Improved understanding of stably stratified boundary layers
Stably stratified boundary layers form when air flows over a cooler surface, such as air flowing from over the open ocean to over sea ice. They also form when the surface is losing heat, for example, nocturnal boundary layers are often stable due to radiative cooling. These boundary layers are difficult to capture in weather forecasting models due to their small scales and intermittent physics. We have been working on improving understanding of the physics of these boundary layers in both transient and steady states using high resolution direct numerical simulations. Results from these studies can be used for development of better models, and also better bias corrections schemes for both the 2-meter air temperature and 10-meter windspeed, which are commonly used in parameterizations over land and sea-ice surfaces. As an example, below two images are shown. The top image visualizes the flow structures in an unstratified boundary layer, whereas the bottom image visualizes the flow structures in a strongly stabie boundary layer. It can be seen that for the unstratified case, the flow structures occupy the entire width of the channel, and are accompanied by vigorous mixing; whereas for the strongly stable boundary layer the turbulence is confined to a spanwise strip, and mixing is supressed.
Non-dissipative methods to regularize the Navier-Stokes equations
The phenomenological view of three-dimensional turbulence is that the energy is transferred from large to small scales through the stretching and tilting of eddies, until the eddies become so small that they can no longer withstand viscous forces and are dissipated into heat. When carrying out computations of turbulence we are practically limited in the range of scales that can be computed. Typically, the smallest scales are not computed directly, and instead the role of these scales is replaced with a model. The vast majority of these models add a dissipative term to the momentum equations.
The LANS-alpha or NS-alpha model is a different approach. The governing equations can be physically interpreted as arising from a smoothing of the velocity that advects and stretches the eddies, which limits the smallest scales that can be generated. However, the origins of the model are rigorous, in that the equations are derived from first principles using Hamilton's principle through the averaging of particle trajectories.
While the equations themselves possess a number of interesting properties, the work I have done has been in applying these equations to different problems in fluid mechanics. For example, one of the key questions in ocean modelling that is relevant today concerns the role of eddies in the Arctic, and whether the heat these eddies can transfer from the ocean to the ice is contributing to the decrease in sea ice extent and the sea ice thickness. This is a difficult problem because the size of the eddies which transfer heat in the ocean decreases with increasing latitude, so fine numerical meshes are required to capture the eddies in the Arctic. It is hoped that the NS-alpha model can alleviate this constraint as it has been shown to produce strong eddies at coarse resolution in several studies. In particular, the NS-alpha model equations have been shown to allow baroclinic instability to occur at a lower wave number than the Navier-Stokes equations, without requiring additional energy to be input to the system (unlike viscosity based approaches). To capture this process in realistic simulations, specification of the model parameter, alpha, which represents a smoothing scale, is critical.
For example, in an idealized model of the Antarctic Circumpolar Current, when the LANS-alpha model is not included, no eddies are generated. With the model included, some eddies are generated as the flow goes over a ridge at the bottom of the domain (this was done in Peterson et al., JCP, 2008) using the POP ocean model. I introduced an alternative definition of alpha that depends on the flow velocity and density. With this defintion the eddy kinetic energy is much closer to that from a higher resolution simulation.