Wavebreaking of inertia-gravity waves revisited

We have been examining the dynamics of breaking internal waves as a function of primary wave amplitude and frequency by means of 3D high-resolution numerical simulations, with an emphasis on the structure of the resulting turbulence and mixing.
Specifically, we would like to:

(i) describe the structure of the turbulence resulting from wavebreaking as a function of primary wave frequency and amplitude and to assess the applicability of the sheet-and-layer model that has proven useful in describing the turbulent stage of high-frequency (nonrotating) internal wave breaking (Bouruet-Aubertot et al., 2004) ,

(ii) quantify the resulting mixing efficiency as a function of primary wave frequency and amplitude, using the general formulation of Winters et al., (1995). The instability mechanism varies with wave frequency and amplitude (e.g. Lelong and Dunkerton, 1998ab) and it is anticipated that the mixing created by the wavebreaking will depend on the characteristics of the primary wave.

Below are a few examples of the different regimes encountered. In all cases illustrated below, the initial condition consists of a single, monochromatic wave propagating in an unsheared, linearly stratified fluid. The coordinate system is chosen such that the wave propagates in the x-z plane. Wave amplitudes have been normalized with the convective instability threshold. The wave is seeded with white noise and breaks. All simulations have been performed with a reduced ratio of buoyancy to Coriolis frequency (N/f = 10) while preserving dynamical similarity with the more realistic regime of N/f=100. Dynamical similarity between the numerical simulations and more realistic geophysical cases is maintained by decreasing the horizontal scales by a factor of ten. Vertical scales are unaffected. Three different-frequency primary wave breakdowns are contrasted below:

1. High-frequency wave (omega = 1.8f)

We compare the evolution of two high-frequency inertia-gravity wave instabilities, with different amplitudes.

(a) Low-amplitude (stable to shear and convective instability), a=0.7

At t=0, there is no variation in the y-z plane.

After slightly more than two inertial periods, the wave begins to break. Vertical and horizontal scales of instability are quite small compared to the scales of the primary wave. Breakdown is visible along all positions of the wave phase.

After 6 inertial periods, the primary wave structure has been destroyed. Overturning continues on small vertical scales.

(b) High-amplitude (unstable to both shear and convective instability), a=1.5

2. Intermediate-frequency wave (omega = 1.3f) 3. Low-frequency (near-inertial) wave (omega = 1.1f)