scholarly journals Generation of internal waves in a two-layered stratified system with a free surface by coupled mass sources

2022 ◽  
Vol 243 ◽  
pp. 110234
Author(s):  
Dongyi Yan ◽  
Dongming Liu ◽  
Jijian Lian
Keyword(s):  
Free Surface ◽  
Internal Waves ◽  
Mass Sources

scholarly journals Surface and internal waves in a liquid of variable depth

1969 ◽  
Vol 1 (1) ◽  
pp. 29-46 ◽  
Author(s):  
D. G. Hurley ◽  
J. Imberger
Keyword(s):  
Free Surface ◽  
Gravity Wave ◽  
Internal Waves ◽  
Infinite Number ◽  
Variable Depth ◽  
Constant Depth ◽  
Stratified Liquid

Consider a stably stratified liquid, whose density varies exponentially with the vertical co-ordinate, that is bounded above by a free surface and below by a bed whose height depends on only one of the horizontal co-ordinates. Suppose that a gravity wave, that may be either a surface or an internal one, is travelling in a direction normal to the lines of constant depth. It is shown that if the frequency is below a certain value an infinite number of waves, all of the same frequency but having differing wave lengths, are generated and expressions for their amplitude are given in terms of the changes in depth which are assumed to be small.

scholarly journals Internal Waves at an Interface between Two Layers of Differing Stability

2009 ◽  
Vol 66 (6) ◽  
pp. 1845-1855 ◽  
Author(s):  
John McHugh
Keyword(s):  
Free Surface ◽  
Internal Waves ◽  
Density Profile ◽  
Wave Speed ◽  
Wave Amplitude ◽  
Buoyancy Frequency ◽  
Higher Harmonics ◽  
Free Surface Waves ◽  
Interfacial Boundary ◽  
Upper Boundary

Abstract Internal waves in a two-layer fluid are considered. The layers have different values of the buoyancy frequency, assumed to be constant in each layer. The density profile is chosen to be continuous across the interface and the flow is Boussinesq. The solution is an expansion in the wave amplitude, similar to a Stokes expansion for free surface waves. The results show that the nonlinear terms in the interfacial boundary conditions require higher harmonics and result in nonlinear wave steepening at the interface. The first few harmonics are scattered by the interface, whereas the higher harmonics are evanescent in the vertical. The second-order correction to the wave speed is negative, similar to previous results with a rigid upper boundary.

Internal waves in a circular channel

1976 ◽  
Vol 74 (1) ◽  
pp. 183-192 ◽  
Author(s):  
W. H. Yang ◽  
Chia-Shun Yih
Keyword(s):  
Free Surface ◽  
Internal Wave ◽  
Internal Waves ◽  
Flow Patterns ◽  
Circular Channel ◽  
Fluid Layers ◽  
Wave Modes

The frequencies of the first four sloshing internal wave modes in two superposed fluid layers contained in a circular channel are calculated for two positions of the free surface and for various ratios of the depths of the two layers. Flow patterns are given for the first four sloshing modes for the case in which the fluids occupy a semicircular space and the depth of the upper layer is one-quarter of the radius.It is hoped that the results obtained will provide a guide for estimating the frequencies of sloshing internal wave modes in long lakes.

scholarly journals Laboratory experiments and simulations for solitary internal waves with trapped cores

2014 ◽  
Vol 757 ◽  
pp. 354-380 ◽  
Author(s):  
Paolo Luzzatto-Fegiz ◽  
Karl R. Helfrich
Keyword(s):  
Free Surface ◽  
Numerical Simulations ◽  
Internal Waves ◽  
Number Fields ◽  
Rate Of Change ◽  
Shear Instability ◽  
Homogeneous Layer ◽  
Uniform Density ◽  
The Core ◽  
Solitary Internal Waves

AbstractWe perform simultaneous coplanar measurements of velocity and density in solitary internal waves with trapped cores, as well as viscous numerical simulations. Our set-up comprises a thin stratified layer (approximately 15 % of the overall fluid depth) overlaying a deep homogeneous layer. We consider waves propagating near a free surface, as well as near a rigid no-slip lid. In the free-surface case, all trapped-core waves exhibit a strong shear instability. We propose that Marangoni effects are responsible for this instability, and use our velocity measurements to perform quantitative calculations supporting this hypothesis. These surface-tension effects appear to be difficult to avoid at the experimental scale. By contrast, our experiments with a no-slip lid yield robust waves with large cores. In order to consider larger-amplitude waves, we complement our experiments with viscous numerical simulations, employing a longer virtual tank. Where overlap exists, our experiments and simulations are in good agreement. In order to provide a robust definition of the trapped core, we propose bounding it as a Lagrangian coherent structure (instead of using a closed streamline, as has been done traditionally). This construction is less sensitive to small errors in the velocity field, and to small three-dimensional effects. In order to retain only flows near equilibrium, we introduce a steadiness criterion, based on the rate of change of the density in the core. We use this criterion to successfully select within our experiments and simulations a family of quasi-steady robust flows that exhibit good collapse in their properties. The core circulation is small (at most, around 10 % of the baroclinic wave circulation). The core density is essentially uniform; the standard deviation of the density, in the core region, is less than 4 % of the full density range. We also calculate the circulation, kinetic energy and available potential energy of these waves. We find that these results are consistent with predictions from Dubreil-Jacotin–Long theory for waves with a uniform-density irrotational core, except for an offset, which we suggest is associated with viscous effects. Finally, by computing Richardson-number fields, and performing a temporal stability analysis based on the Taylor–Goldstein equation, we show that our results are consistent with empirical stability criteria in the literature.

The limiting form of internal waves

1984 ◽  
Vol 394 (1807) ◽  
pp. 329-344 ◽  
Keyword(s):  
Free Surface ◽  
Internal Wave ◽  
Internal Waves ◽  
Solitary Waves ◽  
The Other ◽  
Stokes Wave ◽  
Internal Solitary Waves ◽  
Two Dimensional ◽  
Extreme Form ◽  
Eddy Formation

The bifurcation of two-dimensional internal solitary waves in a perfect density stratified fluid between horizontal walls under gravity is studied near to a point of incipient eddy formation. It is shown that eddies do not attach to the walls. Moreover, along the bifurcating branch there is always a flow with a singular cusped streamline before the formation of eddies. This flow with the cusped streamline is an example of what we call an internal wave of limiting form, by analogy with the Stokes wave of extreme form in the free surface problem. Two examples are given where the primary density stratification ensures the existence of a limiting wave of depression in one case, and of elevation in the other.

scholarly journals An analytical and numerical study of a vertically discretized multi-paddle wavemaker for generating free surface and internal waves

2021 ◽  
Vol 165 ◽  
pp. 103840
Author(s):  
Yeulwoo Kim ◽  
Sangyoung Son ◽  
Taehwa Jung ◽  
Timu Gallien
Keyword(s):  
Free Surface ◽  
Internal Waves ◽  
Numerical Study
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