Fluid dynamics across scales: Insights from compressible turbulence and large-scale tropical atmospheric dynamics

Fluid flows in nature and engineering exhibit a wide range of spatial and temporal scales. This talk presents two problems across this range: compressible turbulence in channel flows and large-scale vorticity dynamics in the tropical atmosphere.

The first part of the talk focuses on compressible turbulence, which plays a key role in many aerospace flows, including supersonic and hypersonic flight, shock-boundary layer interactions, and scramjet combustion. In contrast to incompressible turbulence, compressible turbulence is characterised by fluctuations in both thermodynamic variables of density, temperature and pressure, in addition to velocity. Using Lie symmetry theory, we derive scaling laws for velocity and thermodynamic statistics in compressible channel flows. As a first step, we derive a hierarchy of unclosed equations for the probability density function and its Fourier transform, the characteristic function, that accounts for both flow and thermodynamics statistics. Then, the Lie point symmetries of the characteristic function hierarchy are derived. Finally, the symmetry groups are used to obtain the scaling laws for channel flows, and are verified against the data from direct numerical simulations.

The second part of the talk focuses on understanding the large-scale meridional structure of vertical vorticity in the intertropical convergence zone (ITCZ), the near-equatorial region where the trade winds converge and produce a planetary-scale band of precipitation. We show that the vorticity away from the latitude of the ITCZ can be understood approximately through conservation of absolute vorticity, whereas, within the ITCZ, vortex stretching plays a dominant role. As a result, the relative vorticity in the ITCZ increases as the ITCZ moves poleward.

Divya Sri Praturi is a postdoctoral researcher at the Max Planck Institute for Meteorology, Hamburg. She obtained her PhD in Aerospace Engineering from Texas A&M University, College Station, USA, and Bachelors and Masters degrees in Aerospace Engineering from the Indian Institute of Technology, Kharagpur. She was also a recipient of the Humboldt Fellowship for postdoctoral researchers and Amelia Earhart Fellowship for PhD students. Her research interests lie broadly in the areas of tropical atmospheric and climate dynamics, stability and turbulence in conducting and non-conducting compressible shear flows. She employs pen-and-paper calculations, group theoretical methods and high resolution numerical simulations to derive mechanistic insights into these flows.