Nonlinear inertial effects on the instability of a single long wave of finite amplitude at the interface of two viscous fluids

1991 ◽  
Vol 42 (5) ◽  
pp. 663-679 ◽  
Author(s):  
Henry Power ◽  
Miguel Villegas ◽  
Carlos Carmona
Keyword(s):  
Finite Amplitude ◽  
Viscous Fluids ◽  
Inertial Effects ◽  
Long Wave

Propagation of finite-amplitude long-wave disturbances in aerosols

1981 ◽  
Vol 21 (5) ◽  
pp. 602-606 ◽  
Author(s):  
A. A. Borisov ◽  
A. F. Vakhgel't ◽  
V. E. Nakoryakov
Keyword(s):  
Finite Amplitude ◽  
Wave Disturbances ◽  
Long Wave

scholarly journals Topographically forced long waves on a sheared coastal current. Part 2. Finite amplitude waves

1997 ◽  
Vol 343 ◽  
pp. 153-168 ◽  
Author(s):  
S. R. CLARKE ◽  
E. R. JOHNSON
Keyword(s):  
Wave Equation ◽  
Initial Conditions ◽  
Finite Amplitude ◽  
Coastal Current ◽  
Constant Vorticity ◽  
Long Wave ◽  
Long Time ◽  
Wave Limit ◽  
Parameter Values ◽  
Upstream Flow

This paper analyses the finite-amplitude flow of a constant-vorticity current past coastal topography in the long-wave limit. A forced finite-amplitude long-wave equation is derived to describe the evolution of the vorticity interface. An analysis of this equation shows that three distinct near-critical regimes occur. In the first the upstream flow is restricted, with overturning of the vorticity interface for sufficiently large topography. In the second quasi-steady nonlinear waves form downstream of the topography with weak upstream influence. In the third regime the upstream rotational fluid is partially blocked. Blocking and overturning are enhanced at headlands with steep rear faces and decreased at headlands with steep forward faces. For certain parameter values both overturning and partially blocked solutions are possible and the long-time evolution is critically dependent on the initial conditions. The reduction of the problem to a one-dimensional nonlinear wave equation allows solutions to be followed to much longer times and parameter space to be explored more finely than in the related pioneering contour-dynamical integrations of Stern (1991).

The distortion of short internal waves produced by a long wave, with application to ocean boundary mixing

1989 ◽  
Vol 208 ◽  
pp. 395-415 ◽  
Author(s):  
S. A. Thorpe
Keyword(s):  
Density Gradient ◽  
Internal Waves ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Finite Amplitude ◽  
Constant Density ◽  
Boundary Mixing ◽  
Short Waves ◽  
Long Wave ◽  
Boussinesq Fluid

The propagation of a train of short, small-amplitude, internal waves through a long, finite-amplitude, two-dimensional, internal wave is studied. An exact solution of the equations of motion for a Boussinesq fluid of constant density gradient is used to describe the long wave, and its distortion of the density gradient as well as its velocity field are accounted for in determining the propagation characteristics of the short waves. To illustrate the magnitude of the effects on the short waves, particular numerical solutions are found for short waves generated by an idealized flow induced by a long wave adjacent to sloping, sinusoidal topography in the ocean, and the results are compared with a laboratory experiment. The theory predicts that the long wave produces considerably distortion of the short waves, changing their amplitudes, wavenumbers and propagation directions by large factors, and in a way which is generally consistent with, but not fully tested by, the observations. It is suggested that short internal waves generated by the interaction of relatively long waves with a rough sloping topography may contribute to the mixing observed near continental slopes.

Propagation of long waves of finite amplitude at the interface of two viscous fluids

1985 ◽  
Vol 11 (4) ◽  
pp. 481-502 ◽  
Author(s):  
G. Ooms ◽  
A. Segal ◽  
S.Y. Cheung ◽  
R.V.A. Oliemans
Keyword(s):  
Finite Amplitude ◽  
Viscous Fluids ◽  
Long Waves

The initial-value problem for long waves of finite amplitude

1964 ◽  
Vol 20 (1) ◽  
pp. 161-170 ◽  
Author(s):  
Robert R. Long
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Integration ◽  
Initial Value Problem ◽  
Finite Amplitude ◽  
Long Waves ◽  
Initial Value ◽  
Partial Differential ◽  
Long Wave ◽  
Constant Slope

Derived herein is a set of partial differential equations governing the propagation of an arbitrary, long-wave disturbance of small, but finite amplitude. The equations reduce to that of Boussinesq (1872) when the assumption is made that the disturbance is propagating in one direction only. The equations are hyperbolic with characteristic curves of constant slope. The initial-value problem can be solved very readily by numerical integration along characteristics. A few examples are included.

Differential equations for long-period gravity waves on fluid of rapidly varying depth

1977 ◽  
Vol 83 (2) ◽  
pp. 289-310 ◽  
Author(s):  
James Hamilton
Keyword(s):  
Gravity Waves ◽  
Wave Equations ◽  
Velocity Potential ◽  
Taylor Series Expansion ◽  
Finite Amplitude ◽  
Necessary Condition ◽  
Exact Equation ◽  
Rapid Convergence ◽  
Long Period ◽  
Long Wave

The conventional long-wave equations for waves propagating over fluid of variable depth depend for their formal derivation on a Taylor series expansion of the velocity potential about the bottom. The expansion, however, is not possible if the depth is not an analytic function of the horizontal co-ordinates and it is a necessary condition for its rapid convergence that the depth is also slowly varying. We show that if in the case of two-dimensional motions the undisturbed fluid is first mapped conformally onto a uniform strip, before the Taylor expansion is made, the analytic condition is removed and the approximations implied in the lowest-order equations are much improved.In the limit of infinitesimal waves of very long period, consideration of the form of the error suggests that by modifying the coefficients of the reformulated equation we may find an equation exact for arbitrary depth profiles. We are thus able to calculate the reflexion coefficients for long-period waves incident on a step change in depth and a half-depth barrier. The forms of the coefficients of the exact equation are not simple; however, for these particular cases, comparison with the coefficients of the reformulated long-wave equation suggests that in most cases the latter may be adequate. This opens up the possibility of beginning to study finite amplitude and frequency effects on regions of rapidly varying depth.

scholarly journals Instability of the interface of two viscous fluids moving in a channel. Part II a. Nonlinear problem

1989 ◽  
Vol 11 (3) ◽  
pp. 52-59
Author(s):  
Tran Van Tran
Keyword(s):  
Steady State ◽  
Nonlinear Problem ◽  
Hydrodynamic Stability ◽  
Evolution Equations ◽  
Finite Amplitude ◽  
Viscous Fluids ◽  
Weakly Nonlinear ◽  
Concurrent Flow ◽  
Periodic Steady State

In this paper, the method of multiple scaling is used for obtaining the am-altitude evolution equations from the weakly nonlinear problem of hydrodynamic stability of concurrent flow of two viscous fluids in a channel It. is shown that in the case of stability the, interface may evolve to some finite amplitude with periodic steady state.

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