Sill controlled flow. Stratified fluid is accelerated from left to right beginning from rest at t=0. (Flow accelerates to right over first 1/4 tidal period T_f with maximum rightward flow at t/T_f=0.25, i.e. the tidal flow reverses at t/T_f=0.5) A thin strongly stratified surface layer overlies a weaker stratification below. At this point in time, the flow is still accelerating to the right yet upstream of the sill a packet of interfacial waves forms, steepens and propagates to the left against the accelerating tidal flow. Above the sill crest, the strongly stratified surface layer bifurcates and numerous KH billows are shed that migrate down and to the right, often pairing as they do so. These billows entrain dense fluid from below and act to create a pool of intermediate (light blue) fluid that remains approximately stagnant above the downstream flank of the sill.

Parallel scaling results. Upper panel: time to execute 1 time step (excluding initialization and IO) vs 1/n where n is the number of processors. The test problem was the rigid-lid internal wave configuration with 64 x 8193 x 513 gridpoints using a two-dimensional data decomposition. Timing results were fit to the model

t = alpha/n + beta

See movie (7MB) in your browser (slowly!) by clicking here, or download the file by right-clicking and play in a movie player such as Quicktime (recommended).

(Animation over 1 forcing period here.)

High contrast visualization of the density field in the lee of a sill. Near surface layer is strongly stratified, overlying weaker stratification below. (Incomplete animated version here.) In this run, which hasn't yet progressed very far, an oscillatory body force is applied beginning impulsively at t=0. Because the forced flow is fairly nonlinear, there is quite a bit of inertia after the first half period of forcing (to the right) and so the second half period (to the left) is only barely able to reverse the flow. This temporal and left/right bias will reduce over time but it will take several forcing periods to approach a quasi periodic, quasi symmetrical flow. From looking at the animation, I can see that an important dimensionless parameter is the fraction of a tidal cycle over which the flow is supercritical at the sill crest.