Spike-like solitary waves in incompressible boundary layers driven by a travelling wave

2016 ◽  
Vol 26 (6) ◽  
pp. 063104 ◽  
Author(s):  
Peihua Feng ◽  
Jiazhong Zhang ◽  
Wei Wang
Keyword(s):  
Boundary Layers ◽  
Solitary Waves ◽  
Travelling Wave ◽  
Incompressible Boundary

Recent Developments in Calculation Methods for Turbulent Boundary Layers With Pressure Gradients and Heat Transfer

1966 ◽  
Vol 33 (2) ◽  
pp. 429-437 ◽  
Author(s):  
J. C. Rotta
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Temperature Distribution ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Calculation Methods ◽  
Recent Developments ◽  
Incompressible Boundary

A review is given of the recent development in turbulent boundary layers. At first, for the case of incompressible flow, the variation of the shape of velocity profile with the pressure gradient is discussed; also the temperature distribution and heat transfer in incompressible boundary layers are treated. Finally, problems of the turbulent boundary layer in compressible flow are considered.

scholarly journals NUMERICAL MODELING OF A TURBULENT BOTTOM BOUNDARY LAYER UNDER SOLITARY WAVES ON A SMOOTH SURFACE

2018 ◽  
pp. 26
Author(s):  
Ahmad Sana ◽  
Hitoshi Tanaka
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Solitary Waves ◽  
Bottom Boundary Layer ◽  
Stream Velocity ◽  
Bottom Boundary ◽  
Sediment Movement ◽  
Bottom Boundary Layers ◽  
Turbulent Models

A number of studies on bottom boundary layers under sinusoidal and cnoidal waves were carried out in the past owing to the role of bottom shear stress on coastal sediment movement. In recent years, the bottom boundary layers under long waves have attracted considerable attention due to the occurrence of huge tsunamis and corresponding sediment movement. In the present study two-equation turbulent models proposed by Menter(1994) have been applied to a bottom boundary layer under solitary waves. A comparison has been made for cross-stream velocity profile and other turbulence properties in x-direction.

Correlated incompressible and compressible boundary layers

1949 ◽  
Vol 200 (1060) ◽  
pp. 84-100 ◽  
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Boundary Layers ◽  
Absolute Temperature ◽  
Stream Velocity ◽  
Main Stream ◽  
Boundary Layer Equations ◽  
Compressible Boundary Layers ◽  
Incompressible Boundary ◽  
Similar Solutions

The boundary-layer equations for a compressible fluid are transformed into those for an incompressible fluid, assuming that the boundary is thermally insulating, that the viscosity is proportional to the absolute temperature, and that the Prandtl number is unity. Various results in the theory of incompressible boundary layers are then taken over into the compressible theory. In particular, the existence of ‘similar’ solutions is proved, and Howarth’s method for retarded flows is applied to determine the point of separation for a uniformly retarded main stream velocity. A comparison with an exact solution is used to show that this method gives a closer approximation than does Pohlhausen’s.

Modular Korteweg - de Vries equation: Riemann, cnoidal and solitary waves

2020 ◽  
Author(s):  
Efim Pelinovsky ◽  
Anna Kokorina ◽  
Alexey Slunyaev ◽  
Elena Tobisch
Keyword(s):  
Solitary Waves ◽  
Kdv Equation ◽  
Travelling Waves ◽  
Elliptic Functions ◽  
Travelling Wave ◽  
Scattering Transform ◽  
De Vries ◽  
Dispersionless Limit ◽  
Pseudo Spectral Method ◽  
Appl Math

<p>The review paper by Oleg Rudenko [1] suggests several examples of elastic systems with so-called modular nonlinearities. In this study we consider the modular Korteweg - de Vries (KdV) equation in the form u_t + 6 u u_x + u_{xxx} = 0. This equation is not integrable by means of the Inverse Scattering Transform in the general case, but sign-defined functions which never change the sign satisfy the integrable KdV equation, and hence possess an exact solution. Firstly, we consider the dispersionless limit of the modular KdV equation and analyze the evolution of a simple nonlinear wave (Riemann wave) and its Fourier transform including the asymptotics when the wave tends to break [2]. Then, we study the structure of travelling waves. If the waves propagate on a pedestal and do not cross the zero level u = 0, they coincide with the well-known travelling wave solutions of the classic KdV equation in the form of cnoidal and solitary waves. If the pedestal is zero, the structure of sign-varying travelling waves is expressed through Jacobi elliptic functions. The interaction of solitary waves of different polarities is studied numerically using an implicit pseudo-spectral method. The simulation has revealed the inelastic character of the collision; in the course of the interaction the solitons can alter their amplitudes (the small soliton decreases and the large one grows) and emit small-amplitude waves. The inelastic effects are most pronounced when the solitons’ amplitudes are close. When their amplitudes differ significantly, the maximum wave height which is attained during the absorb-emit interaction tends to the sum of the heights of the solitons with the polarity inherited from the large soliton, as predicted in the frameworks of different long-wave integrable models in [3, 4]. As a result of the collision the solitons may experience non-classic phase shifts as they both jump back.</p><p>[1] O.V. Rudenko. Physics – Uspekhi, Vol. 56(7), 683-690 (2013).</p><p>[2] E. Tobisch, and E. Pelinovsky. Appl. Math. Lett., Vol. 97, 1-5 (2019).</p><p>[3] A.V. Slunyaev, and E.N. Pelinovsky. Phys. Rev. Lett., Vol. 117, 214501 (2016).</p><p>[4] A. Slunyaev. Stud. Appl. Math., Vol. 142, 385-413 (2019).</p>

scholarly journals Asymmetric gravity–capillary solitary waves on deep water

2014 ◽  
Vol 759 ◽  
Author(s):  
Z. Wang ◽  
J.-M. Vanden-Broeck ◽  
P. A. Milewski
Keyword(s):  
Wave Propagation ◽  
Solitary Waves ◽  
Travelling Wave ◽  
Propagation Direction ◽  
Travelling Wave Solutions ◽  
Two Dimensional ◽  
Bifurcation Curve ◽  
Wave Propagation Direction ◽  
Wave Solutions ◽  
Deep Fluid

AbstractWe present new families of gravity–capillary solitary waves propagating on the surface of a two-dimensional deep fluid. These spatially localised travelling-wave solutions are non-symmetric in the wave propagation direction. Our computation reveals that these waves appear from a spontaneous symmetry-breaking bifurcation, and connect two branches of multi-packet symmetric solitary waves. The speed–energy bifurcation curve of asymmetric solitary waves features a zigzag behaviour with one or more turning points.

scholarly journals Entrainment of short-wavelength free-stream vortical disturbances in compressible and incompressible boundary layers

2016 ◽  
Vol 797 ◽  
pp. 683-728 ◽  
Author(s):  
Xuesong Wu ◽  
Ming Dong
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Free Stream ◽  
Base Flow ◽  
Bypass Transition ◽  
Leading Order ◽  
Compressible Boundary Layers ◽  
Characteristic Wavelength ◽  
Incompressible Boundary ◽  
Edge Layer

The fundamental difference between continuous modes of the Orr–Sommerfeld/Squire equations and the entrainment of free-stream vortical disturbances (FSVD) into the boundary layer has been investigated in a recent paper (Dong & Wu, J. Fluid Mech., vol. 732, 2013, pp. 616–659). It was shown there that the non-parallel-flow effect plays a leading-order role in the entrainment, and neglecting it at the outset, as is done in the continuous-mode formulation, leads to non-physical features of ‘Fourier entanglement’ and abnormal anisotropy. The analysis, which was for incompressible boundary layers and for FSVD with a characteristic wavelength of the order of the local boundary-layer thickness, is extended in this paper to compressible boundary layers and FSVD with even shorter wavelengths, which are comparable with the width of the so-called edge layer. Non-parallelism remains a leading-order effect in the present scaling, which turns out to be more general in that the equations and solutions in the previous paper are recovered in the appropriate limit. Appropriate asymptotic solutions in the main and edge layers are obtained to characterize the entrainment. It is found that when the Prandtl number $\mathit{Pr}<1$, free-stream vortical disturbances of relatively low frequency generate very strong temperature fluctuations within the edge layer, leading to formation of thermal streaks. A composite solution, uniformly valid across the entire boundary layer, is constructed, and it can be used in receptivity studies and as inlet conditions for direct numerical simulations of bypass transition. For compressible boundary layers, continuous spectra of the disturbance equations linearized about a parallel base flow exhibit entanglement between vortical and entropy modes, namely, a vortical mode necessarily induces an entropy disturbance in the free stream and vice versa, and this amounts to a further non-physical behaviour. High Reynolds number asymptotic analysis yields the relations between the amplitudes of entangled modes.

Simplified Analysis of Boundary-Layer Oscillations

1960 ◽  
Vol 4 (03) ◽  
pp. 37-54
Author(s):  
Robert Betchov
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Nonlinear Effects ◽  
Adverse Pressure Gradient ◽  
Neutral Curves ◽  
Elastic Wall ◽  
Unstable Boundary Layer ◽  
Incompressible Boundary ◽  
Negative Damping ◽  
The Stability

The stability of an incompressible boundary layer is analyzed in terms of three basic processes. These are (a) the oscillations of a boundary layer when friction is disregarded, (b) the effects of friction at the wall, and (c) the effects of friction at the critical layer. These processes are separately discussed and evaluated. Simple models are presented. A general equation leads to the eigenvalues. The neutral curves corresponding to five typical cases are determined—parabolic and Blasius boundary layers, boundary layers with suction and with adverse pressure gradient, two-dimensional Poiseuille flow. The unstable boundary layer is discussed briefly. The nonlinear effects of the oscillation on the velocity profile are evaluated. Finally, the case of a boundary layer along an elastic wall is considered, and it is found that the wall may have a significant effect on the layer. In particular, a wall with negative damping could completely stabilize the boundary layer.

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