I am currently studying pattern-formation in Rayleigh-Benard convection system. Specifically, we are attempting to reproduce(numerically) some of the classic experimental results near onset of convection in rotating convection cells.  

Domain chaos:The image on the right is a top-view of a rotating Rayleigh-Benard convection cell of aspect ratio 25 at Rayleigh number 2500. The red color indicates rising fluid and blue indicates the cooler fluid which is coming down. The instability that is seen here is called as "Kuppers-Lortz" instability. You can see the evolution of this instability in this mpeg movie. The evolution seen here is happening over 38 vertical diffusion times. Collaborators: Henry Greenside, Paul Fischer, Mike Cross, Mark Paul. The webpage of the group can be found here.

Hydrodynamics in Complex Fluids

At Penn State my focus was in analyzing simple flows in complex fluids. Prof. Andrew Belmonte and I  studied some simple hydrodynamic experiments in micellar fluids. We found that spheres falling though certain worm-like micellar fluids do not reach steady state. Instead, its velocity oscillates as the sphere falls. We conjecture that this phenomenon might be due to formation of flow induced structures in the fluid. Details regarding this can be obtained here. 

A simulation of falling sphere can be found here.

Unstable Electrostatic waves in plasmas

Some friends and collaborators  

Publications: 

• A. Jayaraman, J.D. Scheel, H.S. Greenside and P.F.Fischer, "Characterization of the domain chaos convection state by the largest Lyapunov exponent " , Phys. Rev. E 74, 016209 (2006).

• A. Jayaraman and A. Belmonte, "Oscillations of a solid sphere falling through a wormlike micellar fluid " , (physics/0205067), Phys. Rev. E 67, 065301(R) (2003). (micel.ps.gz, micel.pdf)

• A. Belmonte, J. Jacobsen and A. Jayaraman " Monotone Solutions of a Nonautonomous Differential Equation for a Sedimenting Sphere" , Electronic Journal of Differential Equations, Vol 2001(2001), No. 62, pp. 1-17. (sphere.ps.gz, sphere.pdf)

• J.D. Crawford, A. Jayaraman, " First Principles Justification of the 'Single Wave Model'", Phys. of Plasmas 6 (1999) Pg 666 - 673. (POP-swm.ps.gz, POP-swm.pdf)

• J.D. Crawford, A. Jayaraman, "Amplitude Equations for Electrostatic Waves: multiple species ". J. Math . Phy. 39 (1998) 4546. (JMP-multiple.ps.gz, JMP-multiple.pdf ) 

• J.D. Crawford, A. Jayaraman , " Nonlinear saturation of electrostatic waves: mobile ions modify trapping scaling" Phys. Rev. Lett. 77 (1996) 3549.  (PRL96.ps.gz, PRL96.pdf )