The following videos are not of highest quality and do not do justice to resolutions of the simulations form which I made them. If you like to use them please get in touch so then I can provide you with better quality versions. 

Potential Vorticity on DIMES Isopycnal

Time evolution of PV on neutral density surface 27.9 kg/m^3. The simulation represents 260 days. Acc flows from top of the domain to down. The region of focus is the Drake Passage to West Scotia Sea in the Southern Ocean (the land in the top-right corner is the tip of Chile; Antarctica is to left). A close look shows the upward propagating waves that generate as the mesoscale eddies interact with rough topography. The wave field is better shown below. [see Mashayek et al. Nature Comm. 2017 for more information]

Vertical Velocity in Drake Passage

This clip shows the vertical velocity in unit of m/s on the constant depth level Z=-3000m. The region is the same region as discussed above. This simulation has a horizontal resolution of ~500m and a vertical grid spacing ranging from 10 in upper ocean to ~100 in the deepest part of domain. While this is a high resolution, still not sufficiently high to get the vertical velocity accurate. Two videos down I go to higher resolution to resolve W. This attests to difficulty of measuring, quantifying and parameterizing such intermittent and heterogeneous process on regional and global scale. 

DIMES Tracer Evolution

Same simulation as above, but showing evolution of a tracer that is initiated after the real DIMES tracer. The model tracer reproduces DIMES tracer lateral dispersion reasonably well. Vertical planes show density levels (isopycnals): note shoaling towards Antarctica to the left; also note significant heaving of isopycnals as eddies pass over topography. Enhanced bottom mixing, isopycnal heaving, and tracer stirring over rough topography together lead to a net large mixing experienced by the tracer as a whole.

High Resolution Dynamics over Phoenix Ridge

This clip shows vertical velocity along a section of a 3D domain from a very high resolution simulation of ACC flow over the Phoenix Ridge in the Drake Passage. Vertical resolution is uniform 10m and horizontal resolution is ~200m. Vertical velocity is now resolved and in the realistic range. Also note the bottom trapped structures. A non-hydrostatic version of this is in the making. This slice is the left-right plane in the 3D plot of the domain shown under the Gallery tab titled Lee Wave Generation.

Dipycnal Velocity in Drake Passage

Same simulation as above, but now I am showing the cross-density (diapycnal) velocity. The simulation time is 25 days. Red indicates upwelling and blue downwelling. A time average over the whole period shows that there is net upwelling along boundaries and net downwelling in the interior. This could be a first 3D "realistic" evidence for boundary upwelling over a large domain (direct observational evidence [I think] is non-existent). Note that cross density velocity in the mixed-layer is not meaningful, so ignore the top part. 

Wave Breaking (Shear Instability)

Shear instability is a very special form of internal waves (it is formed when two counter-propagating vertically trapped internal waves get phase-locked). Nevertheless, it has proven a canonical example of small-scale mixing processes in the ocean (see Mashayek et al. GRL 2017 for evidence of its applicability to ocean mixing in general). This clip shows a sample breaking event in a 2D simulation. Red & blue represent dense and light waters. 

Breaking in 3D

In recent years we became capable of running direct numerical simulations of wave breaking in 3D at sufficiently high Reynolds numbers. This is from one such example; the field shown is dissipation of kinetic energy  (see Mashayek et al. JFM 2013 for details). Comparison with above clip shows major differences between 2D and 3D turbulence. The latter is much more intermittent and importantly does not go through an upscale cascade. 2D simulations have historically agreed better with assumptions underlying mixing parameterizations (Osborn and Cox-Osborn). The recent high Reynolds number 3D cases further violate such assumptions, implying we might be underestimating mixing from observations of dissipation of kinetic energy or of tracer variance.