–411. http://dx.doi.org/10.1017/jfm.2013.570.
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AbstractWe study the longitudinal linear optimal perturbations (which maximize the energy gain up to a prescribed time $T$) to inviscid parallel shear flow, which present unbounded energy growth due to the lift-up mechanism. Using the phase invariance with respect to time, we show that for an arbitrary base flow profile and optimization time, the computation of the optimal longitudinal perturbation reduces to the resolution of a single one-dimensional eigenvalue problem valid for all times. The optimal perturbation and its amplification are then derived from the lowest eigenvalue and its associated eigenfunction, while the remainder of the infinite set of eigenfunctions provides an orthogonal base for decomposing the evolution of arbitrary perturbations. With this new formulation we obtain, asymptotically for large spanwise wavenumber ${k}_{z} , $ a prediction of the optimal gain and the localization of inviscid optimal perturbations for the two main classes of parallel flows: free shear flow with an inflectional velocity profile, and wall-bounded flow with maximum shear at the wall. We show that the inviscid optimal perturbations are localized around the point of maximum shear in a region with a width scaling like ${ k}_{z}^{- 1/ 2} $ for free shear flow, and like ${ k}_{z}^{- 2/ 3} $ for wall-bounded shear flows. This new derivation uses the stationarity of the base flow to transform the optimization of initial conditions in phase space into the optimization of a temporal phase along each trajectory, and an optimization among all trajectories labelled by their intersection with a codimension-1 subspace. The optimization of the time phase directly imposes that the initial and final energy growth rates of the optimal perturbation should be equal. This result requires only time invariance of the base flow, and is therefore valid for any linear optimal perturbation problem with stationary base flow.
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Meroney, R. N. "Inviscid Shear Flow Analysis of Corner Eddies Ahead of a Channel Flow Contraction." Journal of Fluids Engineering 107, no. 2 (June 1, 1985): 212–17. http://dx.doi.org/10.1115/1.3242464.
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The steady rotational flow of an inviscid fluid in a two-dimensional channel toward a sink or a contraction is treated. The velocity distribution at upstream infinity is approximated by a linear combination of uniform flow, linear shear flow, and a cosine curve. The combinations were adjusted to simulate flows ranging from laminar to turbulent. Vorticity is assumed conserved on streamlines. The resulting linear equations of motion are solved exactly. The solution show the dependence of the corner eddy separation and reattachment on flow geometry and approach flow vorticity and velocity distribution typified by a shape factor.
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Deguchi, Kengo. "Inviscid instability of a unidirectional flow sheared in two transverse directions." Journal of Fluid Mechanics 874 (July 15, 2019): 979–94. http://dx.doi.org/10.1017/jfm.2019.500.
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Linear inviscid stability of general unidirectional flows sheared in one transverse direction has long been investigated by numerous researchers using the Rayleigh equation. However, unlike the simple shear flow considered in this equation, most physically relevant unidirectional flows vary in two transverse directions. Here the inviscid instability of such flows is studied by the large-Reynolds-number limit asymptotic analysis. We derive an a priori necessary condition for the existence of a limiting neutral mode, and develop a new numerical method to accurately capture singular neutral modes.
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Chen, Yong, Yiyong Huang, and Xiaoqian Chen. "Fourier–Bessel theory on flow acoustics in inviscid shear pipeline fluid flow." Communications in Nonlinear Science and Numerical Simulation 18, no. 11 (November 2013): 3023–35. http://dx.doi.org/10.1016/j.cnsns.2013.04.011.
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Draper, S., T. Nishino, T. A. A. Adcock, and P. H. Taylor. "Performance of an ideal turbine in an inviscid shear flow." Journal of Fluid Mechanics 796 (April 28, 2016): 86–112. http://dx.doi.org/10.1017/jfm.2016.247.
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Although wind and tidal turbines operate in turbulent shear flow, most theoretical results concerning turbine performance, such as the well-known Betz limit, assume the upstream velocity profile is uniform. To improve on these existing results we extend the classical actuator disc model in this paper to investigate the performance of an ideal turbine in steady, inviscid shear flow. The model is developed on the assumption that there is negligible lateral interaction in the flow passing through the disc and that the actuator applies a uniform resistance across its area. With these assumptions, solution of the model leads to two key results. First, for laterally unbounded shear flow, it is shown that the normalised power extracted is the same as that for an ideal turbine in uniform flow, if the average of the cube of the upstream velocity of the fluid passing through the turbine is used in the normalisation. Second, for a laterally bounded shear flow, it is shown that the same normalisation can be applied, but allowance must also be made for the fact that non-uniform flow bypassing the turbine alters the background pressure gradient and, in turn, the turbines ‘effective blockage’ (so that it may be greater or less than the geometric blockage, defined as the ratio of turbine disc area to cross-sectional area of the flow). Predictions based on the extended model agree well with numerical simulations approximating the incompressible Euler equations. The model may be used to improve interpretation of model-scale results for wind and tidal turbines in tunnels/flumes, to investigate the variation in force across a turbine and to update existing theoretical models of arrays of tidal turbines.
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Balmforth, N. J., and P. J. Morrison. "A Necessary and Sufficient Instability Condition for Inviscid Shear Flow." Studies in Applied Mathematics 102, no. 3 (April 1999): 309–44. http://dx.doi.org/10.1111/1467-9590.00113.
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Hirota, M., P. J. Morrison, and Y. Hattori. "Variational necessary and sufficient stability conditions for inviscid shear flow." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2172 (December 8, 2014): 20140322. http://dx.doi.org/10.1098/rspa.2014.0322.
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A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by developing a novel variational principle, where the velocity profile is assumed to be monotonic and analytic. It is shown that unstable eigenvalues of Rayleigh's equation (which is a non-self-adjoint eigenvalue problem) can be associated with positive eigenvalues of a certain self-adjoint operator. The stability is therefore determined by maximizing a quadratic form, which is theoretically and numerically more tractable than directly solving Rayleigh's equation. This variational stability criterion is based on the understanding of Kreĭn signature for continuous spectra and is applicable to other stability problems of infinite-dimensional Hamiltonian systems.
16
McHugh, John P. "Surface waves on an inviscid shear flow in a channel." Wave Motion 19, no. 2 (March 1994): 135–44. http://dx.doi.org/10.1016/0165-2125(94)90062-0.
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Mchugh, John P. "Stability and waves on a two-dimensional inviscid shear flow." Computers & Fluids 24, no. 4 (May 1995): 369–76. http://dx.doi.org/10.1016/0045-7930(94)00044-y.
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Sahu, Kirti Chandra, and Rama Govindarajan. "Instability of a free-shear layer in the vicinity of a viscosity-stratified layer." Journal of Fluid Mechanics 752 (July 11, 2014): 626–48. http://dx.doi.org/10.1017/jfm.2014.361.
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AbstractThe stability of a mixing layer made up of two miscible fluids, with a viscosity-stratified layer between them, is studied. The two fluids are of the same density. It is shown that unlike other viscosity-stratified shear flows, where species diffusivity is a dominant factor determining stability, species diffusivity variations over orders of magnitude do not change the answer to any noticeable degree in this case. Viscosity stratification, however, does matter, and can stabilize or destabilize the flow, depending on whether the layer of varying velocity is located within the less or more viscous fluid. By making an inviscid model flow with a slope change across the ‘viscosity’ interface, we show that viscous and inviscid results are in qualitative agreement. The absolute instability of the flow can also be significantly altered by viscosity stratification.
19
Fu, Qing-fei, Li-zi Qin, and Li-jun Yang. "Spatial-Temporal Instability of an Inviscid Shear Layer." International Journal of Aerospace Engineering 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/8532507.
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In this work, we explore the transition of absolute instability and convective instability in a compressible inviscid shear layer, through a linear spatial-temporal instability analysis. From linearized governing equations of the shear layer and the ideal-gas equation of state, the dispersion relation for the pressure perturbation was obtained. The eigenvalue problem for the evolution of two-dimensional perturbation was solved by means of shooting method. The zero group velocity is obtained by a saddle point method. The absolute/convective instability characteristics of the flow are determined by the temporal growth rate at the saddle point. The absolute/convective nature of the flow instability has strong dependence on the values of the temperature ratio, the velocity ratio, the oblique angle, and M number. A parametric study indicates that, for a great value of velocity ratio, the inviscid shear layer can transit to absolute instability. The increase of temperature ratio decreases the absolute growth rate when the temperature ratio is large; the effect of temperature ratio is opposite when the temperature ratio is relatively small. The obliquity of the perturbations would cause the increase of the absolute growth rate. The effect of M number is different when the oblique angle is great and small. Besides, the absolute instability boundary is found in the velocity ratio, temperature ratio, and M number space.
20
Bryan, George H., and Richard Rotunno. "Gravity Currents in Confined Channels with Environmental Shear." Journal of the Atmospheric Sciences 71, no. 3 (February 27, 2014): 1121–42. http://dx.doi.org/10.1175/jas-d-13-0157.1.
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Abstract This study examines properties of gravity currents in confined channels with sheared environmental flow. Under the assumptions of steady and inviscid flow, two-dimensional analytic solutions are obtained for a wide range of shear values. The slope of a gravity current interface just above the surface increases as environmental shear α increases, which is consistent with previous studies, although here it is shown that the interface slope can exceed 80° for nondimensional shear α > 2. Then the inviscid-flow analytic solutions are compared with two- and three-dimensional numerical model simulations, which are turbulent and thus have dissipation. The simulated current depths are systematically lower, compared to a previous study, apparently because of different numerical techniques in this study that allow for a faster transition to turbulence along the gravity current interface. Furthermore, simulated gravity current depths are 10%–40% lower than the inviscid analytic values. To explain the model-produced current depths, a steady analytic theory with energy dissipation is revisited. It is shown that the numerical model current depths are close to values associated with the maximum possible dissipation rate in the simplest form of the analytic model for all values of α examined in this study. A primary conclusion is that dissipation plays an important and nonnegligible role in gravity currents within confined channels, with or without environmental shear.
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REES, S. J., and M. P. JUNIPER. "The effect of confinement on the stability of viscous planar jets and wakes." Journal of Fluid Mechanics 656 (May 25, 2010): 309–36. http://dx.doi.org/10.1017/s0022112010001060.
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This theoretical study examines confined viscous planar jet/wake flows with continuous velocity profiles. These flows are characterized by the shear, confinement, Reynolds number and shear-layer thickness. The primary aim of this paper is to determine the effect of confinement on viscous jets and wakes and to compare these results with corresponding inviscid results. The secondary aim is to consider the effect of viscosity and shear-layer thickness. A spatio-temporal analysis is performed in order to determine absolute/convective instability criteria. This analysis is carried out numerically by solving the Orr–Sommerfeld equation using a Chebyshev collocation method. Results are produced over a large range of parameter space, including both co-flow and counter-flow domains and confinements corresponding to 0.1 < h2/h1 < 10, where the subscripts 1 and 2 refer to the inner and outer streams, respectively. The Reynolds number, which is defined using the channel width, takes values between 10 and 1000. Different velocity profiles are used so that the shear layers occupy between 1/2 and 1/24 of the channel width. Results indicate that confinement has a destabilizing effect on both inviscid and viscous flows. Viscosity is found always to be stabilizing, although its effect can safely be neglected above Re = 1000. Thick shear layers are found to have a stabilizing effect on the flow, but infinitely thin shear layers are not the most unstable; having shear layers of a small, but finite, thickness gives rise to the strongest instability.
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HEATON, C. J. "Optimal growth of the Batchelor vortex viscous modes." Journal of Fluid Mechanics 592 (November 14, 2007): 495–505. http://dx.doi.org/10.1017/s0022112007008634.
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We present calculations of optimal linear growth in the Batchelor (or q) vortex. The level of transient growth is used to quantify the effect of the viscous centre modes found at large Reynolds number and large swirl. The viscous modes compete with inviscid-type transients, which are seen to provide faster growth at short times. Following a smooth transition, the viscous modes emerge as dominant in a different regime at later times. A comparison is drawn with two-dimensional shear flows, such as boundary layers, in which weak instability modes (Tollmien–Schlichting waves) also compete with inviscid transients (streamwise streaks). We find the competition to be more evenly balanced in the Batchelor vortex, because the inviscid transients are damped faster in a swirling jet than a two-dimensional shear flow, so that despite their weak growth rates the viscous modes may be relevant in some situations.
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Cramer, M. S., and F. Bahmani. "Effect of large bulk viscosity on large-Reynolds-number flows." Journal of Fluid Mechanics 751 (June 17, 2014): 142–63. http://dx.doi.org/10.1017/jfm.2014.294.
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AbstractWe examine the inviscid and boundary-layer approximations in fluids having bulk viscosities which are large compared with their shear viscosities for three-dimensional steady flows over rigid bodies. We examine the first-order corrections to the classical lowest-order inviscid and laminar boundary-layer flows using the method of matched asymptotic expansions. It is shown that the effects of large bulk viscosity are non-negligible when the ratio of bulk to shear viscosity is of the order of the square root of the Reynolds number. The first-order outer flow is seen to be rotational, non-isentropic and viscous but nevertheless slips at the inner boundary. First-order corrections to the boundary-layer flow include a variation of the thermodynamic pressure across the boundary layer and terms interpreted as heat sources in the energy equation. The latter results are a generalization and verification of the predictions of Emanuel (Phys. Fluids A, vol. 4, 1992, pp. 491–495).
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Khamis, Doran, and Edward James Brambley. "Acoustic boundary conditions at an impedance lining in inviscid shear flow." Journal of Fluid Mechanics 796 (May 4, 2016): 386–416. http://dx.doi.org/10.1017/jfm.2016.273.
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The accuracy of existing impedance boundary conditions is investigated, and new impedance boundary conditions are derived, for lined ducts with inviscid shear flow. The accuracy of the Ingard–Myers boundary condition is found to be poor. Matched asymptotic expansions are used to derive a boundary condition accurate to second order in the boundary layer thickness, which shows substantially increased accuracy for thin boundary layers when compared with both the Ingard–Myers boundary condition and its recent first-order correction. Closed-form approximate boundary conditions are also derived using a single Runge–Kutta step to solve an impedance Ricatti equation, leading to a boundary condition that performs reasonably even for thicker boundary layers. Surface modes and temporal stability are also investigated.
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Kaneda, Yukio, Toshiyuki Gotoh, and Naoaki Bekki. "Dynamics of inviscid truncated model of two‐dimensional turbulent shear flow." Physics of Fluids A: Fluid Dynamics 1, no. 7 (July 1989): 1225–34. http://dx.doi.org/10.1063/1.857345.
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Brevdo, L. "On the linear stability of a compressible inviscid parallel shear flow." Acta Mechanica 100, no. 3-4 (September 1993): 195–203. http://dx.doi.org/10.1007/bf01174789.
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Chen, Michael J., and Lawrence K. Forbes. "Waves in two-layer shear flow for viscous and inviscid fluids." European Journal of Mechanics - B/Fluids 30, no. 4 (July 2011): 387–404. http://dx.doi.org/10.1016/j.euromechflu.2011.04.004.
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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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ADOUA, RICHARD, DOMINIQUE LEGENDRE, and JACQUES MAGNAUDET. "Reversal of the lift force on an oblate bubble in a weakly viscous linear shear flow." Journal of Fluid Mechanics 628 (June 1, 2009): 23–41. http://dx.doi.org/10.1017/s0022112009006090.
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We compute the flow about an oblate spheroidal bubble of prescribed shape set fixed in a viscous linear shear flow in the range of moderate to high Reynolds numbers. In contrast to predictions based on inviscid theory, the numerical results reveal that for weak enough shear rates, the lift force and torque change sign in an intermediate range of Reynolds numbers when the bubble oblateness exceeds a critical value that depends on the relative shear rate. This effect is found to be due to the vorticity generated at the bubble surface which, combined with the velocity gradient associated with the upstream shear, results in a system of two counter-rotating streamwise vortices whose sign is opposite to that induced by the classical inviscid tilting of the upstream vorticity around the bubble. We show that this lift reversal mechanism is closely related to the wake instability mechanism experienced by a spheroidal bubble rising in a stagnant liquid.
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GARRETT, CHRIS, and FRANK GERDES. "Hydraulic control of homogeneous shear flows." Journal of Fluid Mechanics 475 (January 25, 2003): 163–72. http://dx.doi.org/10.1017/s0022112002002884.
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If a shear flow of a homogeneous fluid preserves the shape of its velocity profile, a standard formula for the condition for hydraulic control suggests that this is achieved when the depth-averaged flow speed is less than (gh)1/2. On the other hand, shallow-water waves have a speed relative to the mean flow of more than (gh)1/2, suggesting that information could propagate upstream. This apparent paradox is resolved by showing that the internal stress required to maintain a constant velocity profile depends on flow derivatives along the channel, thus altering the wave speed without introducing damping. By contrast, an inviscid shear flow does not maintain the same profile shape, but it can be shown that long waves are stationary at a position of hydraulic control.
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Dériat, Emmanuel. "A new approximation for a general shear inviscid flow past a circle." International Journal of Aerodynamics 4, no. 1/2 (2014): 4. http://dx.doi.org/10.1504/ijad.2014.057800.
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ASMOLOV, EVGENY S., and FRANÇOIS FEUILLEBOIS. "Far-field disturbance flow induced by a small non-neutrally buoyant sphere in a linear shear flow." Journal of Fluid Mechanics 643 (January 15, 2010): 449–70. http://dx.doi.org/10.1017/s0022112009992230.
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The disturbance flow due to the motion of a small sphere parallel to the streamlines of an unbounded linear shear flow is evaluated at small Reynolds number using the method of matched expansions. Decaying laws are obtained for all velocity components in a far inviscid region and viscous wakes. The z component (in the direction of the shear-rate gradient) of the disturbance velocity is cylindrically symmetric in the inviscid region. It decays with the distance r from the sphere like r−5/3, while the y component (in the direction of vorticity) decays like r−4/3. The widths of two viscous wakes, located upstream and downstream of the sphere, grow with the longitudinal coordinate x as yw ~ zw ~ |x|1/3. The maximum x and z components of the velocity are located in the wake cores; they scale like |x|−2/3 and |x|−1 respectively. For two particles interacting through their outer regions, the migration velocity of each particle is the sum of the velocity of an isolated particle and of a disturbance velocity induced by the other one. Particles placed in the normal or transversal directions repel each other. When each particle is located in a wake of the other one, they may either attract or repel each other.
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ELCRAT, ALAN R., BENGT FORNBERG, and KENNETH G. MILLER. "Steady axisymmetric vortex flows with swirl and shear." Journal of Fluid Mechanics 613 (October 1, 2008): 395–410. http://dx.doi.org/10.1017/s002211200800342x.
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A general procedure is presented for computing axisymmetric swirling vortices which are steady with respect to an inviscid flow that is either uniform at infinity or includes shear. We consider cases both with and without a spherical obstacle. Choices of numerical parameters are given which yield vortex rings with swirl, attached vortices with swirl analogous to spherical vortices found by Moffatt, tubes of vorticity extending to infinity and Beltrami flows. When there is a spherical obstacle we have found multiple solutions for each set of parameters. Flows are found by numerically solving the Bragg–Hawthorne equation using a non-Newton-based iterative procedure which is robust in its dependence on an initial guess.
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D'AGOSTINO, LUCA, FABRIZIO D'AURIA, and CHRISTOPHER E. BRENNEN. "On the inviscid stability of parallel bubbly flows." Journal of Fluid Mechanics 339 (May 25, 1997): 261–74. http://dx.doi.org/10.1017/s0022112097005211.
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This paper investigates the effects of bubble dynamics on the stability of parallel bubbly flows of low void fraction. The equations of motion for the bubbly mixture are linearized for small perturbations and the parallel flow assumption is used to obtain a modified Rayleigh equation governing the inviscid stability problem. This is then used for the stability analysis of two-dimensional shear layers, jets and wakes. Inertial effects associated with the bubble response and energy dissipation due to the viscosity of the liquid, the heat transfer between the two phases, and the liquid compressibility are included. Numerical solutions of the eigenvalue problems for the modified Rayleigh equation are obtained by means of a multiple shooting method. Depending on the characteristic velocities of the various flows, the void fraction, and the ambient pressure, the presence of air bubbles can induce significant departures from the classical stability results for a single-phase fluid.
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Caulfield, Colm-Cille P. "Multiple linear instability of layered stratified shear flow." Journal of Fluid Mechanics 258 (January 10, 1994): 255–85. http://dx.doi.org/10.1017/s0022112094003320.
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We develop a simple model for the behaviour of an inviscid stratified shear flow with a thin mixed layer of intermediate fluid. We find that the flow is simultaneously unstable to oscillatory disturbances that are a generalization of those discussed by Holmboe (1962), purely unstable modes analogous to those considered by Taylor (1931), and a new type of oscillatory disturbance at large wavelength. The relative significance of these different types of instability depends on the ratio R of the depth of the intermediate layer to the depth of the shear layer. For small values of R, the new type of oscillatory wave has both the largest growthrate for given bulk Richardson number Ri0, and is also primarily unstable to disturbances propagating at an angle to the mean flow, i.e. such modes violate the conditions of Squire's theorem (1933), and thus the assumption of initial two dimensionality of such flows is invalid. For intermediate values of R, the Holmboe-type modes and the Taylor-types modes may have wavelengths and phase speeds conducive to the formation of a resonant triad over a wide range of Ri0. Thus the presence of an intermediate layer in a stratified shear flow markedly changes its stability properties.
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Hall, Philip. "On the breakdown of Rayleigh’s criterion for curved shear flows: a destabilization mechanism for a class of inviscidly stable flows." Journal of Fluid Mechanics 734 (October 7, 2013): 36–82. http://dx.doi.org/10.1017/jfm.2013.446.
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AbstractThe stability of a high-Reynolds-number flow over a curved surface is considered. Attention is focused on spanwise-periodic vortices of wavelength comparable with the boundary layer thickness. The wall curvature and the Görtler number for the flow are assumed large, so that stable or unstable vortices of wavelength comparable with the boundary layer thickness are dominated by inviscid effects. The growth or decay rate determined by using the viscous correction to the inviscid prediction is found to give a good approximation to the exact value for a range of wavenumbers. For the stable configuration, it is shown that the flow can be destabilized by arbitrarily small wall waviness, with the critical configuration involving only geometric properties of the flow. This destabilization mechanism has consequences for a number of flows of aerodynamic interest, particularly those where surface waviness under loading occurs. Control strategies based on how the curvature is distributed are discussed, and it is demonstrated how small regions of varying curvature can be used to remove the exponentially growing modes. The development of the parametric instabilities is continued into the strongly nonlinear regime. The nonlinear evolution is found to be governed by a generalized form of the cubic amplitude equation, generally referred to as the Stuart–Landau equation. The novel feature of the new equation is that the nonlinearity is not in the form of a power of the amplitude but is fixed by the solution of an associated nonlinear partial differential equation boundary value problem. Numerical solutions of the nonlinear partial differential system that fix the disturbance amplitude are given. The mechanism of destabilization described is shown to be directly relevant to a number of flows that are inviscidly stable in the presence of body forces. Thus it is shown how Rayleigh–Bénard convection or Taylor vortices can, at high Rayleigh or Taylor numbers, be destabilized by asymptotically small modulation in time or space.
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SAXENA, VIVEK, SIDNEY LEIBOVICH, and GAL BERKOOZ. "Enhancement of three-dimensional instability of free shear layers." Journal of Fluid Mechanics 379 (January 25, 1999): 23–38. http://dx.doi.org/10.1017/s0022112098003267.
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Enhancement of the temporal growth rate of inviscid three-dimensional instability waves in free shear layers by deformation of the basic flow is studied. The deformation of a two-dimensional mixing layer is assumed to yield a base flow that remains unidirectional, but has a steady spanwise speed variation in addition to the two- dimensional shear. The computed growth rates for hyperbolic tangent base flow, perturbed this way, show enhanced instability in the sense that the neutral waves of the unperturbed flow exhibit positive growth rates. For each imposed spanwise periodicity, an oblique mode is selected that shows maximum growth rate. The results are consistent with related theoretical studies and with qualitative observations in experiments.
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HEALEY, J. J. "Inviscid axisymmetric absolute instability of swirling jets." Journal of Fluid Mechanics 613 (October 1, 2008): 1–33. http://dx.doi.org/10.1017/s0022112008003236.
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The propagation characteristics of inviscid axisymmetric linearized disturbances to swirling jets are investigated for two families of model velocity profiles. Briggs' method is applied to dispersion relations to determine when the basic swirling jets are absolutely or convectively unstable. The method is also applied to the neutral inertial waves used by Benjamin to characterize the subcritical or supercritical nature of the flow. Although these waves are neutral, Briggs' method nonetheless indicates a qualitative change in behaviour at Benjamin's criticality condition. The first model jet has uniform axial velocity, rigid-body rotation and issues into still fluid. A known difficulty in the application of Briggs' method to the analytical dispersion relation for inviscid waves in this flow is resolved. The difficulty is that the pinch point can cross into the left half of the complex-wavenumber plane, where waves grow exponentially with radius and fail to satisfy homogeneous boundary conditions. In this paper the physical consequences of this behaviour are explained. It is shown that if the still fluid is of infinite extent in the radial direction, then the jet is convectively unstable to axisymmetric waves, but if the jet is confined by an outer cylinder concentric with the jet axis, then it becomes absolutely unstable to axisymmetric waves provided that the swirl (ratio of azimuthal to axial velocity) is large enough. This destabilizing effect of confinement occurs however large the radius of the outer cylinder. A second family of model swirling jets with smooth profiles and a finite thickness shear layer at the jet edge is also studied. The inviscid stability equations are solved numerically in this case. The results from the analytical dispersion relations are reproduced as the shear layer thickness tends to zero. However, increasing this thickness acts to destabilize the absolute instability of axisymmetric waves, apparently due to the centrifugal instability present in the shear layer. It is suggested that the transition from convective to absolute instability could be associated with the onset of an unsteady vortex breakdown. The swirl required to produce this transition can be either greater, or less, than the swirl required to produce the transition from supercritical to subcritical flow, depending on the details of the basic velocity profiles. A codimension-two point in parameter space can exist where the unsteady bifurcation associated with the convective–absolute transition coincides with the steady bifurcation associated with the supercritical–subcritical transition. Such codimension-two points can control a rich variety of nonlinear dynamical behaviour.
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Johnson, M. W. "The Computation of Secondary Flow in a 90° Rectangular Cross-Section Bend." Proceedings of the Institution of Mechanical Engineers, Part C: Mechanical Engineering Science 203, no. 6 (November 1989): 403–9. http://dx.doi.org/10.1243/pime_proc_1989_203_134_02.
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An explicit time-marching scheme for incompressible inviscid three-dimensional flow is presented. The procedure uses an alternative method to the pseudo compressibility technique and uses the energy equation in place of the continuity equation. Calculations are performed for predicting the strong secondary flows produced when a shear flow enters a 90° bend with a rectangular cross-section. Good agreement is achieved with experimental results and rotation of the Bernoulli surfaces through almost 180° is obtained. Discrepancies in the predictions are largely due to the absence of the viscous terms in the computational model equations.
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Hack, M. J. Philipp, and Parviz Moin. "Coherent instability in wall-bounded shear." Journal of Fluid Mechanics 844 (April 13, 2018): 917–55. http://dx.doi.org/10.1017/jfm.2018.202.
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The mechanism underlying the coherent hairpin process in wall-bounded shear flows is studied. An algorithm for the identification and analysis of flow structures based on morphological operations is presented. The method distils the topology of the flow field into a discrete data set and enables the time-resolved sampling of coherent flow processes across multiple scales. Application to direct simulation data of transitional and turbulent boundary layers at moderate Reynolds number sheds light on the flow physics of the hairpin process. The analysis links the hairpin to an exponential instability which is amplified in the flow distorted by a negative perturbation in the streamwise velocity component. Linear analyses substantiate the connection to an inviscid instability mechanism of varicose type. The formation of packets of hairpins is related to a self-similar process which originates from a single patch of low-speed fluid and describes a recurrence of the dynamics that leads to the formation of an individual hairpin. Analysis of the evolution of several thousand turbulent hairpins provides a statistical characterization of the principal dynamics and yields a time-resolved average of the hairpin process. Comparisons with the transitional hairpin show qualitatively consistent trends and thus support earlier hypotheses of their equivalence. In terms of the causality of events, the results suggest that the hairpin is a manifestation of the varicose instability and as such is a consequence rather than a cause of the primary perturbations of the flow.
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Hall, Philip. "Vortex–wave interaction arrays: a sustaining mechanism for the log layer?" Journal of Fluid Mechanics 850 (July 2, 2018): 46–82. http://dx.doi.org/10.1017/jfm.2018.425.
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Vortex–wave interaction theory is used to describe new kinds of localised and distributed exact coherent structures. Starting with a localised vortex–wave interaction state driven by a single inviscid wave, regular arrays of interacting vortex–wave states are investigated. In the first instance the arrays described are operational in an infinite uniform shear flow; we refer to them as ‘uniform shear vortex–wave arrays’. The basic form of the interaction remains identical to the canonical one found by Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666) and subsequently used to describe exact coherent structures by Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). Thus in each cell of a vortex–wave array a roll stress jump is induced across the critical layer of an inviscid wave riding on the streak part of the flow. The theory is extended to arbitrary shear flows using a nonlinear Wentzel–Kramers–Brillouin–Jeffreys or ray theory approach with the wave–roll–streak field operating on a shorter length scale than the mean flow. The evolution equation governing the slow dynamics of the interaction turns out to be a modified form of the well-known mean equation for a turbulent flow, and its particular form can be interpreted as a ‘closure’ between the small and large scales of the flow. If the array structure is taken to be universal, in the sense that it applies to arbitrary shear flows, then the array takes on a form which supports a logarithmic mean velocity profile trapped between what can be identified with the ‘wake region’ and a ‘buffer layer’ well known in the context of wall-bounded turbulent flows. The many similarities between the distributed structures described and wall-bounded turbulence suggest that vortex–wave arrays might be involved in the self-sustaining process supporting the log layer. The modification of the mean profile within each cell of the array leads to ‘staircase’-like streamwise velocity profiles similar to those observed experimentally in turbulent flows. The wave field supporting the ‘staircase’ is concentrated in critical layers which can be associated with the shear layer structures that have been attributed by experimentalists to be the mechanism supporting the uniform-momentum zones of the staircase.
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Rizzi, Arthur, and Charles J. Purcell. "Inviscid vortex-stretched turbulent shear-layer flow computed around a cranked delta wing." Communications in Applied Numerical Methods 2, no. 2 (March 1986): 139–44. http://dx.doi.org/10.1002/cnm.1630020204.
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Wei, Dongyi, Zhifei Zhang, and Weiren Zhao. "Linear Inviscid Damping for a Class of Monotone Shear Flow in Sobolev Spaces." Communications on Pure and Applied Mathematics 71, no. 4 (October 24, 2016): 617–87. http://dx.doi.org/10.1002/cpa.21672.
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Grigor’yev, Yu N., and I. V. Yershov. "The linear stability of inviscid shear flow of a vibrationally excited diatomic gas." Journal of Applied Mathematics and Mechanics 75, no. 4 (January 2011): 410–18. http://dx.doi.org/10.1016/j.jappmathmech.2011.09.006.
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Baines, Peter G., and Humio Mitsudera. "On the mechanism of shear flow instabilities." Journal of Fluid Mechanics 276 (October 10, 1994): 327–42. http://dx.doi.org/10.1017/s0022112094002582.
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In homogeneous and density-stratified inviscid shear flows, the mechanism for instability that is most commonly invoked and discussed is Kelvin–Helmholtz instability, as it occurs for a simple velocity discontinuity. There is a second mechanism, the wave-interaction mechanism, which is much more general, and is the subject of this paper. This mechanism depends on two free waves that propagate in opposite directions in a stratified shear flow, and which may become stationary relative to each other because of the shear. If this occurs, and their relative phase is suitably chosen, the velocity field of each wave increases the displacement of the other, and so the disturbance grows.We show that this mechanism is responsible for instability in a general class of symmetric but otherwise arbitrary velocity and density profiles, provided that the Richardson number Ri < ¼ in a central region of arbitrarily small thickness. A critical layer exists in this central region for the growing disturbance, but its role in the instability process is incidental. When Ri > ¼ everywhere, the flow is stable because the free waves described above are absorbed by the critical layer, and hence are heavily damped. The necessary criteria of Rayleigh and Fjortoft for instability in homogeneous fluid are seen to provide a suitable geometry for two interacting waves. Some specific examples are given, including a succinct explanation of Holmboe waves.
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DIMITRAKOPOULOS, P., and J. J. L. HIGDON. "On the displacement of three-dimensional fluid droplets adhering to a plane wall in viscous pressure-driven flows." Journal of Fluid Mechanics 435 (May 25, 2001): 327–50. http://dx.doi.org/10.1017/s0022112001003883.
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The yield conditions for the displacement of three-dimensional fluid droplets adhering to a plane solid boundary in pressure-driven flows are studied through a series of numerical computations. The study considers low-Reynolds-number flows between two parallel plates and includes interfacial forces with constant surface tension. A comprehensive study is conducted, covering a wide range of viscosity ratio λ, capillary number Ca, advancing and receding contact angles, θA and θR, and dimensionless plate separation H/h (where H is the plate spacing and h is the unperturbed droplet height). This study seeks the optimal shape of the contact line which yields the maximum flow rate (or Ca) for which a droplet can adhere to the surface. The critical shear rates are presented as functions Ca(λ, H/h, θA, Δθ) where Δθ = θA − θR is the contact angle hysteresis. The numerical solutions are based on an efficient, three-dimensional Newton method for the determination of equilibrium free surfaces and an optimization algorithm which is combined with the Newton iteration to solve the nonlinear optimization problem. The critical shear rate is found to be sensitive to viscosity ratio with qualitatively different results for viscous and inviscid droplets. As the viscosity of a droplet increases, the critical flow rate decreases, facilitating the displacement. This is consistent with our previous results for shear flows (Dimitrakopoulos & Higdon 1997, 1998), which represent the limit of infinite plate spacing. As the plate spacing is reduced, the critical flow rate increases until a maximum value is reached. Further reduction in the plate spacing decreases the critical flow rate. The effects of both viscosity ratio and plate separation are much more pronounced for high contact angles. Inviscid droplets (or bubbles) show behaviour dramatically different from that of viscous droplets. For these droplets, a significantly higher flow rate is required for drop displacement, but this critical flow rate decreases monotonically as the distance between the plates decreases. In the Appendix, we clarify the necessary conditions for low-Reynolds-number flows past low viscosity droplets or bubbles.
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JIMÉNEZ, JAVIER, MARKUS UHLMANN, ALFREDO PINELLI, and GENTA KAWAHARA. "Turbulent shear flow over active and passive porous surfaces." Journal of Fluid Mechanics 442 (August 24, 2001): 89–117. http://dx.doi.org/10.1017/s0022112001004888.
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The behaviour of turbulent shear flow over a mass-neutral permeable wall is studied numerically. The transpiration is assumed to be proportional to the local pressure fluctuations. It is first shown that the friction coefficient increases by up to 40% over passively porous walls, even for relatively small porosities. This is associated with the presence of large spanwise rollers, originating from a linear instability which is related both to the Kelvin–Helmholtz instability of shear layers, and to the neutral inviscid shear waves of the mean turbulent profile. It is shown that the rollers can be forced by patterned active transpiration through the wall, also leading to a large increase in friction when the phase velocity of the forcing resonates with the linear eigenfunctions mentioned above. Phase-lock averaging of the forced solutions is used to further clarify the flow mechanism. This study is motivated by the control of separation in boundary layers.
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Chen, Yong, Yiyong Huang, Xiaoqian Chen, and Dengpeng Hu. "Effect of Shear on Ultrasonic Flow Measurement Using Nonaxisymmetric Wave Modes." Shock and Vibration 2014 (2014): 1–17. http://dx.doi.org/10.1155/2014/912404.
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Nonaxisymmetric wave propagation in an inviscid fluid with a pipeline shear flow is investigated. Mathematical equation is deduced from the conservations of mass and momentum, leading to a second-order differential equation in terms of the acoustic pressure. Meanwhile a general boundary condition is formulated to cover different types of wall configurations. A semianalytical method based on the Fourier-Bessel theory is provided to transform the differential equation to algebraic equations. Numerical analysis of phase velocity and wave attenuation in water is addressed in the laminar and turbulent flow. Meanwhile comparison among different kinds of boundary condition is given. In the end, the measurement performance of an ultrasonic flow meter is demonstrated.
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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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Kozlov, V., N. Kuznetsov, and E. Lokharu. "On the Benjamin–Lighthill conjecture for water waves with vorticity." Journal of Fluid Mechanics 825 (July 24, 2017): 961–1001. http://dx.doi.org/10.1017/jfm.2017.361.
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We consider the nonlinear problem of steady gravity-driven waves on the free surface of a two-dimensional flow of an inviscid, incompressible fluid (say, water). The water motion is supposed to be rotational with a Lipschitz continuous vorticity distribution, whereas the flow of finite depth is assumed to be unidirectional. We verify the Benjamin–Lighthill conjecture for flows with values of Bernoulli’s constant close to the critical one. For this purpose it is shown that a set of near-critical waves consists only of Stokes and solitary waves provided their slopes are bounded by a constant. Moreover, the subset of waves with crests located on a fixed vertical is uniquely parametrised by the flow force, which varies between its values for the supercritical and subcritical shear flows of constant depth. There exists another parametrisation for this set; it involves wave heights varying between the constant depth of the subcritical shear flow and the height of a solitary wave.