A Lagrangian solution for internal waves (original) (raw)
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Tellus, 1981
A study of non-linear internal waves is introduced with the shallow water theory, in two layers of perfect fluids. After the establishment of a general differential system, the particular case of progressive waves and standing waves is more completely studied and the development leads to a Boussinesq equation for the first-order term. A solution is found as a cnoidal wave in both cases. Laboratory experiments are carried out to test the analytical solution on a standing internal wave and show that even for highly non-linear internal waves our first-order solution describes the wave shape with an accuracy better than 5%.
First stage of growth of internal waves in stably stratified fluids
Archives for Meteorology, Geophysics, and Bioclimatology Series A, 1982
A theoretical analysis of the first stage of growth of internal waves in stably stratified fluids is given. It is shown how, during the first stage, the profiles obtained by means of the lineadzed theory are maintained by the growing waves. The linearized theory seems also to model properly the mixing layers in a stably stratified fluid subject to forcing at the boundaries. The results of this work are confirmed by the analysis of the experimental data for a particular geophysical situation studied in a preceding article.
Modelling the motion of an internal solitary wave over a bottom ridge in a stratified fluid
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Laboratory measurements are presented for the case of an internal solitary wave of depression propagating in a gravitationally-stable two layer fluid system in which the upper and lower layer are stably stratified and homogeneous respectively. The effect of the presence of a bottom ridge upon the propagation characteristics of the wave are investigated. Results confirm that that the strongest encounters with the ridge are observed when large amplitude waves and tall ridges are involved. Such strong encounters are manifested by (i) wave breaking, (ii) vortex generation in both layers and (iii) enhanced mixing in the upper layer. The data indicate that the strength of the mixing can be quantified conveniently in terms of (i) the buoyancy anomaly profiles within the layers and (ii) the thickness of the upper mixed layer. Non-dimensionalised plots are presented to show the dependence of both of these parameters upon the normalised wave amplitude and ridge height, respectively.
Doklady Physics, 2001
The pattern of attached internal waves [1] as an analogue of lee waves in the atmosphere [2] and ocean , as calculated by the source-sink method , agrees satisfactorily with observations and laboratory measurements on waves past perfectly shaped obstacles when the wake effect can be ignored. The wave field around a symmetric body dipped into a continuously stratified fluid is antisymmetric about the horizontal plane passing through the line of motion of the body center. In some flow regimes with waves interacting actively with vortices in the wake, the antisymmetric wave pattern evolves into a symmetric one at a large distance from the obstacle [6]. In a real situation, the obstacles are generally irregular in shape and, therefore, a skew in the flow can affect the field structure of radiated waves. This work is devoted to the experimental study of the internal waves generated by a vertical or inclined plate towed uniformly when not only a drag force but also a lifting force arises.
On short-crested waves: experimental and analytical investigations
European Journal of Mechanics B-fluids, 1999
Analytical and experimental investigations were conducted on short-crested wave fields generated by a sea-wall reflection of an incident plane wave. A perturbation method was used to compute analytically the solution of the basic equations up to the sixth order for capillary-gravity waves in finite depth, and up to the ninth order for gravity waves in deep water. For the experiments, we developed a new video-optical tool to measure the full three dimensional wave field η(x, y, t). A good agreement was found between theory and experiments. The spatio-temporal bi-orthogonal decomposition technique was used to exhibit the periodic and progressive properties of the short-crested wave field. © 1999 Éditions scientifiques et médicales Elsevier SAS O. Kimmoun et al.
A Numerical Calculation for Internal Waves Over Topography
Coastal Engineering Proceedings
The internal waves propagating from the deep to shallow, and the shallow to deep, areas in the two-layer fluid systems, have been numerically simulated by solving the set of nonlinear equations, based on the variational principle in consideration of both the strong nonlinearity and strong dispersion of internal waves. The incident wave in the deep area, is the BO-type downward convex internal wave, which is the numerical solution obtained for the present fundamental equations. In the cases where the interface elevation is below, or equal to, the critical level in the shallow area, the disintegration of the internal waves occurs remarkably, leading to a long wave train. The lowest elevation of the interface, increases after its gradual decrease in the shallow area, where the interface is above the critical level, while the lowest elevation of the interface, increases through the internal-wave propagation in the shallow area, where the interface elevation is below, or equal to, the cr...
Linear generation theory of 2D and 3D periodic internal waves in a viscous stratified fluid
Environmetrics, 2001
We investigated analytically and experimentally 1D and 2D periodic internal waves generated by small harmonic oscillations of a plate and of an impermeable vertical cylindrical tube in an exponentially strati_ed viscous~uid[ The linearized governing equations were solved by an integral transform method[ The exact boundary conditions on the surface of a body\ as well as the governing equations are satis_ed if\ in addition to propagating internal waves\ internal boundary currents on the emitting surface are taken into account[ On the basis of these two forms of~uid motion\ we constructed a complete linear theory of the wave generation\ without any external parameters [ We calculated wave amplitudes and evolution along the beam of the so!called {St[ Andrew|s Cross| wave shape\ namely the number of maxima in the wave amplitude cross!section[ The spatial decay of the wave was di}erent in 1D and 2D problems due to geometry[ The distance from the source\ where transition from a bi!modal beam to the uni!modal beam takes place\ is de_ned[ Small viscosity smoothes out the singularity that arises in the wave _eld along the inviscid characteristics and in the critical angles[ Experimental observations and probe measurements of a periodic wave pattern con_rmed the theoretical results for the far _eld wave structure[ The absolute values of calculated wave amplitudes di}ered from the experimental values by a factor less than 0[4[ Indirect evidence of the internal boundary currents in Schlieren photographs of the~ow pattern were presented [ Copyright Þ 1990 John Wiley + Sons\ Ltd[ KEY WORDS] strati_ed~uid^viscous~uids^internal waves^internal boundary currents^linear theoryl aboratory experiments Correspondence to] Yu[ D[ Chashechkin\ The Institute for Problems in Mechanics of the Russian Academy of Sciences\ 090 prospect Vernadskogo\ 006415 Moscow\ Russia[ $ E!mail] chakinÝipmnet[ru YU[ D[ CHASHECHKIN ET AL[
Breaking and Cascade of Internal Gravity Waves in a Continuously Stratified Fluid
Fluid mechanics and its applications, 1993
The evolution of a few large scale high frequency standing internal waves confined to a vertical plane is studied numerically. The growth of nonlinear interactions leads to a transfer of energy toward small vertical scales and lower frequencies: the result is a steep energy decrease due to wave breaking. Induced mixing is evaluated. A parametric forcing is also introduced in order to compare with laboratory experiments. Wave breaking also occurs but as opposed to the unforced case different phases are next observed: internal wave growth due to constructive forcing alternate with energy decrease.