Vortex merging dynamics: Vortex merging in shear layers plays a crucial role in the transition to turbulence. We have provided a mechanistic understanding of merging, and have predicted fully nonlinear merging patterns solely from the linear initial conditions. Next we are investigating how we can tune initial conditions to obtain optimal turbulence and mixing.

Internal gravity waves: Internal waves in oceans are often formed when tides cause the stratified ocean water to move to and fro past an underwater topography (as shown in the bottom panel). Using sophisticated mathematical tools as well as numerics, we are investigating multiple problems on internal gravity waves. The top panel shows the surface signature of internal waves, which we are using to reconstruct ocean’s density stratification from surface signature (by forming an inverse problem). Some other problems we are investigating pertain to weakly nonlinear resonant and near-resonant triad interactions of internal waves, and how bottom topography causes triad detuning.

Bragg resonance: Weakly nonlinear interactions between surface waves and bottom topography (inset shows top-view) can be used for various coastal engineering applications, e.g. wave energy harvesting by wave focussing, wave deflection for protection of off-shore structures. We are investing several theoretical and applied problems on wave-topography interactions.

Particle trapping via surface wave and bottom topography interactions: Ocean surface waves cause floating particles to undergo a slow drift in the direction of propagation of the waves (Stokes drift). We have found that this drift is significantly affected when an incident surface wave travels over a small amplitude, corrugated sea-floor. The inset shows that after some time, the particle's trajectory reverses (anticlockwise motion). Hence, natural or artificial corrugated bottom acts as a non-surface-invasive particle trap. This work has applications in marine pollution mitigation.

Hydrodynamics of fish schooling: Observations suggest that fishes get energetic advantages when they swim in school. These are observed in terms of reduction in tail-beat frequency or in oxygen consumption level compared to solitary swimming. Although it has been conjectured that energetic benefits arise via hydrodynamic interactions with vortices shed by preceding fishes, the real mechanism is still not well understood. We are trying to unravel multiple mysteries surrounding fish swimming.