Nicolas Grisouard

Numerical simulation of a two-dimensional internal wave attractor

Internal (gravity) wave attractors may form in closed containers with boundaries non-parallel and non-normal to the gravity vector. Such attractors have been studied from a theoretical point of view, in laboratory experiments and using linear numerical computations. In the present paper two-dimensional numerical simulations of an internal wave attractor are reported, based upon the nonlinear and non-hydrostatic MIT-gcm numerical code. We first reproduce the laboratory experiment of a wave attractor performed by Hazewinkel et al. (J. Fluid Mech. Vol. 598, 2008 p. 373) and obtain very good agreement with the experimental data. We next propose simple ideas to model the thickness of the attractor. The model predicts that the thickness should scale as the 1/3 power of the non-dimensional parameter measuring the ratio of viscous to buoyancy effects. When the attractor is strongly focusing, the thickness should also scale as the 1/3 power of the spatial coordinate along the attractor. Analysis of the numerical data for two different attractors yields values of the exponent close to 1/3, within 30 %. Finally, we study nonlinear effects induced by the attractor.

The Impact of Finite-Amplitude Bottom Topography on Internal Wave Generation in the Southern Ocean

Direct observations in the Southern Ocean report enhanced internal wave activity and turbulence in akilometer-thicklayeraboveroughbottomtopographycollocatedwiththedeep-reachingfrontsoftheAntarctic Circumpolar Current. Linear theory, corrected for finite-amplitude topography based on idealized, twodimensional numerical simulations, has been recently used to estimate the global distribution of internal wave generation by oceanic currents and eddies. The global estimate shows that the topographic wave generation is a significant sink of energy for geostrophic flows and a source of energy for turbulent mixing in the deep ocean. However, comparison with recent observations from the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean shows that the linear theory predictions and idealized two-dimensional simulations grossly overestimate the observed levelsof turbulent energy dissipation. Thisstudypresentstwo- and three-dimensional, realistic topography simulations of internal lee-wave generation from a steady flow interacting with topography with parameters typical of Drake Passage. The results demonstrate that internal wave generation at threedimensional, finite bottom topography is reduced compared to the two-dimensional case. The reduction is primarilyassociatedwithfinite-amplitudebottomtopographyeffectsthatsuppressverticalmotionsandthusreduce the amplitude of the internal waves radiated from topography. The implication of these results for the global leewave generation is discussed.

Energy Exchanges between Density Fronts and Near-Inertial Waves Reflecting off the Ocean Surface

AbstractInertial waves propagating upward in a geostrophically balanced front experience critical reflections against the ocean surface. Such reflections naturally create oscillations with small vertical scales, and viscous friction becomes a dominant process. Here, friction modifies the polarization relations of internal waves and allows energy from the balanced front to be exchanged with the ageostrophic motions and eventually dissipated. In addition, while in the well-known inviscid case internal waves propagate on only two characteristics, this study demonstrates using an analytical model that strong viscous effects introduce additional oscillatory modes that can exchange energy with the front. Moreover, during a linear, near-critical reflection, the superposition of several of these oscillations induces an even stronger energy exchange with the front. When the Richardson number based on the frontal thermal wind shear is O(1), the rate of energy exchange peaks at wave frequencies that are near inertia...