Atmospheric and oceanic turbulence

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The requested funds are for the study of atmospheric and oceanic fluid turbulence mainly employing high-resolution numerical simulations, but guided by perturbative analytical techniques, statistical closure theories and dimensional analysis. Turbulence is clearly the most complex outstanding problem in fluid dynamics and understanding it better is absolutely necessary to improve high-resolution environmental and climate models. Of crucial importance to large-scale modellers is how geophysical flows mix the various quantities whose distributions are of such great concern to society. In addition, many fields of study including pollutant dispersion modelling, urban meteorology and wind energy generation, require statistical forecast skill on time scales of hours and length scales of 10's to 100's of kilometers, where my group and I have been exploring the more complicated dynamics that prevail. This application concerns only the fundamental research issues. The applicant also values his longstanding collaborations with the numerical weather prediction community and a new urban meteorology group in Hong Kong, along with their HQP and in-kind funding.****** Specifically, the influence of rotation and stratification on classical turbulence statistics will be examined. The subject belongs to the family of studies of waves and vortices in some limits and classical theory suggests that large-scale temperature, pressure and wind are balanced in such a way that high-frequency waves have low amplitudes. The last 10 years have seen rapid progress by many groups worldwide in characterising the wave/vortex nature of turbulence at scales smaller than those of the baroclinic eddies in both atmosphere and ocean. This has been in field observations, lab experiments, numerical simulation and theory and the current vigour in the field is explained by the fact that realistic models have now reached resolutions where our lack of dynamical understanding is detrimental to progress. *** *** My own group has found that balance dynamics cannot exist in the small-scale regime where rotation is less important. Here, there exists a single turbulent time scale and wave/vortex decompositions break down. At larger scales higher-order balance dynamics give rise to steep wave number to the -3 energy spectra, whereas a breakdown of balance yields a -5/3 spectrum consistent with observations. Spontaneous imbalance occurs primarily in regions of large strain. The next step is to formulate parameterisation schemes that dissipate balanced energy in precisely the right locations at the right time, instead of being based on global averages over long periods. The second novelty is that we now include realistic vertical inhomogeneities, such as the ground, ocean surface, thermocline and tropopause, etc., where it is proposed that we are now ready to include the role of waves in boundary-layer turbulence.**