Research Description

My postdoctoral research has broadened my interests from classical wave–structure interactions to fundamental problems in theoretical fluid mechanics and geophysical fluid dynamics. At the Indian Institute of Technology Madras, I investigated hydrodynamic instabilities, nonlinear wave dynamics, internal gravity waves, and low-Reynolds-number flows. Using asymptotic methods, perturbation theory, stability analysis, and complex variable techniques, I developed analytical frameworks for understanding instability mechanisms, wave interactions, and viscous flow phenomena.

Currently, at the Mathematical Institute for Machine Learning and Data Science (MIDS), Katholische Universität Eichstätt-Ingolstadt, my research focuses on multiscale energy transfer processes in atmosphere–ocean systems within the DFG Collaborative Research Centre TRR 181, "Energy Transfers in Atmosphere and Ocean". My work seeks to establish mathematically consistent reduced-order descriptions of unresolved momentum transfer and subgrid-scale processes in geophysical flows. Combining stability theory, spectral methods, dynamical systems concepts, and numerical analysis, I study perturbation growth, coherent structures, and energy pathways across scales in stratified and rotating fluids.

Taken together, my postdoctoral research aims to bridge rigorous mathematical analysis with physically relevant fluid-dynamical problems, spanning wave–structure interactions, hydrodynamic instabilities, geophysical turbulence, and multiscale energy transfer.

My doctoral research was devoted to the mathematical analysis of fluid–structure interaction problems in linear water-wave theory, with particular emphasis on hydroelasticity and wave scattering by submerged structures. The central objective was to develop rigorous and computationally efficient mathematical frameworks for understanding the interaction of surface gravity waves with rigid, porous, and elastic structures of varying geometries and material properties.

A distinguishing feature of my work was the incorporation of non-uniform structural characteristics, such as spatially varying porosity and thickness, moving beyond the conventional assumption of uniform structures commonly adopted in the literature. I investigated a broad class of problems involving horizontally, vertically, and arbitrarily inclined structures, thereby providing more realistic mathematical models for marine and offshore engineering applications.

From a mathematical perspective, my research centred on the formulation and analysis of boundary value problems governed by potential-flow theory. I developed semi-analytical solution methodologies based on Green's functions, Green's integral theorem, hypersingular integral equations, eigenfunction expansions, perturbation methods, and Fourier transform techniques. These approaches enabled the reduction of complex fluid–structure interaction problems to systems of hypersingular integral equations, which were subsequently solved using efficient numerical schemes implemented in MATLAB.

My work contributed to the development of novel frequency-domain and time-domain models for non-uniform elastic structures, with applications ranging from offshore renewable energy systems and wave energy converters to sea-ice dynamics and coastal engineering. Overall, the research advanced both the mathematical theory and computational methodology of hydroelastic wave–structure interactions.