Stratified Turbulence

The Ekman layer is the layer in a fluid where there is a force balance between pressure gradient force, Coriolis force and turbulent drag. In the atmosphere, the linear solution generally overstates the magnitude of the horizontal wind field because it does not account for the velocity shear in the surface layer. Small-scale processes in atmospheric boundary layer flows, which influence the vertical and horizontal exchange of quantities between the surface and the atmosphere as well as the mixing within the atmosphere, show great sensitivity to the turbulence model formulation. The representation of these processes using a turbulence model closure is non-trivial owing to the fact that there are many non-linear processes.

In the ocean, the Ekman layer, with its distinguishing feature the Ekman spiral, is rarely observed. The Ekman layer near the surface of the ocean extends only about 10 – 20 meters deep, and instrumentation sensitive enough to observe a velocity profile in such a shallow depth has only been available since around 1980. Also, wind waves modify the flow near the surface, and make observations close to the surface rather difficult. One of the greatest challenges in the simulation of ocean and, in turn, the global climate is the diapycnal mixing of the interior ocean. Unlike the atmosphere whose structure is determined predominantly by radiative transfer, the ocean is opaque to radiation below ~30m and therefore its interior structure is determined by the balance between the small scale mixing and large scale circulation. This way, small scale mixing is critical to the structure and intensity of the thermohaline circulation at global and millennial scales. To account for the observed oceanic thermohaline structure, the overall global diapycnal mixing coefficient is estimated to be of 10^-4m²/s, which is 1000 times larger than the molecular diffusivity. The major cause of this mixing is believed to be caused by turbulent mixing associated with internal wave breaking at the scales of meters/hours. Furthermore, in situ observations suggest vastly different mixing coefficient in the ocean, ranging from 10 times smaller in the oceanic thermocline to over 10 times larger in “hot spots” near abyssal ridges and oceanic boundaries. This suggests multiple and complex mechanisms for the mixing in different regions. The vast disparity of scales and the variety of mechanisms of the mixing poses a great challenge to multi-scale mathematical modeling.