Grant: Discovery Grants Program - Individual

Investigating relevant turbulent processes at fundamental level is essential to understand geophysical flows in the atmosphere and oceans, and is critical for such varied purposes as weather forecasting, projecting climate change, and mitigating air pollution. Our current conceptual and technical tools are inadequate for explaining turbulence, and have yet to approach towards a comprehensive theory. Inadequate representation of interactions across multiple spatio-temporal scales in the atmosphere and oceans is one stumbling reason for poor performance of numerical models. Satellite observations in the atmosphere and oceans exhibit localized, filamentary structures with relevant scales that are much smaller than scales of global dynamics. Clearly, if we knew how to define and extract such localized structures, this would lead to a promising multi-scale numerical modelling approach. Multi-scale approaches, such as wavelet methods, leads to compressing a signal. What compression of geophysical flows can be achieved optimally using wavelet based numerical models? Can we recover or predict unresolved scales of turbulence using the multi-resolution aspects of wavelets? Note that "recovering" the unresolved motion is the appropriate alternate to classical parameterizing, if we can actually recover. Do we understand the nonlinear evolution of unresolved scales adequately? I, therefore, propose to study the following. i) Multi-scale wavelet methodology for geophysical turbulence. ii) A fully-Lagrangian modelling system to investigate the nonlinear evolution of unresolved scales. iii) Reliability and scalability of numerical model's output after many time steps.