I began my academic career as a lecturer of mathematics in 1995 at the Department of Mathematics, Shahjalal University of Science and Technology, Bangladesh. I moved to Canada in 1998, and had been teaching at the Department of Mathematics and Statistics in Memorial University since 2008. Currently, I am a Professor at the Department of Mathematics and Statistics and also cross-appointed to Physics and Physical Oceanography. I am an associated faculty member at the interdisciplinary Scientific Computing and Data Science and have served as Chair of the Scientific Computing program.

I am a Fluid Dynamicist interested primarily in the turbulent flow of fluids. My research is a blend of fundamental investigations in Computational Fluid Dynamics and applied research relevant to atmospheric turbulence. My scientific interests concern the application of Wavelet Transforms in Turbulent Flows and Nonlinear Dynamics, Wind Energy, and Atmospheric Boundary Layer. My recent research contributions include wavelet-based adaptive mesh generation, scale-adaptive large eddy simulation, canopy-based immersed boundary method, and phase-field method in multiphase flows. My research group focuses on the development and testing of three numerical simulation methods: large eddy simulation (LES) methods, adaptive wavelet methods, and data-driven modeling of complex systems. The goal of such development is to understand the complex interaction between turbulent flows and the environment, with emphasis on energy systems and atmospheric turbulence

I want to understand the way air flows around us when we walk, drive a car, fly with an airplane, or even rest in the house. A focus of my research is on atmosphere-wind farm interaction and atmospheric turbulence in the wake behind ships, cars, aircraft, buildings, and mountains. I want to solve the challenging mathematical problems that help understand the air circulation around us and in fact, these mathematical problems can help us dealing with the effect of climate change.

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.

Climate change is one of the greatest challenges, which demands for detailed understanding of atmospheric turbulence. Turbulence research generally combines physics-based models with numerical simulations, such as in large eddy simulation (LES). Wavelet transforms and neural networks are two promising techniques, which bring artificial intelligence in Scale-Adaptive Large Eddy Simulation (SALES) and in Coherent Vortex Simulation (CVS).

Climate change is strengthening aviation turbulence, increasing the frequency of bumpy flights, which costs the aviation industry $200 to $500 millions annually. It is thus very important to improve our understanding of turbulent flow in the atmosphere.

My research focuses on understanding how such artificial Intelligence (AI) can be utilized to better understand our atmosphere, where we leave and breathe. I study a wide variety of fluid flow phenomena, using numerical methods to solve problems in atmospheric turbulence. The problems I study are mainly about multiscale modeling and data-driven numerical simulations of fluid's turbulence. Scientists and engineers have confounded at predicting and controlling turbulent fluid flows. Turbulence is one of the most challenging problems in science and engineering. It plays a critical role in our everyday life. Turbulence limits the fuel efficiency of our vehicles, leads to bumpy airplane rides, impacts weather patterns and climate change, and affects clean energy technologies.

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.

Wind energy is one of the fast-growing and leading renewable energy technologies. With its large landmass and diversified technological expertise, Canada has the potential to be a world leader in the production and supply of wind energy. In Newfoundland and Labrador, where Memorial University is located, the onshore wind resources are the best in North America. **Wind Energy Science** is a research field that focuses on wind energy research and trains undergraduate and graduate students to be next generation wind energy leaders. Modern Computational Fluid Dynamics (CFD) techniques uses the deep learning approach to simulate various scenario and provides essential feedback for exporting wind energy through the production of hydrogen/ammonia or via transmission lines.

Understanding the interactions between wind farms and the atmospheric boundary layer is an example of a turbulence modelling problem for which advanced computational techiques need to be developed. A wind farm is an array of wind turbines. Each wind turbine in a wind farm converts kinetic energy of the atmosphere into electricity. Wind farm aerodynamics offers many advantages in understanding the complex role of vortices in turbulent flows and the efficiency of numerical simulations.

Modern wind turbines in onshore and offshore wind farms extract kinetic energy at heights between 30 m and 150 m. The distance between two turbines is typically between 500 m and 700 m, depending on the length on the blade. The above picture shows an array of 41 wind turbines. When the turbine rotates, each turbine covers a circular region, which is called rotor disk. In the above picture of an wind farm, the rotor diameter is 126 m. Clearly, a large land area is needed to produce large amount of electricity with wind energy. My team uses numerical simulation to explain various potential ways to optimize wind energy production without expanding the land area usage.

The literature disagree on the deflection wakes caused by the Coriolis force. Some studies think wind farms can increase local temperature, while other studies think of cooling effect. Due to the global demand, the hydrogen market is projected to grow by 1000-fold by 2040, which means the increase of renewable energy installations, which is wind farm for Newfoundland. If we expect a 1.5-degree climate change mitigation, then meeting a quarter of the energy demand with hydrogen will necessitate a massive amount of wind energy.

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.

My research program has projects for BSc, MSc, and PhD students, and for post-doctoral scholars. These projects are primarily funded by NSERC. Interested candidates are encouraged to contact me directly.

This research project focuses on some fundamental questions regarding atmospheric turbulence, particularly the physical mechanism behind the cascade and the dissipation of energy in turbulent flows. Briefly, LES is a numerical method for solving the Navier-Stokes equations. In other words, LES is a numerical method to understand the smoothness and other properties of the solutions of Navier-Stokes equations at high Reynolds number. An actual research project for students will be adjusted to the level of students' degree and background knowledge.

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 dynamics, as well as proficient in code development using C++, Matlab, Python, etc. Interested students are encouraged to contact me directly.

Wavelets are special mathematical functions, often called **mathematical microscope** because wavelets discover hidden patterns underlying any function. Let y = f(x) be a function of x. A wavelet transform discovers hidden patterns of f(x) and we can focus on some important features of interest. Wavelet transforms share many aspects of neural networks (i.e. artificial intelligence and machine learning). Wavelets are useful techniques in computer science, data science, signal processing etc. My research on wavelet aim to develop wavelet-based adaptive numerical methods for solving partial differential equations.

A discrete wavelet transform employs a linear operator and focuses on the missing details - called wavelet coefficients. The modulus operator finds the active wavelets and captures the underlying non-linearity. In contrast, neural networks treat the missing details underlying a linear operator as biases and employ an activation operator, while optimizing the linear operator. Application of wavelets and neural networks to understand atmospheric turbulence is a primary element of my research program and student supervision. I have open PhD positions in this research direction.

This research project also 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 of 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.

Similar to traditional numerical methods, such as finite difference or finite element discretizations, machine learning techniques provide data-driven discretization of nonlinear partial differential equations. In Fluid Dynamics, the Navier-Stokes equations provide an open mathematical challenge, which is the lack of understanding the smoothness of the solution. Unsupervised machine learning, such as proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are commonly used data-driven methods in fluid dynamics research. A potential question is whether DMD captures the solution manifold of the Navier-Stokes equation, thereby providing a hint for the smoothness of its solution and why a smooth fluid flow suddenly becomes violently turbulent. Such an understanding is crucial for wind energy and various other engineering and environmental situations.

Supervised machine learning can use neural networks to learn the discretization of nonlinear partial differential equations and has the potential to address many challenges of turbulence. Neural networks and wavelet transforms shares a lot of similar ideas. Understanding the connection between wavelets and neural networks is an open research area that leads to new data-driven approaches. There is a need to investigate how these techniques can provide a deep insight into atmospheric turbulence.

"Wavelet Transforms and Machine Learning Methods for the Study of Turbulence, Fluids 2023, 8(8), 224" discussed the ideas of deep learning and wavelet-based techniques.