This project seeks to understand the fundamental dynamics of the turbulent motions commonly observed in atmospheric and oceanic flow, or more precisely in geophysical flows over a broad range of periodicities induced by stratification and rotation. The scales of motion found in fluid flow, identified by the amount of energy in fluid motions in each spatial scale, are strongly determined by the kinematic quantities which are conserved following the motion. This project uses computationally intensive integrations of Direct Numerical Simulation (DNS) models to elucidate the fundamental dynamics which determine the power spectrum of geophysical flows and the transfer of energy between scales.
A first-principles theory of the spectral distribution of energy in turbulent fluids has been a grand challenge in fluid dynamics since the inception of the topic. Progress towards such a theory could be transformative for the development of atmospheric and oceanic models, particularly for the development of closure schemes and turbulence parameterizations used in these models. In addition, the work will have a strong educational component, through the education of a graduate student and the mentoring of two postdoctoral researchers. In addition, a workshop is planned for the summer of 2012 on geophysical turbulence. Outreach will be conducted through the Cooperative program for Operational Meteorology, Education, and Training (COMET, at the National Center for Atmospheric Research), through the development of "learning objects" on turbulent flows, to be posted on the COMET website in English, French, and Spanish.
Solar heating, tides and wind stresses are global-scale energy inputs in the atmospheric and oceanic systems. These global flows act in a coherent, though complex, fashion all the way from the planetary scale to the dissipation scale, of the order of the mm. However, on this vast range of scales, different phenomena interact, like inertia-gravity waves, due to a combination of rotation and stratification, and nonlinear structures such as eddies, zonal jets or fronts. Many features of these flows remain obscure, due to the multitude of phenomena that can play and interact in a multi-scale fashion. One common approach is to tackle the problem in its entirety and construct a succession of models with increasing degrees of complexity. Conversely, one can take the simplest problem with what may be the most essential ingredients and examine the dynamics of such flows from a fundamental point of view, an approach taken in this proposal. One of the inherent difficulties is the fact that such flows are represented by four independent dimensionless parameters (the Reynolds, Froude, Rossby and Prandtl numbers), and thus many different dynamical regimes can arise a priori when these parameters change from one flow to another. If waves are simple in principle, think in terms of ripples over the surface of water, turbulent flows on the other hand are intricate, as for example the atmosphere, a fact that renders the prediction of weather difficult as some may have noticed. Turbulence in the presence of such waves proves to be richer and more intricate than for the homogeneous isotropic, simpler, case that was studied until recently. Three main problems were tackled by the team within the boundaries of the present proposal. They can be illustrated with concepts using phenomenology and dimensional analysis, and with results stemming from recent high-resolution high-accuracy direct numerical simulations using the appropriate (Navier-Stokes or Boussinesq) equations and running on national centers (DOE, NCAR, NSF). One world record (the largest run to date for rotating stratified turbulence), was accomplished by the team, if for a short time. One difficulty resides in the fact that rotation and gravity impose a special (say, vertical) direction and thus the flow does not behave in the same way in the horizontal and in the vertical: it is anisotropic. For example, helicity (velocity-vorticity correlations which measure how much helical motions are present on average in geophysical flows) can be generated in rotating stratified turbulence; this is significant since helicity can lead to the creation of large-scale magnetic fields which are observed in the cosmos. Helicity has also been used as an indicator of hurricane activity, and it develops at river confluences, inducing mixing and erosion of river banks. Furthermore, turbulence in the presence of stratification has been shown to display strong intermittency: events with large velocities have a measurably larger probability to occur than for a normal case such as for the homogeneous isotopic case. This takes place because of a balance between nonlinearities and waves. These localized patches of turbulence lead to enhanced mixing in the atmosphere and the ocean, and such a bursty behavior has also been observed in the planetary boundary layer and in the stratosphere. Finally, rotating stratified wave turbulence can produce energy for the large scales, reinforcing large weather patterns, and at the same time it can also send energy to the small scales where it is dissipated (otherwise, the system would explode). During the timeframe of this proposal, the team was efficient in building outreach tools through the mentoring of several students and post-doctoral fellows (five altogether), including minorities. It produced papers and reported the results in national and international venues. The team developed a numerical code and applications for data analysis that are at the disposal of the community, as well as a large data basis on such flows also available for the community, and it also built international collaborations (Argentina, France, Italy, Japan). Both the code and the data sets are being either used or requested by several teams in the U.S. (Georgia, Michigan, Utah) and in Europe.
