Balachandra Suri

Velocity profile in a two-layer Kolmogorov-like flow

In this article, we discuss flows in shallow, stratified horizontal layers of two immiscible fluids. The top layer is an electrolyte which is electromagnetically driven and the bottom layer is a dielectric fluid. Using a quasi-two-dimensional approximation, which assumes a horizontal flow whose direction is independent of the vertical coordinate, we derive a generalized two-dimensional vorticity equation describing the evolution of the horizontal flow. Also, we derive an expression for the vertical profile of the horizontal velocity field. Measuring the horizontal velocity fields at the electrolyte-air and electrolyte-dielectric interfaces using particle image velocimetry, we validate the theoretical predictions of the horizontal velocity and its vertical profile for steady as well as for freely decaying Kolmogorov-like flows. Our analysis shows that by increasing the viscosity of the electrolyte relative to that of the dielectric, one may significantly improve the uniformity of the flow in the electrolyt...

Forecasting Fluid Flows Using the Geometry of Turbulence

The existence and dynamical role of particular unstable solutions (exact coherent structures) of the Navier-Stokes equation is revealed in laboratory studies of weak turbulence in a thin, electromagnetically driven fluid layer. We find that the dynamics exhibit clear signatures of numerous unstable equilibrium solutions, which are computed using a combination of flow measurements from the experiment and fully resolved numerical simulations. We demonstrate the dynamical importance of these solutions by showing that turbulent flows visit their state space neighborhoods repeatedly. Furthermore, we find that the unstable manifold associated with one such unstable equilibrium predicts the evolution of turbulent flow in both experiment and simulation for a considerable period of time.

Analysis of Kolmogorov Flow and Rayleigh-B enard Convection using Persistent Homology

We use persistent homology to build a quantitative understanding of large complex systems that are driven far-fromequilibrium; in particular, we analyze image time series of ow eld patterns from numerical simulations of two important problems in uid dynamics: Kolmogorov ow and Rayleigh-B enard convection. For each image we compute a persistence diagram to yield a reduced description of the ow eld; by applying dierent metrics to the space of persistence diagrams, we relate characteristic features in persistence diagrams to the geometry of the corresponding ow patterns. We also examine the dynamics of the ow patterns by a second application of persistent homology to the time series of persistence diagrams. We demonstrate that persistent homology provides an eective method both for quotienting out symmetries in families of solutions and for identifying multiscale recurrent dynamics. Our approach is quite general and it is anticipated to be applicable to a broad range of open problems exhibiting complex spatio-temporal behavior.

Bifurcations in a quasi-two-dimensional Kolmogorov-like flow

We present a combined experimental and theoretical study of the primary and secondary instabilities in a Kolmogorov-like flow. The experiment uses electromagnetic forcing with an approximately sinusoidal spatial profile to drive a quasi-two-dimensional (Q2D) shear flow in a thin layer of electrolyte suspended on a thin lubricating layer of a dielectric fluid. Theoretical analysis is based on a 2D model (Suri

Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow

{\it et al.}

Coherent structures, instabilities, and the arrow of time

2014), derived from first principles by depth-averaging the full three-dimensional Navier-Stokes equations. As the strength of the forcing is increased, the Q2D flow in the experiment undergoes a series of bifurcations, which is compared with results from direct numerical simulations of the 2D model. The effects of confinement and the forcing profile are studied by performing simulations that assume spatial periodicity and strictly sinusoidal forcing, as well as simulations with realistic no-slip boundary conditions and an experimentally validated forcing profile. We find that only the simulation subject to physical no-slip boundary conditions and a realistic forcing profile provides close, quantitative agreement with the experiment. Our analysis offers additional validation of the 2D model as well as a demonstration of the importance of properly modelling the forcing and boundary conditions.