Journal articles: 'Potential flow theory'

1

COLEMAN, S. E., and J. D. FENTON. "Potential-flow instability theory and alluvial stream bed forms." Journal of Fluid Mechanics 418 (September 10, 2000): 101–17. http://dx.doi.org/10.1017/s0022112000001099.

Full text

Abstract:

The present work constitutes a reassessment of the role of potential-flow analyses in describing alluvial-bed instability. To facilitate the analyses, a new potential-flow description of unsteady alluvial flow is presented, with arbitrary phase lags between local flow conditions and sediment transport permitted implicitly in the flow model. Based on the present model, the explicit phase lag between local sediment transport rate and local flow conditions adopted for previous potential-flow models is shown to be an artificial measure that results in model predictions that are not consistent with observed flow system behaviour. Previous potential-flow models thus do not provide correct descriptions of alluvial flows, and the understanding of bed-wave mechanics inferred based upon these models needs to be reassessed. In contrast to previous potential-flow models, the present one, without the use of an explicit phase lag, predicts instability of flow systems of rippled or dune-covered equilibrium beds. Instability is shown to occur at finite growth rates for a range of wavelengths via a resonance mechanism occurring for surface waves and bed waves travelling at the same celerity. In addition, bed-wave speeds are predicted to decrease with increasing wavelength, and bed waves are predicted to grow and move at faster rates for flows of larger Froude numbers. All predictions of the present potential-flow model are consistent with observations of physical flow systems. Based on the predicted unstable wavelengths for a given alluvial flow, it is concluded that bed waves are not generated from plane bed conditions by any potential-flow instability mechanism. The predictions of instability are nevertheless consistent with instances of accelerated wave growth occurring for flow systems of larger finite developing waves. Potential-flow description of alluvial flows should, however, no longer form the basis of instability analyses describing bed-form (sand-wavelet) generation from flat bed conditions.

APA, Harvard, Vancouver, ISO, and other styles

2

Chadwick, Edmund. "A slender–wing theory in potential flow." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2054 (February 8, 2005): 415–32. http://dx.doi.org/10.1098/rspa.2004.1295.

Full text

Abstract:

Consider uniform, steady potential flow past a slender wing. By considering a horseshoe vortex in the limit as γ / Us → ∞, where γ is the circulation, U is the uniform stream velocity and s is the span, a model representing a vortex sheet is obtained from which the lift on the slender wing can be determined. (This is in contrast to the textbook approach of Batchelor and Katz & Plotkin, who discretize the vortex sheet with horseshoe vortices in the limit as γ / Us → ∞, but then relate the vortex strength to lift by using the two–dimensional limit γ / Us → 0. We shall argue that using these different limits in the same analysis is inconsistent and leads to an incorrect result.) The resulting potential term is shown to be the same as the potential term of the lift Oseenlet in Oseen flow. In the limit of high–Reynolds–number flow, only half the contribution to the lift integral comes from the potential–velocity part of the lift Oseenlet. The other half comes from the vortex–wake–velocity part of the lift Oseenlet. We therefore assume potential flow everywhere except at the vortex sheet, along which we allow a singular vortex–wake–velocity term of the lift Oseenlet. From this, a slender–wing theory is presented together with integral expressions for the lift and change in lift over the wing surface. Applications to slender bodies and large–aspect–ratio wings, in particular, the Lanchester–Prandtl lifting line, are then considered.

APA, Harvard, Vancouver, ISO, and other styles

3

Dassios, G. "The Kelvin transformation in potential theory and Stokes flow." IMA Journal of Applied Mathematics 74, no. 3 (September 9, 2008): 427–38. http://dx.doi.org/10.1093/imamat/hxn027.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

VERHOFF, A. "Two-dimensional potential flow solutions with separation." Journal of Fluid Mechanics 657 (July 21, 2010): 238–64. http://dx.doi.org/10.1017/s0022112010001448.

Full text

Abstract:

A procedure for constructing two-dimensional incompressible potential flowfield solutions with separation and a recirculation region is presented. It naturally makes use of complex variable theory and other analysis techniques such as conformal mapping and the generalized Poisson integral formula. Flowfield determination is reduced to solution of a boundary value problem in various simple domains. The entire velocity field is described analytically; stream function and velocity potential contour maps are readily constructed. Example solutions are presented. Solutions for sharp leading edge airfoils at arbitrary angle of attack are completely determined, including the limiting angle of attack for upper-surface flow re-attachment. For other configurations (e.g. circular cylinder, backward-facing step) the analytical solution contains one or more free parameters, whose values may be inferred from boundary layer theory or experiment.

APA, Harvard, Vancouver, ISO, and other styles

5

Ma, Chao, Yi Zhu, Jiayi He, Chenliang Zhang, Decheng Wan, Chi Yang, and Francis Noblesse. "Nonlinear corrections of linear potential-flow theory of ship waves." European Journal of Mechanics - B/Fluids 67 (January 2018): 1–14. http://dx.doi.org/10.1016/j.euromechflu.2017.07.006.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Baddoo, Peter J. "Lightning Solvers for Potential Flows." Fluids 5, no. 4 (November 30, 2020): 227. http://dx.doi.org/10.3390/fluids5040227.

Full text

Abstract:

We present a method for computing potential flows in planar domains. Our approach is based on a new class of techniques, known as “lightning solvers”, which exploit rational function approximation theory in order to achieve excellent convergence rates. The method is particularly suitable for flows in domains with corners where traditional numerical methods fail. We outline the mathematical basis for the method and establish the connection with potential flow theory. In particular, we apply the new solver to a range of classical problems including steady potential flows, vortex dynamics, and free-streamline flows. The solution method is extremely rapid and usually takes just a fraction of a second to converge to a high degree of accuracy. Numerical evaluations of the solutions are performed in a matter of microseconds and can be compressed further with novel algorithms.

APA, Harvard, Vancouver, ISO, and other styles

7

Stropky, D. M., N. Djilali, I. S. Gartshore, and M. Salcudean. "Application of Momentum Integral Methods and Linearized Potential Theory for Predicting Separation Bubble Characteristics." Journal of Fluids Engineering 112, no. 4 (December 1, 1990): 416–24. http://dx.doi.org/10.1115/1.2909419.

Full text

Abstract:

A new viscous-inviscid interaction procedure of the semi-inverse type has been developed to predict two-dimensional separated flows. The method is applied to incompressible flow over an external backward-facing step, using linearized potential theory for the inviscid region and a simple modification of Pohlhausens’ momentum-integral method in the viscous region. The modified Pohlhausen method, which approximates the reverse flow region with a region of “dead-air,” is first tested without the viscous-inviscid procedure to predict fully developed laminar and turbulent flow in a plane symmetric sudden expansion. Comparisons are made with experimental data, other calculation methods, and finite difference predictions using a modified version of an elliptic code (TEACH-II). Reasonable predictions of the sudden expansion and backward-facing step flows are obtained, provided that the step-height to boundary-layer thickness ratio is large enough for the Pohlhausen type velocity profiles to be effective. The relative simplicity of the zonal equations coupled with the viscous-inviscid interaction procedure makes the present calculation method computationally attractive. The method should also prove useful in more complex separated flow situations, such as bluff-body aerodynamics.

APA, Harvard, Vancouver, ISO, and other styles

8

Zhang, Zhang, and Shang. "A Potential Flow Theory and Boundary Layer Theory Based Hybrid Method for Waterjet Propulsion." Journal of Marine Science and Engineering 7, no. 4 (April 21, 2019): 113. http://dx.doi.org/10.3390/jmse7040113.

Full text

Abstract:

A hybrid method—coupled with the boundary element method (BEM) for wave-making resistance, the empirical method (EM) for viscous resistance, and the boundary layer theory (BLT) for capture of an area’s physical parameters—was proposed to predict waterjet propulsion performance. The waterjet propulsion iteration process was established from the force-balanced waterjet–hull system by applying the hybrid approach. Numerical validation of the present method was carried out using the 1/8.556 scale waterjet-propelled ITTC (International Towing Tank Conference) Athena ship model. Resistance, attitudes, wave cut profiles, waterjet thrust, and thrust deduction showed similar tendencies to the experimental curves and were in good agreement with the data. The application of the present hybrid method to the side-hull configuration research of a trimaran indicates that the side-hull arranged at the rear of the main hull contributed to energy-saving and high-efficiency propulsion. In addition, at high Froude numbers, the “fore-body trimaran” showed a local advantage in resistance and thrust deduction.

APA, Harvard, Vancouver, ISO, and other styles

9

Dillmann, Andreas. "Linear potential theory of steady internal supersonic flow with quasi-cylindrical geometry. Part 2. Free jet flow." Journal of Fluid Mechanics 286 (March 10, 1995): 327–57. http://dx.doi.org/10.1017/s0022112095000759.

Full text

Abstract:

By extending the methods of Part 1, the general problem of steady cylindrical supersonic free jet flow is treated in a similar manner to the flow in quasi-cylindrical ducts. It is shown that the presence of a finite pressure jump at the nozzle lip gives rise to a periodic singularity pattern in the flow field. Basic examples of free jet flows are discussed, and for the case of a nearly ideally expanded axisymmetric jet, theoretical Mach—Zehnder interferograms are calculated by analytical integration of the density field. Excellent agreement with experiment proves the validity of linear theory even close to the singularities and far downstream of the nozzle orifice. Furthermore, it is shown that Pack's formula for the wavelength of the shock cell structure is inconsistent; the correct formula is derived and excellent agreement with Emden's empirical fit is found.

APA, Harvard, Vancouver, ISO, and other styles

10

Dowell, Earl H., and Donald B. Bliss. "New Look at Unsteady Supersonic Potential Flow Aerodynamics and Piston Theory." AIAA Journal 51, no. 9 (September 2013): 2278–81. http://dx.doi.org/10.2514/1.j052088.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Dowell, Earl H., and Donald B. Bliss. "New Look at Unsteady Supersonic Potential Flow Aerodynamics and Piston Theory." AIAA Journal 53, no. 8 (August 2015): 2419. http://dx.doi.org/10.2514/1.j054540.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Li, Shaobin, Zhenxin Tao, and Xizhen Song. "Unsteady Lift Model for Morphing Airfoil Based on Potential Flow Theory." Journal of Aerospace Engineering 31, no. 2 (March 2018): 04018006. http://dx.doi.org/10.1061/(asce)as.1943-5525.0000820.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Lewins, Jeffery. "Bejan’s constructal theory of equal potential distribution." International Journal of Heat and Mass Transfer 46, no. 9 (April 2003): 1541–43. http://dx.doi.org/10.1016/s0017-9310(02)00441-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Dias, F., A. I. Dyachenko, and V. E. Zakharov. "Theory of weakly damped free-surface flows: A new formulation based on potential flow solutions." Physics Letters A 372, no. 8 (February 2008): 1297–302. http://dx.doi.org/10.1016/j.physleta.2007.09.027.

Full text

APA, Harvard, Vancouver, ISO, and other styles

15

Zarrati, A. R., Yee-Chung Jin, A. Shanehsaz-zadeh, and F. Ahadi. "Potential flow solution for a free surface flow past a sudden slope change." Canadian Journal of Civil Engineering 31, no. 4 (August 1, 2004): 553–60. http://dx.doi.org/10.1139/l04-021.

Full text

Abstract:

An analytical model was developed to calculate the pressure distribution in a free surface flow past a sudden change in channel slope. A conformal transformation technique was used to solve the problem analytically in a way that there is no need for trial and error to find the location of the free surface. Two methods were employed for this simulation: flow at a corner and free streamline theory. It was shown that free streamline theory is more accurate. Experiments were conducted to verify the ability of the analytical model to calculate the pressure distribution in a channel with a sudden change in slope. Slope changes of 6.22°, 10°, and 15° were tested with various flow discharges. The analytical model predictions of pressure distribution along the channel bed and with depth agreed well with the experimental measurements. Pressures up to 25 times the hydrostatic pressure were experimentally measured near the point of sudden change in slope. These pressures were reproduced by the model. The analytical model predictions of the water surface profile over a ramp in a prototype spillway were compared with those of a numerical model. The comparison showed a good agreement.Key words: pressure distribution, free surface flow, analytical model, chute spillway, aerator ramp, potential flow.

APA, Harvard, Vancouver, ISO, and other styles

16

Gies, Holger, and René Sondenheimer. "Renormalization group flow of the Higgs potential." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2114 (January 22, 2018): 20170120. http://dx.doi.org/10.1098/rsta.2017.0120.

Full text

Abstract:

We summarize results for local and global properties of the effective potential for the Higgs boson obtained from the functional renormalization group, which allows one to describe the effective potential as a function of both scalar field amplitude and renormalization group scale. This sheds light onto the limitations of standard estimates which rely on the identification of the two scales and helps in clarifying the origin of a possible property of meta-stability of the Higgs potential. We demonstrate that the inclusion of higher-dimensional operators induced by an underlying theory at a high scale (GUT or Planck scale) can relax the conventional lower bound on the Higgs mass derived from the criterion of absolute stability. This article is part of the Theo Murphy meeting issue ‘Higgs cosmology’.

APA, Harvard, Vancouver, ISO, and other styles

17

Baoji, Zhang. "Research on Ship Hull Optimisation of High-Speed Ship Based on Viscous Flow/Potential Flow Theory." Polish Maritime Research 27, no. 1 (March 1, 2020): 18–28. http://dx.doi.org/10.2478/pomr-2020-0002.

Full text

Abstract:

AbstractIn order to quickly obtain practical ship forms with good resistance performance, based on the linear wave-making resistance theory, the optimal design method of ship forms with minimum total resistance is discussed by using the non-linear programming (NLP) method. Taking the total resistance as the objective function (the Michell integral is used to calculate the wave-making resistance and the equivalent plate friction resistance formula is used to calculate the frictional resistance), the hull surface offset as the design variable and appropriate displacement as the basic constraints, and considering the additional constraints, the hull bow shape and the whole ship are optimised, and an improved hull form is obtained. The resistance of the ship before and after optimisation is calculated by the CFD method to further evaluate the resistance reduction effect and performance after optimisation. Finally, an example of optimisation calculation of an actual high-speed ship is given. The obvious resistance reduction results confirm the reliability of the optimisation design method.

APA, Harvard, Vancouver, ISO, and other styles

18

R. Kabiri-Samani, A., M. Amirabdollahian, and F. Farshi. "Analytical Solution for the Free Over-Fall Weir Flow Using Conformal Mapping and Potential Flow Theory." International Journal of Hydraulic Engineering 1, no. 6 (January 7, 2013): 75–82. http://dx.doi.org/10.5923/j.ijhe.20120106.03.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Dubos, Thomas, and Fabrice Voitus. "A Semihydrostatic Theory of Gravity-Dominated Compressible Flow." Journal of the Atmospheric Sciences 71, no. 12 (November 26, 2014): 4621–38. http://dx.doi.org/10.1175/jas-d-14-0080.1.

Full text

Abstract:

Abstract From Hamilton’s least-action principle, compressible equations of motion with density diagnosed from potential temperature through hydrostatic balance are derived. Slaving density to potential temperature suppresses the degrees of freedom supporting the propagation of acoustic waves and results in a soundproof system. The linear normal modes and dispersion relationship for an isothermal state of rest on f and β planes are accurate from hydrostatic to nonhydrostatic scales, except for deep internal gravity waves. Specifically, the Lamb wave and long Rossby waves are not distorted, unlike with anelastic or pseudoincompressible systems. Compared to similar equations derived by A. Arakawa and C. S. Konor, the semihydrostatic system derived here possesses an additional term in the horizontal momentum budget. This term is an apparent force resulting from the vertical coordinate not being the actual height of an air parcel but its hydrostatic height (the hypothetical height it would have after the atmospheric column it belongs to has reached hydrostatic balance through adiabatic vertical displacements of air parcels). The Lagrange multiplier λ introduced in Hamilton’s principle to slave density to potential temperature is identified as the nonhydrostatic vertical displacement (i.e., the difference between the actual and hydrostatic heights of an air parcel). The expression of nonhydrostatic pressure and apparent force from λ allow the derivation of a well-defined linear symmetric positive definite problem for λ. As with hydrostatic equations, vertical velocity is diagnosed through Richardson’s equation. The semihydrostatic system has therefore precisely the same degrees of freedom as the hydrostatic primitive equations, while retaining much of the accuracy of the fully compressible Euler equations.

APA, Harvard, Vancouver, ISO, and other styles

20

Gao, Yangyang, Danielle S. Tan, Zhiyong Hao, Xikun Wang, and Soon Keat Tan. "Application of Potential Theory to Steady Flow Past Two Cylinders in Tandem Arrangement." Mathematical Problems in Engineering 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/495179.

Full text

Abstract:

The wake flow patterns associated with flow past a cylinder and a cylinder-pair in tandem configuration are revisited, compared, and evaluated with respect to the streamline patterns generated based on potential flow theory and superposition of various potential flow elements. The wakes, which are vortex shedding in the lee of the cylinder(s), are reproduced by placing pairs of equal but opposite circulation elements in the potential flow field. The strength of the circulation elements determines the size of the vortices produced. The streamline patterns of flow past a pair of unequal cylinders in tandem configuration provide an indirect means to establish the threshold condition for the wake transition from that of a single bluff body to alternating reattachment behavior. This threshold condition is found to be a function of the diameter ratio,d/D(diametersdandD,d≤D), spacing ratio,L/D(centre-to-centre distance,L, to cylinder diameter,D), and equivalent incident flow speed,U.A unique functional relationshipf(L/D,d/D,U) of this threshold condition is established.

APA, Harvard, Vancouver, ISO, and other styles

21

Asthana, Rishi, Mukesh Kumar Awasthi, and G. S. Agrawal. "Viscous Potential Flow Analysis of Rayleigh-Taylor Instability of Cylindrical Interface." Applied Mechanics and Materials 110-116 (October 2011): 769–75. http://dx.doi.org/10.4028/www.scientific.net/amm.110-116.769.

Full text

Abstract:

The present paper deals with the study of Rayleigh-Taylor instability at the cylindrical interface using viscous potential flow theory. In the inviscid potential flow theory, the viscous term in Navier-Stokes equation vanishes as viscosity is zero. In viscous potential flow, the viscous term in Navier-Stokes equation vanishes as vorticity is zero but viscosity is not zero. Viscosity enters through normal stress balance in viscous potential flow theory and tangential stresses are not considered. A dispersion relation is derived and stability is discussed in terms of various parameters such as Ohnesorge number, density ratio etc. A condition for neutral stability is obtained and it is given in terms of critical value of the wave number. It is observed that the Ohnesorge number has destabilizing effect while inner fluid fraction has stabilizing effect on the stability of the system.

APA, Harvard, Vancouver, ISO, and other styles

22

Song Wu-Chao, Wei Ying-Jie, Lu Li-Rui, Wang Cong, and Lu Jia-Xing. "Dynamic characteristics of parallel water-entry cavity based on potential flow theory." Acta Physica Sinica 67, no. 22 (2018): 224702. http://dx.doi.org/10.7498/aps.67.20181375.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

El-Sayed, M. F., N. T. Eldabe, M. H. Haroun, and D. M. Mostafa. "Nonlinear electroviscoelastic potential flow instability theory of two superposed streaming dielectric fluids." Canadian Journal of Physics 92, no. 10 (October 2014): 1249–57. http://dx.doi.org/10.1139/cjp-2013-0446.

Full text

Abstract:

The nonlinear electrohydrodynamic Kelvin–Helmholtz instability of two superposed viscoelastic Walters B′ dielectric fluids in the presence of a tangential electric field is investigated in three dimensions using the potential flow analysis. The method of multiple scales is used to obtain a dispersion relation for the linear problem, and a nonlinear Ginzburg–Landau equation with complex coefficients for the nonlinear problem. The linear and nonlinear stability conditions are obtained and discussed both analytically and numerically. In the linear stability analysis, we found that the fluid velocities and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities, and surface tension have stabilizing effects; and that the system in the three-dimensional disturbances is more stable than in the corresponding case of two-dimensional disturbances. While in the nonlinear analysis, for both two- and three-dimensional disturbances, we found that the fluid velocities, surface tension, and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities have stabilizing effects, and that the system in the three-dimensional disturbances is more unstable than its behavior in the two-dimensional disturbances for most physical parameters except the kinematic viscosities.

APA, Harvard, Vancouver, ISO, and other styles

24

Tausch, J. "Sparse BEM for potential theory and Stokes flow using variable order wavelets." Computational Mechanics 32, no. 4-6 (December 1, 2003): 312–18. http://dx.doi.org/10.1007/s00466-003-0488-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Tran-Cong, Ton. "A potential theory for the steady separated flow about an aerofoil section." Ingenieur-Archiv 58, no. 4 (1988): 285–94. http://dx.doi.org/10.1007/bf00535938.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Yao, Xiong-liang, and A.-man Zhang. "A numerical investigation of bubble dynamics based on the potential-flow theory." Journal of Marine Science and Application 5, no. 4 (December 2006): 14–21. http://dx.doi.org/10.1007/s11804-006-6031-z.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Noblesse, Francis, and Dane Hendrix. "On the Theory of Potential Flow About a Ship Advancing in Waves." Journal of Ship Research 36, no. 01 (March 1, 1992): 17–29. http://dx.doi.org/10.5957/jsr.1992.36.1.17.

Full text

Abstract:

This study considers the three-dimensional potential flow due to a ship advancing with constant average speed in a train of regular waves. A modified integro-differential equation for determining the velocity potential on the mean position of the hull surface is obtained, and a solid theoretical basis for obtaining a numerical solution of the equation via a panel method is developed following the approach used by Kochin more than 50 years ago. In short, the approach is essentially based on a Fourier representation of the solution of a modified integro-differential equation. This approach circumvents the fundamental difficulties associated with the numerical evaluation of the Green function and its gradient, and their subsequent integration over the panels used to approximate the hull surface of a ship.

APA, Harvard, Vancouver, ISO, and other styles

28

Yang, Qiang, Zhuofu Tao, and Yaoru Liu. "Internal Variable Theory Formulated by One Extended Potential Function." Journal of Non-Equilibrium Thermodynamics 45, no. 3 (July 26, 2020): 311–18. http://dx.doi.org/10.1515/jnet-2020-0017.

Full text

Abstract:

AbstractIn the kinetic rate laws of internal variables, it is usually assumed that the rates of internal variables depend on the conjugate forces of the internal variables and the state variables. The dependence on the conjugate force has been fully addressed around flow potential functions. The kinetic rate laws can be formulated with two potential functions, the free energy function and the flow potential function. The dependence on the state variables has not been well addressed. Motivated by the previous study on the asymptotic stability of the internal variable theory by J. R. Rice, the thermodynamic significance of the dependence on the state variables is addressed in this paper. It is shown in this paper that the kinetic rate laws can be formulated by one extended potential function defined in an extended state space if the rates of internal variables do not depend explicitly on the internal variables. The extended state space is spanned by the state variables and the rate of internal variables. Furthermore, if the rates of internal variables do not depend explicitly on state variables, an extended Gibbs equation can be established based on the extended potential function, from which all constitutive equations can be recovered. This work may be considered as a certain Lagrangian formulation of the internal variable theory.

APA, Harvard, Vancouver, ISO, and other styles

29

Chow, S. S., and G. F. Carey. "Finite element error estimates for subsonic flow." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 29, no. 1 (July 1987): 88–102. http://dx.doi.org/10.1017/s0334270000005646.

Full text

Abstract:

AbstractError estimates are derived for a finite element analysis of plane steady subsonic flows described by the full potential equation. The analysis is based on the use of the theory of variational inequalities to accomodate the subsonic flow constraint and leads to a suboptimal estimate relative to that obtained for linear potential flow. We then consider an alternative dual formulation of the problem and obtain an optimal estimate subject to reasonable regularity assumptions.

APA, Harvard, Vancouver, ISO, and other styles

30

MacKay, R. S., and J. D. Robinson. "Aggregation of Markov flows I: theory." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2118 (March 19, 2018): 20170232. http://dx.doi.org/10.1098/rsta.2017.0232.

Full text

Abstract:

A Markov flow is a stationary measure, with the associated flows and mean first passage times, for a continuous-time regular jump homogeneous semi-Markov process on a discrete state space. Nodes in the state space can be eliminated to produce a smaller Markov flow which is a factor of the original one. Some improvements to the elimination methods of Wales are given. The main contribution of the paper is to present an alternative, namely a method to aggregate groups of nodes to produce a factor. The method can be iterated to make hierarchical aggregation schemes. The potential benefits are efficient computation, including recomputation to take into account local changes, and insights into the macroscopic behaviour. This article is part of the theme issue ‘Hilbert’s sixth problem’.

APA, Harvard, Vancouver, ISO, and other styles

31

Zhuge, Hai, Weiyu Guo, and Xiang Li. "The potential energy of knowledge flow." Concurrency and Computation: Practice and Experience 19, no. 15 (2007): 2067–90. http://dx.doi.org/10.1002/cpe.1143.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Dillmann, Andreas. "Linear potential theory of steady internal supersonic flow with quasi-cylindrical geometry. Part 1. Flow in ducts." Journal of Fluid Mechanics 281 (December 25, 1994): 159–91. http://dx.doi.org/10.1017/s0022112094003071.

Full text

Abstract:

Based on linear potential theory, the general three-dimensional problem of steady supersonic flow inside quasi-cylindrical ducts is formulated as an initial-boundary-value problem for the wave equation, whose general solution arises as an infinite double series of the Fourier–Bessel type. For a broad class of solutions including the general axisymmetric case, it is shown that the presence of a discontinuity in wall slope leads to a periodic singularity pattern associated with non-uniform convergence of the corresponding series solutions, which thus are unsuitable for direct numerical computation. This practical difficulty is overcome by extending a classical analytical method, viz. Kummer's series transformation. A variety of elementary flow fields is presented, whose complex cellular structure can be qualitatively explained by asymptotic laws governing the propagation of small perturbations on characteristic surfaces.

APA, Harvard, Vancouver, ISO, and other styles

33

Wagner, G. L., and W. R. Young. "Available potential vorticity and wave-averaged quasi-geostrophic flow." Journal of Fluid Mechanics 785 (November 23, 2015): 401–24. http://dx.doi.org/10.1017/jfm.2015.626.

Full text

Abstract:

We derive a wave-averaged potential vorticity equation describing the evolution of strongly stratified, rapidly rotating quasi-geostrophic (QG) flow in a field of inertia-gravity internal waves. The derivation relies on a multiple-time-scale asymptotic expansion of the Eulerian Boussinesq equations. Our result confirms and extends the theory of Bühler & McIntyre (J. Fluid Mech., vol. 354, 1998, pp. 609–646) to non-uniform stratification with buoyancy frequency $N(z)$ and therefore non-uniform background potential vorticity $f_{0}N^{2}(z)$, and does not require spatial-scale separation between waves and balanced flow. Our interest in non-uniform background potential vorticity motivates the introduction of a new quantity: ‘available potential vorticity’ (APV). Like Ertel potential vorticity, APV is exactly conserved on fluid particles. But unlike Ertel potential vorticity, linear internal waves have no signature in the Eulerian APV field, and the standard QG potential vorticity is a simple truncation of APV for low Rossby number. The definition of APV exactly eliminates the Ertel potential vorticity signal associated with advection of a non-uniform background state, thereby isolating the part of Ertel potential vorticity available for balanced-flow evolution. The effect of internal waves on QG flow is expressed concisely in a wave-averaged contribution to the materially conserved QG potential vorticity. We apply the theory by computing the wave-induced QG flow for a vertically propagating wave packet and a mode-one wave field, both in vertically bounded domains.

APA, Harvard, Vancouver, ISO, and other styles

34

ESLER, J. G. "The turbulent equilibration of an unstable baroclinic jet." Journal of Fluid Mechanics 599 (March 6, 2008): 241–68. http://dx.doi.org/10.1017/s0022112008000153.

Full text

Abstract:

The evolution of an unstable baroclinic jet, subject to a small perturbation, is examined numerically in a quasi-geostrophic two-layer β-channel model. After a period of initial wave growth, wave breaking leads to turbulence within each layer, and to the eventual equilibration of the flow. The equilibrated flow must satisfy certain dynamical constraints: total momentum is conserved, the total energy is bounded and the flow must be realizable via some area-preserving (diffusive) rearrangement of the initial potential vorticity field in each layer. A theory is introduced that predicts the equilibrated flow in terms of the initial flow parameters. The idea is that the equilibrated state minimizes available potential energy, subject to the constraints on total momentum and total energy, and the further ‘kinematic’ constraint that the potential vorticity changes through a process of complete homogenization within well-delineated regions in each layer. Within a large region of parameter space, the theory accurately predicts the cross-channel structure and strength of the equilibrated jet, the regions where potential vorticity mixing takes place, and total eddy mass (temperature) fluxes. Results are compared with predictions from a maximum-entropy theory that allows for more general rearrangements of the initial potential vorticity field, subject to the known dynamical constraints. The maximum-entropy theory predicts that significantly more available potential energy is released than is observed in the simulations, and that an unphysical ‘exchange’ of bands of fluid will occur across the channel in the lower layer. The kinematic constraint of piecewise potential vorticity homogenization is therefore important in limiting the ‘efficiency’ of release of available potential energy in unstable baroclinic flows. For a typical initial flow, it is demonstrated that if the dynamical constraints alone are considered, then over twice as much potential energy is available for release compared to that actually released in the simulations.

APA, Harvard, Vancouver, ISO, and other styles

35

Lifshits, Yu B., and V. S. Sakovich. "The potential approximation in the theory of conical flows." Fluid Dynamics 25, no. 3 (1990): 424–30. http://dx.doi.org/10.1007/bf01049825.

Full text

APA, Harvard, Vancouver, ISO, and other styles

36

Berci, M. "Lift-Deficiency Functions of Elliptical Wings in Incompressible Potential Flow: Jones’ Theory Revisited." Journal of Aircraft 53, no. 2 (March 2016): 599–602. http://dx.doi.org/10.2514/1.c033515.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Berci, M. "Lift-Deficiency Functions of Elliptical Wings in Incompressible Potential Flow: Jones’ Theory Revisited." Journal of Aircraft 54, no. 2 (March 2017): 856. http://dx.doi.org/10.2514/1.c034360.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

GERHARDT, F. C., R. G. J. FLAY, and P. RICHARDS. "Unsteady aerodynamics of two interacting yacht sails in two-dimensional potential flow." Journal of Fluid Mechanics 668 (December 16, 2010): 551–81. http://dx.doi.org/10.1017/s0022112010004842.

Full text

Abstract:

In this paper, unsteady thin aerofoil theory is extended to the case of two interacting aerofoils that oscillate harmonically perpendicular to the direction of the incident flow. The two aerofoils represent the headsail and mainsail of a yacht that sails upwind in waves. The developed theory is validated against theoretical data from the literature and results from wind tunnel tests with rigid, high-aspect ratio sail models oscillating at reduced frequencies fromk= 0 tok= 0.68. Good agreement is found between the predicted and measured chordwise pressure distributions. An application of the theory to the case of an International America's Cup Class yacht reveals that the time-varying components of the aerodynamic forces are small and that the thrust gain is minimal, i.e. only very little energy can be extracted from the unsteady flow about the sails. No attempt is made to investigate the influence of the flexibility of the sails, three-dimensional effects or phenomena related to dynamic stall.

APA, Harvard, Vancouver, ISO, and other styles

39

Dommermuth, Douglas G., Dick K. P. Yue, W. M. Lin, R. J. Rapp, E. S. Chan, and W. K. Melville. "Deep-water plunging breakers: a comparison between potential theory and experiments." Journal of Fluid Mechanics 189 (April 1988): 423–42. http://dx.doi.org/10.1017/s0022112088001089.

Full text

Abstract:

The primary objective of this paper is to provide a detailed confirmation of the validity of potential-flow theory for describing steep gravity waves produced in an experimental tank. Very high-resolution computations are carried out which use a refined mixed Eulerian-Lagrangian solution scheme under the assumptions of potential flow. The numerical results for a plunging breaker produced by a programmed piston-type wavemaker are found to be in excellent agreement with tank measurements up to and including overturning. The calculated free-surface elevations are almost indistinguishable from measured profiles, even close to where the wave plunges. The horizontal and vertical water-particle velocities measured with a laser anemometer throughout the water depth at two longitudinal stations are also well predicted by the theory. In contrast to the fully nonlinear theory, predictions based on linearized theory become poorer as the wave packet moves down the tank. To allow other investigators to evaluate the computations and experiments, the Fourier amplitudes and phases which completely specify the time history of the wavemaker's velocity are given in Appendix B.

APA, Harvard, Vancouver, ISO, and other styles

40

Balasuriya, S. "Gradient evolution for potential vorticity flows." Nonlinear Processes in Geophysics 8, no. 4/5 (October 31, 2001): 253–63. http://dx.doi.org/10.5194/npg-8-253-2001.

Full text

Abstract:

Abstract. Two-dimensional unsteady incompressible flows in which the potential vorticity (PV) plays a key role are examined in this study, through the development of the evolution equation for the PV gradient. For the case where the PV is conserved, precise statements concerning topology-conservation are presented. While establishing some intuitively well-known results (the numbers of eddies and saddles is conserved), other less obvious consequences (PV patches cannot be generated, some types of Lagrangian and Eulerian entities are equivalent) are obtained. This approach enables an improvement on an integrability result for PV conserving flows (if there were no PV patches at time zero, the flow would be integrable). The evolution of the PV gradient is also determined for the nonconservative case, and a plausible experiment for estimating eddy diffusivity is suggested. The theory is applied to an analytical diffusive Rossby wave example.

APA, Harvard, Vancouver, ISO, and other styles

41

Sanz, A. "On the Two-Dimensional Theory of Incompressible Flow Over Inlets." Journal of Applied Mechanics 53, no. 4 (December 1, 1986): 947–51. http://dx.doi.org/10.1115/1.3171886.

Full text

Abstract:

The linearized solution for the two-dimensional flow over an inlet of general form has been derived, assuming incompressible potential flow. With this theory suction forces at sharp inlet lips can be estimated and ideal inlets can be designed.

APA, Harvard, Vancouver, ISO, and other styles

42

Migdal, Alexander. "Vortex sheet turbulence as solvable string theory." International Journal of Modern Physics A 36, no. 05 (February 20, 2021): 2150062. http://dx.doi.org/10.1142/s0217751x21500627.

Full text

Abstract:

We study steady vortex sheet solutions of the Navier–Stokes in the limit of vanishing viscosity at fixed energy flow. We refer to this as the turbulent limit. These steady flows correspond to a minimum of the Euler Hamiltonian as a functional of the tangent discontinuity of the local velocity parametrized as [Formula: see text]. This observation means that the steady flow represents the low-temperature limit of the Gibbs distribution for vortex sheet dynamics with the normal displacement [Formula: see text] of the vortex sheet as a Hamiltonian coordinate and [Formula: see text] as a conjugate momentum. An infinite number of Euler conservation laws lead to a degenerate vacuum of this system, which explains the complexity of turbulence statistics and provides the relevant degrees of freedom (random surfaces). The simplest example of a steady solution of the Navier–Stokes equation in the turbulent limit is a spherical vortex sheet whose flow outside is equivalent to a potential flow past a sphere, while the velocity is constant inside the sphere. Potential flow past other bodies provide other steady solutions. The new ingredient we add is a calculable gap in tangent velocity, leading to anomalous dissipation. This family of steady solutions provides an example of the Euler instanton advocated in our recent work, which is supposed to be responsible for the dissipation of the Navier–Stokes equation in the turbulent limit. We further conclude that one can obtain turbulent statistics from the Gibbs statistics of vortex sheets by adding Lagrange multipliers for the conserved volume inside closed surfaces, the rate of energy pumping, and energy dissipation. The effective temperature in our Gibbs distribution goes to zero as [Formula: see text] with Reynolds number [Formula: see text] in the turbulent limit. The Gibbs statistics in this limit reduces to the solvable string theory in two dimensions (so-called [Formula: see text] critical matrix model). This opens the way for nonperturbative calculations in the Vortex Sheet Turbulence, some of which we report here.

APA, Harvard, Vancouver, ISO, and other styles

43

ADAMS, J., N. TETRADIS, J. BERGES, F. FREIRE, C. WETTERICH, and S. BORNHOLDT. "SOLVING NONPERTURBATIVE FLOW EQUATIONS." Modern Physics Letters A 10, no. 31 (October 10, 1995): 2367–79. http://dx.doi.org/10.1142/s0217732395002520.

Full text

Abstract:

Nonperturbative exact flow equations describe the scale dependence of the effective average action. We present a numerical solution for an approximate form of the flow equation for the potential in a three-dimensional N-component scalar field theory. The critical behavior, with associated critical exponents, can be inferred with good accuracy.

APA, Harvard, Vancouver, ISO, and other styles

44

Almeida, Fernando, and Zoltán Buzády. "Learning Entrepreneurship in Higher Education Through Flow Theory and FLIGBY Game." International Journal of Virtual and Personal Learning Environments 9, no. 1 (January 2019): 1–15. http://dx.doi.org/10.4018/ijvple.2019010101.

Full text

Abstract:

This article performs an exploratory study of the potential of flow theory and FLIGBY game to contribute to develop entrepreneurship competencies among higher education students. For this purpose, this study considers the use of a focus group consisting of eight students enrolled in the entrepreneurship course in a higher educational institution in Portugal, in which students for two months explored FLIGBY. The results obtained allowed us to conclude that FLIGBY was also suitable to be explored in the context of entrepreneurship classes. Students emphasized the potential of the game to be applied for training of management skills, the recognition of their leadership skills, and the exploration of new approaches to the management challenges. Finally, it should be noted that the benefits offered by FLIGBY were experienced differently by students with professional experience in IT and management fields. Those students emphasized the application of the game to the real world and the potential offered for FLIGBY for allowing students to explore new skills and actions.

APA, Harvard, Vancouver, ISO, and other styles

45

Metcalfe, Guy, Daniel Lester, Alison Ord, Pandurang Kulkarni, Murray Rudman, Mike Trefry, Bruce Hobbs, Klaus Regenaur-Lieb, and Jeffery Morris. "An experimental and theoretical study of the mixing characteristics of a periodically reoriented irrotational flow." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1918 (May 13, 2010): 2147–62. http://dx.doi.org/10.1098/rsta.2010.0037.

Full text

Abstract:

The minimum-energy method to generate chaotic advection should be to use an irrotational flow. However, irrotational flows have no saddle connections to perturb in order to generate chaotic orbits. To the early work of Jones & Aref (Jones & Aref 1988 Phys. Fluids 31 , 469–485 ( doi:10.1063/1.866828 )) on potential flow chaos, we add periodic reorientation to generate chaotic advection with irrotational experimental flows. Our experimental irrotational flow is a dipole potential flow in a disc-shaped Hele-Shaw cell called the rotated potential mixing flow; it leads to chaotic advection and transport in the disc. We derive an analytical map for the flow. This is a partially open flow, in which parts of the flow remain in the cell forever, and parts of it pass through with residence-time and exit-time distributions that have self-similar features in the control parameter space of the stirring. The theory compares well with the experiment.

APA, Harvard, Vancouver, ISO, and other styles

46

Janosik, L. A., and S. F. Duffy. "A Viscoplastic Constitutive Theory for Monolithic Ceramics—I." Journal of Engineering for Gas Turbines and Power 120, no. 1 (January 1, 1998): 155–61. http://dx.doi.org/10.1115/1.2818069.

Full text

Abstract:

This paper, which is the first of two in a series, provides an overview of a viscoplastic constitutive model that accounts for time-dependent material deformation (e.g., creep, stress relaxation, etc.) in monolithic ceramics. Using continuum principles of engineering mechanics, the complete theory is derived from a scalar dissipative potential function first proposed by Robinson (1978), and later utilized by Duffy (1988). Derivations based on a flow potential function provide an assurance that the inelastic boundary value problem is well posed, and solutions obtained are unique. The specific formulation used here for the threshold function (a component of the flow potential function) was originally proposed by Willam and Warnke (1975) in order to formulate constitutive equations for time-independent classical plasticity behavior observed in cement and unreinforced concrete. Here constitutive equations formulated for the flow law (strain rate) and evolutionary law employ stress invariants to define the functional dependence on the Cauchy stress and a tensorial state variable. This particular formulation of the viscoplastic model exhibits a sensitivity to hydrostatic stress, and allows different behavior in tension and compression.

APA, Harvard, Vancouver, ISO, and other styles

47

Baldi, M., G. A. Dalu, and R. A. Pielke. "Vertical Velocities and Available Potential Energy Generated by Landscape Variability—Theory." Journal of Applied Meteorology and Climatology 47, no. 2 (February 1, 2008): 397–410. http://dx.doi.org/10.1175/2007jamc1539.1.

Full text

Abstract:

Abstract It is shown that landscape variability decreases the temperature in the surface layer when, through mesoscale flow, cool air intrudes over warm patches, lifting warm air and weakening the static stability of the upper part of the planetary boundary layer. This mechanism generates regions of upward vertical motion and a sizable amount of available potential energy and can make the environment of the lower troposphere more favorable to cloud formation. This process is enhanced by light ambient wind through the generation of trapped propagating waves, which penetrate into the midtropospheric levels, transporting upward the thermal perturbations and weakening the static stability around the top of the boundary layer. At moderate ambient wind speeds, the presence of surface roughness changes strengthens the wave activity, further favoring the vertical transport of the thermal perturbations. When the intensity of the ambient wind is larger than 5 m s−1, the vertical velocities induced by the surface roughness changes prevail over those induced by the diabatic flux changes. The analysis is performed using a linear theory in which the mesoscale dynamics are forced by the diurnal diabatic sensible heat flux and by the surface stress. Results are shown as a function of ambient flow intensity and of the wavelength of a sinusoidal landscape variability.

APA, Harvard, Vancouver, ISO, and other styles

48

Scherer, K., A. Noack, J. Kleimann, H. Fichtner, and K. Weis. "The interaction of multiple stellar winds in stellar clusters: potential flow." Astronomy & Astrophysics 616 (August 2018): A115. http://dx.doi.org/10.1051/0004-6361/201832696.

Full text

Abstract:

Context. While several studies have investigated large-scale cluster winds resulting from an intra-cluster interaction of multiple stellar winds, as yet they have not provided details of the bordering flows inside a given cluster. Aims. The present work explores the principal structure of the combined flow resulting from the interaction of multiple stellar winds inside stellar clusters. Methods. The theory of complex potentials is applied to analytically investigate stagnation points, boundaries between individual outflows, and the hydrodynamic structure of the asymptotic large-scale cluster wind. In a second part, these planar considerations are extended to fully three-dimensional, asymmetric configurations of wind-driving stars. Results. We find (i) that one can distinguish regions in the large-scale cluster wind that are determined by the individual stellar winds, (ii) that there are comparatively narrow outflow channels, and (iii) that the large-scale cluster wind asymptotically approaches spherical symmetry at large distances. Conclusions. The combined flow inside a stellar cluster resulting from the interaction of multiple stellar winds is highly structured.

APA, Harvard, Vancouver, ISO, and other styles

49

Silkina, Elena F., Evgeny S. Asmolov, and Olga I. Vinogradova. "Electro-osmotic flow in hydrophobic nanochannels." Physical Chemistry Chemical Physics 21, no. 41 (2019): 23036–43. http://dx.doi.org/10.1039/c9cp04259h.

Full text

Abstract:

An analytical theory of electroosmosis in hydrophobic nanochannels of large surface potential/charge density incorporates a mobility of adsorbed charges and hydrodynamic slip, and is valid both for thin and strongly overlapping diffuse layers.

APA, Harvard, Vancouver, ISO, and other styles

50

Taha, Haithem, and Amir S. Rezaei. "Viscous extension of potential-flow unsteady aerodynamics: the lift frequency response problem." Journal of Fluid Mechanics 868 (April 8, 2019): 141–75. http://dx.doi.org/10.1017/jfm.2019.159.

Full text

Abstract:

The application of the Kutta condition to unsteady flows has been controversial over the years, with increased research activities over the 1970s and 1980s. This dissatisfaction with the Kutta condition has been recently rejuvenated with the increased interest in low-Reynolds-number, high-frequency bio-inspired flight. However, there is no convincing alternative to the Kutta condition, even though it is not mathematically derived. Realizing that the lift generation and vorticity production are essentially viscous processes, we provide a viscous extension of the classical theory of unsteady aerodynamics by relaxing the Kutta condition. We introduce a trailing-edge singularity term in the pressure distribution and determine its strength by using the triple-deck viscous boundary layer theory. Based on the extended theory, we develop (for the first time) a theoretical viscous (Reynolds-number-dependent) extension of the Theodorsen lift frequency response function. It is found that viscosity induces more phase lag to the Theodorsen function particularly at high frequencies and low Reynolds numbers. The obtained theoretical results are validated against numerical laminar simulations of Navier–Stokes equations over a sinusoidally pitching NACA 0012 at low Reynolds numbers and using Reynolds-averaged Navier–Stokes equations at relatively high Reynolds numbers. The physics behind the observed viscosity-induced lag is discussed in relation to wake viscous damping, circulation development and the Kutta condition. Also, the viscous contribution to the lift is shown to significantly decrease the virtual mass, particularly at high frequencies and Reynolds numbers.

APA, Harvard, Vancouver, ISO, and other styles

Journal articles on the topic 'Potential flow theory'

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles