Numerical study of internal wave–wave interactions in a stratified fluid

Abstract

A finite volume method is used to study the generation, propagation and interaction of internal waves in a linearly stratified fluid. The internal waves were generated using single and multiple momentum sources. The full unsteady equations of motion were solved using a SIMPLE scheme on a non-staggered grid. An open boundary, based on the Sommerfield radiation condition, allowed waves to propagate through the computational boundaries with minimum reflection and distortion. For the case of a single momentum source, the effects of viscosity and nonlinearity on the generation and propagation of internal waves were investigated.Internal wave–wave interactions between two wave rays were studied using two momentum sources. The rays generated travelled out from the sources and intersected in interaction regions where nonlinear interactions caused the waves to break. When two rays had identical properties but opposite horizontal phase velocities (symmetric interaction), the interactions were not described by a triad interaction mechanism. Instead, energy was transferred to smaller wavelengths and, a few periods later, to standing evanescent modes in multiples of the primary frequency (greater than the ambient buoyancy frequencies) in the interaction region. The accumulation of the energy caused by these trapped modes within the interaction region resulted in the overturning of the density field. When the two rays had different properties (apart from the multiples of the forcing frequencies) the divisions of the forcing frequencies as well as the combination of the different frequencies were observed within the interaction region.The model was validated by comparing the results with those from experimental studies. Further, the energy balance was conserved and the dissipation of energy was shown to be related to the degree of nonlinear interaction.

Intrinsic Nonlinearity and Spectral Structure of Internal Tides at an Idealized Mid-Atlantic Bight Shelf Break

“…A study by Korobov and Lamb (2008) examined the generation of subinertial, trapped waves using twodimensional numerical simulations and attributed the phenomenon to nonlinear nonresonant interaction of internal waves. Their findings echo observations of standing evanescent waves at frequencies greater than N in the intersections of two internal-wave beams in both laboratory (Teoh et al 1997) and numerical (Javam et al 1999(Javam et al , 2000 settings. Here, the transfer of internal-wave energy from the primary frequency to other (sub and super) harmonics is quantified for the chosen shelfbreak environment.…”

Internal gravity wave beams as invariant solutions of Boussinesq equations in geophysical fluid dynamics

“…The process and interaction of internal wave beams has been studied both experimentally (see e.g., Dalziel et al [6] or Teoh et al [32]), numerically (Javam et al [18]) and analytically. In particular, reflection and colliding internal wave beams have been studied in detail using the small-amplitude expansions and the consecutive perturbation approach by Tabaei et al [30,31] in case if the Earth's rotation is ignored.…”

Quantitative laboratory observations of internal wave reflection on ascending slopes

“…Besides, fully nonlinear numerical simulations have also been performed to examine the behavior of largeamplitude internal gravity waves impinging on a slope. 8,9,18,19,24 Here we present the results of laboratory experiments in which a beam of internal waves is reflected on an oblique slope. Experiments were carried out in the 13-m-diam Coriolis platform, in Grenoble, filled with salted water.…”