Rama Govindarajan

Caustics and clustering in the vicinity of a vortex

We study the formation of caustics in vortex-dominated flows. We find that only particles starting within a critical distance of a vortex which scales as the square roots of the particle inertia and the circulation can form sling caustics. We show that particles starting in an annular region around this critical radius contribute the densest clusters in the flow. The large density spikes occurring for such particles, even at small inertia, are indicative that these particles will experience large collision rates.

Numerical study of laminar, standing hydraulic jumps in a planar geometry

We solve the two-dimensional, planar Navier-Stokes equations to simulate a laminar, standing hydraulic jump using a Volume-of-Fluid method. The geometry downstream of the jump has been designed to be similar to experimental conditions by including a pit at the edge of the platform over which liquid film flows. We obtain jumps with and without separation. Increasing the inlet Froude number pushes the jump downstream and makes the slope of the jump weaker, consistent with experimental observations of circular jumps, and decreasing the Reynolds number brings the jump upstream while making it steeper. We study the effect of the length of the domain and that of a downstream obstacle on the structure and location of the jump. The transient flow which leads to a final steady jump is described for the first time to our knowledge. In the moderate Reynolds number regime, we obtain steady undular jumps with a separated bubble underneath the first few undulations. Interestingly, surface tension leads to shortening of wavelength of these undulations. We show that the undulations can be explained using the inviscid theory of Benjamin and Lighthill (Proc. R. Soc. London, Ser. A, 1954). We hope this new finding will motivate experimental verification.

BiGlobal and Point Vortex Methods for the Instability Analysis of Wakes

To better understand destruction mechanisms of wake-vortices behind aircraft, the point vortex method for stability (inviscid) used by Crow is here compared with viscous modal global stability analysis of the linearized Navier-Stokes equations acting on a two-dimensional basic flow, i.e. BiGlobal stability analysis. nThe fact that the BiGlobal method is viscous, and uses a flnite area vortex model, gives rise to results somewhat different from the point vortex model. It adds more parameters to the problem, but is more realistic.

Linear stability analysis and direct numerical simulation of two layer channel flow

We study the stability of two-fluid flow through a plane channel at Reynolds numbers of a hundred to a thousand in the linear and nonlinear regimes. The two fluids have the same density but different viscosities. The fluids, when miscible, are separated from each other by a mixed layer of small but finite thickness, across which viscosity changes from that of one fluid to that of the other. When immiscible, the interface is sharp. Our study spans a range of Schmidt numbers, viscosity ratios and location and thickness of the mixed layer. A region of instability distinct from that of the Tollmien-Schlichting mode is obtained at moderate Reynolds numbers. We show that the overlap of the layer of viscosity-stratification with the critical layer of the dominant disturbance provides a mechanism for this instability. At very low values of diffusivity, the miscible flow behaves exactly like the immiscible in terms of stability characteristics. High levels of miscibility make the flow more stable. At intermediate levels of diffusivity however, in both linear and non-linear regimes, miscible flow can be more unstable than the corresponding immiscible flow without surface tension.

Relaxation of a highly deformed elastic filament at a fluid interface

We perform experiments to investigate the relaxation of a highly deformed elastic filament at a liquid-air interface. The dynamics for filaments of differing length, diameter and elastic modulus collapse to a single curve when the time-dependence is scaled by a time scale

Vortex Filament and Global Instability Analysis of the Crow Mode

tau = 8 pi mu L_o^4/B

Global Linear Instability of Flow Through a Converging–Diverging Channel

. The relaxation, however, is completed in a very small fraction of the time

The Effect of Initial Momentum Flux on the Circular Hydraulic Jump

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Linear stability of high-speed boundary layer flows at varying Prandtl numbers

. Even though the time scale

On Global Instability of Variable Aspect Ratio Channel Flows

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