My primary research focus lies in the application of advanced numerical methods and algorithms to address fluid dynamics problems, including but not limited to global spectral methods, spectral-element methods, and optimisation techniques. I am particularly drawn to the intricate nature of geophysical, astrophysical, and industrial fluid flows, which demand a high degree of freedom for accurate solutions. To tackle these challenges, I leverage the power of high-performance computing, a vital tool in the current scientific paradigm.

More precisely, my work focused on the quantification of small-scale quantities for stably stratified turbulence (SST) and convective turbulence, for which I was involved in developing the global spectral code TARANG (Chatterjee et al., 2017)  and the finite-volume code OpenFOAM (Kumar & Verma, 2018). An important unsolved problem in the field of buoyancy-driven turbulence is how to quantify the spectra and fluxes of kinetic and potential energies. Using high-resolution DNS, performed at a grid resolution of $4096^3$ in a cubical box, we have shown a delicate balance of dissipation and energy supply rate by buoyancy (Kumar et al., 2014; Verma et al., 2017). This balance leads to a constant kinetic energy (KE) flux, and therefore, we observe Kolmogorov’s spectrum exhibited in figure (c). On the other hand, at moderate stratification for stably stratified turbulent flows, we have shown that the energy supply rate by buoyancy is negative, which indicates the conversion of kinetic energy to potential energy by buoyancy; thus, the KE flux decreases with wavenumber (Kumar et al., 2017). As a result, the system exhibits Bolgiano-Obukhov (BO) scaling. Further, we have confirmed these scaling results by applying the low-dimensional shell model (Kumar & Verma, 2015).