A multiscale modelling and simulation methodology for turbulent geophysical flows

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We live and breathe at the bottom of an atmosphere that contains both gases and tiny particles of dust and smoke. Our health and environment are affected by the very complex mechanisms of the extremely turbulent atmosphere. On a sunny day, the land warms up faster than the ocean, which drags cool air from over the ocean to the land. Through this process, energy is exchanged via enhanced turbulent mixing. Turbulent kinetic energy of hurricanes (and other natural disasters) causes damage to lives and their environment. Answering environmental questions - such as why hurricanes develop, why global temperature increases, why the rate of melting polar ice has increased, or why sea level rises - leans heavily on the complete understanding of the turbulent mixing and transport in the atmosphere. For example, in order to project the future distribution of such vital ingredients as carbon-dioxide (CO2) or other pollutants, one needs to know their sources and sinks, and how these pollutants are mixed in the turbulent atmosphere. **However, the turbulent mixing mechanism is brutally affected when atmospheric models (either air pollution or weather prediction) employ a typical mesoscale grid at 10-20 km resolution. Our current modelling and simulation techniques are inadequate for representing turbulence at this truncated resolution, and have yet to approach a comprehensive development for parameterizing the truncated physics across a wide range of scales; note, there is a factor of about 100 million between the scale at which energy is added and that at which turbulent mixing occurs. One way to move forward is through the development of turbulent models for the atmospheric boundary layer under various conditions, and to utilize the gathered detailed knowledge on turbulence to parameterize unresolved physics of mesoscale meteorological models. **My research program encompasses fundamental developments on a wavelet based multiscale methodology and its application to explain the influence of turbulence and other small scale meteorological variability on forecasting meso-scale phenomena. **The proposed research thus aims to develop and exploit a robust, reliable, and computationally efficient new wavelet based dynamical core for a non-hydrostatic multiscale meteorological methodology over complex terrains. In contrast to contemporary atmospheric models, the proposed mesoscale modelling approach will capture the significant proportion of the flow with a multi-scale wavelet basis, and the residual motion will be parameterized. A multiscale parameterization technique will be developed for a two-way nesting of energetic eddies within a mesoscale model, employing the second generation wavelet transform. This new wavelet method will explore both the sub-mesoscale and sub-LES scale phenomena, which is an important aspect of the proposed development. **In the field of atmospheric modelling, a faithful parameterization of boundary layer eddies or other convective phenomena on a mesoscale grid of 10-20 km resolution is one of the most challenging and demanding topics. Similarly, meteorological data may be available on the mesoscale resolution from a satellite; however, incorporating the observed meteorological feedback into the prediction of sub-mesoscale (e.g. a tornado) or micro-scale (e.g. boundary layer eddies) phenomena is necessary and also challenging. The success of the proposed wavelet based multiscale methodology for dynamically nesting turbulence and other small scale meteorological variability in a mesoscale model will advance state-of-the-art contemporary atmospheric models, thereby paving a new avenue toward the prediction of the mesoscale and the microscale weather phenomena.