I am a Fluid Dynamicist interested primarily in the turbulent flow of fluids. I had been teaching at the Department of Mathematics and Statistics in Memorial University since 2008. My research is a blend of fundamental investigations in Computational Fluid Dynamics and applied research relevant for atmospheric turbulence. I focus on the use of large eddy simulation (LES) methods, adaptive wavelet methods, and data-driven modeling of complex systems.

I studied at Chittagong University, Bangladesh (BSc honours and MSc in Mathematics), University of Alberta, Canada (MSc), and McMaster University, Canada (PhD). Previously, I served as a full-time faculty member at the Department of Mathematics, Shahjalal University of Science and Technology, Bangladesh, as a post-doctoral scholar at the Department of Earth and Environmental Science, University of Waterloo, Canada, and as a short term visiting research scholar at the Department of Atmospheric Sciences, National Taiwan University.

My research interests are about multiscale modeling and physics-driven numerical simulations of fluid's turbulence. Imagine a hurricane passing over a city, or a forest of giant wind turbines with blades rotating at a height of 100 to 500 meters above the ground. Representing such a complex system in laboratory experiments is nearly impossible. A simplified representation of such complex systems is known as turbulence modeling. An open challenge is how to define what aspects of the dynamics would constitute a simplified model of a complex system? My interests about atmospheric turbulence is primarily motivated by the need for solutions to problems like greenhouse gases, urbanization, and continuous growth in energy demand. For example, wind farm aerodynamics offers many advantages in understanding the complex role of vortices and the efficiency of numerical simulations. Moreover, wind energy is currently one of the fastest-growing energy sources in the world. My research program uses wind farm simulations to explain atmospheric turbulence, while addressing the challenges to greater use of wind energy. One of the open scientific challenges is the lack of a comprehensive theory of how energy is transported by turbulence from the free atmosphere, where it is produced, to the wind farm, where it is harnessed. In numerical simulations of wind farms, I consider stretching of vortex tubes and Helmholtz vortex theorem to model subgrid-scale turbulence stresses. More about the simulated wind farm shown in this figure can be found from this article.

This research program focuses on some fundamental questions regarding atospheric turbulence, particularly the physical mechanism behind the cascade the dissipation of energy in turbulent flows. In the Figure (on left), the region with blue color indicates stretching of vortex tubes, and that with red color indicates vortex sheets. The dominancy of blue over red indicates the posibility of vortex stretching to be the dynamical mechanism. I use the LES method to understand whether the stretching of vortex filaments be assocated with the principal mechanical cause of dissipation in turbulent motion. Despite the evidences from LES that the energy cascade is driven by vortex stretching, a precise connection between the two has been openly debated. A new LES approach, which is based on vortex stretching phenomena, has been presented in this article.

Scientists and engineers believe that the Navier-Stokes equation can explain why we are not able to fly with an airplane smoothly if the atmosphere becomes turbulent. The Clay Institute of Mathematics declared a prize of one million dollars to be offered to whoever can mathematically prove the smoothness of solution of turbulence. It means that turbulence is not only an academic challenge, but also equally important in the aerospace and automobile industry.

One of my ideas include teaching theory of turbulence to talented students. I train my research team to be highly efficient in computational science and fluid dyanamics, as well as proficient in code development using C++, Matlab, Python, etc. Interested students are encouraged to contact me directly.

This research project investigates the theory of compressive sensing toward a new approach to turbulence modelling. In this direction, I study discrete wavelet transforms in order to incorporate two principles in turbulence modeling: sparsity, which concerns the significant dynamics of interest, and incoherence, which concerns fidelity compressive sensing. The wavelet theory exploits the fact that turbulence is extremely intermettent, and thus, a turbulent flow posseses sparsity when expressed in wavelet basis. Incoherence extends the idea that a sparse dynamics must be spread out, just like a spike does.

This research program intends to give proper training about the data-driven approaches and investigate how these techniques can provide a deep insight into atmospheric turbulence.