Atmospheric and oceanic turbulence below the deformation scale

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Turbulence has been identified by some of the foremost scientists of all time as the most important outstanding question of classical physics. Over the last 50 years the physicists have largely handed it over to applied mathematics. The prestigious Isaac Newton Institute for the Mathematical Sciences in Cambridge thinks it necessary to hold a programme on turbulence once a decade, approximately. At the last such meeting in 2008 it was concluded by most participants that the most progress since the previous meeting in 1999 had occurred in the field of stratified turbulence. Clearly, meteorology and oceanography are in a position to benefit from this progress and that is the aim of this application. The applicant has been an enthusiastic participant in this work for the last two decades. The requested funds are to continue the study of atmospheric and oceanic fluid turbulence employing high-resolution numerical simulations, perturbative analytical techniques, statistical closure theories and dimensional analysis. Specifically, the influence of aspects of the atmospheric and oceanic setting on classical turbulence statistics will be examined. For example, the nonlinear interactions between the various wave motions and the vortices, known to be ubiquitous in these flows, will be a primary focus as well as the small-scale breakdown of the simplifying balance assumptions employed at larger scales. Of crucial importance to environmental modellers is how such flows mix various quantities whose distributions are of present concern to society. In addition, wind energy generation requires statistical forecast skill on a time scale of hours and length scales of 10's of kilometers, where these dynamics are prevalent. Given the progress made over the last decade, we are now in a position to investigate the connection between this regime and the familiar quasigeostrophic flow at large scales. The effect of condensation and evaporation of water on turbulent mixing, mesoscale predictability, spontaneous breakdown of high-order balance and its role in oceanic and atmospheric energy budgets are among the subjects that need addressing. Finally, an important part of the proposal concerns the effect of adding internal and external boundaries.