Research Projects

This project aims to (a) understand the role of coherent and optimal structures in turbulence transition in a stratified channel flow, (b) the dynamics of these structures in transitional and fully developed turbulence to understand their interactions and role in sustaining the near-wall turbulence and (c) the importance of these structures in turbulent mixing, energy cascade and exchange of states in turbulence to improve turbulent mixing parameterisation for use in large-scale numerical models like global and regional ocean and climate models. Coherent structures are organised structures that are connected by a phase-correlated vorticity and are dominant in both transitional and fully-developed turbulence. These are generated by instabilities of the flow and can take a variety of forms like hairpin vortices, streamwise rolls, puffs etc. In many cases, these structures are themselves responsible for the transition to turbulence. Nonlinear optimal disturbances are a type of coherent structure that are the lowest energy disturbances that cause flow transition from laminar to turbulence and exhibit similar self-organising behaviour. Once the whole fluid domain has transitioned, these structures can still persist and the interaction between the coherent and the incoherent parts of turbulence is an extremely important area of research both from the fundamental perspective and in applied science. From a fundamental point of view, subcritical transition to turbulence and turbulence altogether has been a long-standing unsolved classical problem. Our research will contribute to understanding the transition process in stratified shear flows at low Reynolds numbers. It has been observed that the transition process explores a set of organised structures and these can be understood when we approximate the flow as an infinite dimensional phase space and flow state to be an evolving trajectory. Understanding the interactions and the path traversed in phase space has a significant impact on the state of turbulence that the flow finally ends up in. If we have an estimate of the resultant turbulent state from an initial state, it will improve our ability to parameterise mixing. This parameterisation has an important application in numerical ocean and climate models to understand geophysical turbulence as simulations have never resolved the centimetre-scale Kolmogorov length and the effect of turbulence is always parameterised. This project will employ direct numerical simulations, adjoint-based stability analysis, and dynamic mode decomposition to decouple the coherent structures from the rest of the flow. We will conduct various numerical experiments with varying Reynolds numbers in the subcritical range in a short-length stratified channel. We will also understand the scale-specific energy transfer by looking at interscale transport due to the nonlinear terms in the decomposed (into mean, coherent and incoherent parts) Navier--Stokes equations.