Particle dispersion and mixing induced by breaking internal gravity waves

The purpose of this paper is to analyze diapycnal mixing induced by the bre aking of an internal gravity wave - the primary wave - either standing or p ropagating. To achieve this aim we apply two different methods. The first m ethod consists of a direct estimate of vertical eddy diffusion from particl e dispersion while the second method relies upon potential energy budgets [ Winters, K.B., Lombard, P.N., Riley, J.J., D'Asaro, E.A., 1995. J. Fluid Me ch. 289, 115-128; Winters, K.B., D'Asaro, E.A., 1996. J. Fluid Mech. 317, 1 79-193]. The primary wave we consider is of small amplitude and is statical ly stable, a case for which the breaking process involves two-dimensional i nstabilities. The dynamics of the waves have been previously analyzed by me ans of two-dimensional direct numerical simulations [Bouruet-Aubertot, P., Sommeria, J., Staquet, C., 1995. J. Fluid Mech. 285, 265-301; Bouruet-Auber tot, P., Sommeria, J., Staquet, C., 1996. Dyn. Atmos. Oceans 29, 41-63; Kou della, C., Staquet, C., 1998. In: Davis, P. (Ed.), Proceedings of the IMA C onference on Mixing and Dispersion on Stably-stratified Flows, Dundee, Sept ember 1996. IMA Publication]. High resolution three-dimensional calculation s of the same wave are also reported here [Koudella, C., 1999]. A local estimate of mixing is first inferred from the time evolution of set s of particles released in the flow during the breaking regime. We show tha t, after an early evolution dominated by shear effects, a diffusion law is reached and the dispersion coefficient is fairly independent of the initial seeding location of the particles in the flow. The eddy diffusion coefficient, K,is then estimated from the diapycnal diff usive flux. A good agreement with the value inferred from particle dispersi on is obtained. This finding is of particular interest regarding the interp retation of in situ estimates of K inferred either from tracer dispersion o r from microstructure measurements. Computation of the Cox number equal to the ratio of eddy diffusivity to molecular diffusivity, shows that the Cox number varies within the interval [9, 262], which corresponds to the range of vertical eddy diffusivity measured in the interior of the ocean. The Cox number is found to depend on the turbulent Froude number squared. We show eventually that mixing results in a weak distortion of the initial density profile and we relate this result to observations made at small sca le in the ocean. Comparisons between the analysis of the two-dimensional and high resolution (256(3)) three-dimensional direct numerical simulations of the primary wav e were also conducted. We show that the energetics and the amount of mixing are very close when the primary wave is of small amplitude. This results f rom the fact that, for a statically stable wave, the dynamics of the initia lly two-dimensional primary wave remains mostly two-dimensional even after the onset of wavebreaking. (C) 2001 Elsevier Science B.V. All rights reserv ed.