Can artificial intelligence (AI) solve the problem of turbulence? Current state-of-the-art AI cannot solve unsolved problems. Turbulence is a ubiquitous natural phenomena, and is one of the unsolved problems of classical physics. I am facinated about the coherent and chaotic beauty of turbulence. I like to learn more about turbulence, and teach it to others. Wavelet transforms provide intelligent algorithms; it was shown, for the first time, by Marie Farge (a French scientists) that wavelets have the intellingence to solve turbulence. The beauty of wavelets motivated me to write a PhD thesis on "A space-time wavelet method for turubulence".
The above illustration represents a pair of upward moving hot air - called updraft (by meteorologists). The red colour means that an upward moving air rotates counter clockwise; the blue colour means there is a clockwise rotation; and the yellow colour indicates a random and chaotic small-scale turbulent motion. Observe that the movement of air is simultaneously chaotic and coherent.
Scientists struggle to understand turbulence. Whether it is a car or an airplane or a house, every such object of our daily life must pass through some hindrance of the turbulent air. In a clear sky, pilots often encounter turbulence which they cannot detect with radars. At night or in regions with a cool ground, episodes of wind gusting often appear as turbulent bursts. Scientists and engineers have difficulty to measure turbulent drag experienced by an object that interacts turbulence - known as drag crisis. Industries pay an extremely high cost to manage turbulence induced drag.
My research focuses on the Large Eddy Simulation (LES) technique in which LES learns about atmospheric turbulence from a majority (e.g. 80%) of the large eddies (modes of turbulence) in order for robust identification of the effects of the remaining (e.g. 20%) modes. I consider, among other techniques, the singular value decomposition (SVD) of the velocity gradient tensor as a potential method for the robust identification of localized small-scale turbulence. Combining this approach with wavelet transforms leads to a data-driven reduced order model (ROM) for the study of atmospheric turbulence.
Dara-driven Reduced-Order Model (ROM) of atmospheric turbulence, utilizing POD, hierarchical wavelet decomposition, and LES. My research program employs data-driven (ROM) simulation techniques to visualize the inner secretes of turbulence. I am advancing the second-generation wavelet transform approach for the numerical simulation of atmospheric turbulence. The wavelet thresholding method projects the available turbulence data onto a reduced-order wavelet basis. This approach has a great potential for simultaneously utilizing the classical proper orthogonal decomposition (POD) technique.
Notice from this illustration that the wake behind an obstacle is very complex. However, the air circulation seems to consist of an organized/coherent motion. We see clearly that the coherent motion is captured reasonably accurately with the data-driven ROM approach. The ROM simulation result is quite similar to the result obtained with a classical Computational Fluid Dyinamics (CFD) simulation, where I have used LES although it is a two-dimensional laminar flow.
The actual turbulent atmosphere has a multiscale characteristics, as illustrated with the first figure displayed at the top of this page. I am interested in the development of robust methods that identify the large-scale organized motion of atmospheric turbulence. To develop the fastest numerical simulation technique of atmospheric turbulence, I am developing mathematical models for the small-scale random and chaotic part of the turbulence in which I consider the transport of vorticity in defining the two-way coupling between the large- and the small-scale motions. Moreover, I am interested in two approaches for the purpose of directly capturing the large-scale organized part. First, I look for robust methods to identify large-scale motion and separate it from its chaotic background. Second, I apply wavelet compression technique to obtain a near optimal adaptive mesh.
Understanding atmospheric turbulence is very important to improve our techological knowledge on harvesting wind energy. I study atmospheric turbulence, and work for the development of a wavelet-based Large Eddy Simulation (LES) methodology to explain atmospheric turbulence. I am particularly interested on the boundary layer processes lying at the broader context of atmosphere-land-ocean interaction, where relatively small scale processes (<10km) have rich three-dimensional structures, but their influences on the meso-scale dynamics are poorly understood. This includes how the boundary layer turbulence could impact on mesoscale weather events, or possibly penetrate into upper atmosphere through internal wave breaking. Wind farms have the potential to convert the kinetic energy from these rich energy containing turbulence eddies.
My current research team utilizes object oriented C++ programming, adaptive mesh wavelet method, and/or fully Lagrangian techniques for explaining multi-scale nature of geophysical flows. Potential graduate applicants are encouraged to contact me. However, only candidates with suitable background are expected to get a reply due to the large number of emails I receive. Applicants with appropriate background may also discuss with me on the possibility of receiving slightly higher scholarship compared to current departmental average.
Currently, I am an Associate Professor at the Dept. of Mathematics, Memorial University, Canada. Before joining Memorial, I was a SHARCNET post-doctoral fellow in atmospheric modelling at the Department of Earth and Environmental Sciences , University of Waterloo, Canada.
I studied computational fluid dynamics, turbulence, and atmospheric science through my education at the U of Alberta, McMaster University, and U of Waterloo, respectively.