Gravity waves in a heterogeneous incompressible fluid

Yanowitch, Michael

doi:10.1002/cpa.3160150104

Cited by 28 publications

(11 citation statements)

References 9 publications

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“…., and the higher the mode number n, the more accurate formula (67) is. Notice also the well-known fact that the wave speed decreases with the mode number for the fixed value of k. These results agree with the results by Yanowitch [20] who has proven that the greatest speed of water waves which can be attained in stratified fluid with piecewise smooth density profile is (gh) 1/2 . If, however, the parameter δ (see above) is pure imaginary, so that δ = iκ where κ is real, then the solution of Equation (62)…”

Section: The Exponential Dependence Of Density On the Stream Functionsupporting

confidence: 91%

“…Now, when all boundary conditions were addressed and satisfied, determine function f (y); it can be found from the solution of the DJL Equation (20). By substitution of the trial solution (21) into Equation (20), one finds that to the first-order approximation in a, function f (y) obeys the second-order linear ordinary differential equation (ODE):…”

Section: Waves Of Infinitesimal Amplitudementioning

confidence: 99%

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Stationary Gravity Waves with the Zero Mean Vorticity in Stratified Fluid

Clamond

Stepanyants

2011

Stud Appl Math

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A new approach to the description of stationary plane waves in ideal density stratified incompressible fluid is considered without the application of Boussinesq approximation. The approach is based on the Dubreil-Jacotin-Long equation with the additional assumption that the mean vorticity of the flow is zero. It is shown that in the linear approximation the spectrum of eigenmodes and corresponding dispersion equations can be found in closed analytical forms for many particular relationships between the fluid density and stream function. Examples are presented for waves of infinitesimal amplitude. Exact expression for the velocity of solitary wave of any amplitude is derived.

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Section: The Exponential Dependence Of Density On the Stream Functionsupporting

confidence: 91%

Section: Waves Of Infinitesimal Amplitudementioning

confidence: 99%

Stationary Gravity Waves with the Zero Mean Vorticity in Stratified Fluid

Clamond

Stepanyants

2011

Stud Appl Math

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“…The equations of set I are well known and their implications have been studied by a number of authors, notably Fjeldstadt (1933), Groen (1948)) Groen & Heyna (1958)) Yih (1960) and Yanowitch (1962). (These writers didnot make the Boussinesq approximation, but their results, quoted below, continue to apply here.)…”

Section: S a T H O R Pmentioning

confidence: 94%

“…Internal waves of tidal and shorter periods have been observed on the continental shelf (Summers & Emery 1963 mention a number of these observations; see also Lafond 1959) and mechanisms by which they might be generated through the motion of surface waves over an uneven bottom have been described by Rattray (1960), and Cox & Sandstrom (1962). There is also some experimental (Sandstrom 1908) and theoretical (Yanowitch 1960;Cherkesov 1962) work on internal waves generated by moving surface pressures, but a general description or observational investigation of such waves has not been made. We shall discuss here a mechanism for the generation of internal gravity waves, which is quite different from any of the mechanisms mentioned, and which, for a source of energy, depends on interacting wave trains at the free surface.…”

Section: Introductionmentioning

confidence: 99%

On wave interactions in a stratified fluid

Thorpe

1966

J. Fluid Mech.

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Interactions between waves in a stably stratified fluid with a free or fixed upper surface may occur at second order when the horizontal wave-numbers, ki, and frequencies, σi, of the three interacting waves satisfy the relations \[ {\bf k}_1 \pm{\bf k}_2 \pm {\bf k}_3 = 0,\quad \sigma_1 \pm \sigma_2 \pm \sigma_3 = 0. \] These relations may be satisfied in the case when two free surface waves interact with an internal wave, or in the case when all three waves are internal, provided that they do not all belong to the same mode. The theory is applied to situations which might be realized in the laboratory.

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“…In studying the behavior of the functions Xsj, we used the following properties [14] of dispersion relations for waves in a layer of continuously stratified fluid:…”

Section: ~ _;~ (A+~oo) ~A(r ~ ~')mentioning

confidence: 99%

The development of three-dimensional waves generated by perturbations of varying intensity in a flow of continuously stratified fluid

Dotsenko

Savos'kin

1984

Fluid Dyn

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An analysis is made in the linear formulation of the three-dimensional structure of unsteady waves created in a flow of continuously stratified fluid by a region of pressures which are harmonic with respect to time.The three-dimensional problem of the generation of surface waves by a moving vibrator was first considered in [1] for a fluid occupying a half-space.This study was developed further in [2][3][4][5][6][7].A study of wave fronts corresponding to a moving vibrator was made in [8] for tunbounded uniformly stratified media.The original method proposed in [8] was then used to solve more general problems of waves excited in unbounded media by generators of varying intensity (see [9, I0] and the literature cited in them).A general procedure for the asymptotic analysis of three-dimensional waves generated by moving perturbations of varying intensity is proposed in [ll, 12] for a layer of continuously stratified fluid.Unsteady plane internal waves were studied in [13].

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Gravity waves in a heterogeneous incompressible fluid

Cited by 28 publications

References 9 publications

Stationary Gravity Waves with the Zero Mean Vorticity in Stratified Fluid

Stationary Gravity Waves with the Zero Mean Vorticity in Stratified Fluid

On wave interactions in a stratified fluid

The development of three-dimensional waves generated by perturbations of varying intensity in a flow of continuously stratified fluid

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