2-D Turbulence: von Karman vortex street

  HD and MHD case

Idea:

This research was inspired by two ideas. First, I am interested in the magnetically controlled turbulence: can the magnetic field be used to control the direction of the flow, the size of the vortices, the separation time, etc.? Second, the Direct Numerical Simulation (DNS) of the MagnetoHydroDynamic (MHD) flows is not feasible for high Reynolds and magnetic Reynolds numbers, since the iterative method fails to converge within the time constraints of the problem. Hence, the Approximate Deconvolution Models (ADMs) are employed.

Experimental Results (obtained using FreeFEM, FreeFEM++ and Matlab)

First, consider the HD case. The parabolic flow u=[y(1-y),0] in [0,1]X[0,1] with the obstacle [x=0.25+0.05cos(t), y=0.5+0.05sin(t)], t=0,..,2pi. The fully developed von Karman vortex street (at Re=10000) past the obstacle is captured here
(the movies are best viewed with the RealPlayer)
Now consider the MHD case. The same parabolic flow in [0,1]X[0,1] with the obstacle, but in the magnetic field B=[x*e^(t/4), -y*e^(t/4)]. The DNS in the case Re=Re_m=100 was performed, and the 8-second movie shows the changes in the flow behavior.

However, in the case Re=Re_m=10000 the DNS is not an option already (the iterations fail to converge due to high sensitivity of the flow). Hence, the ADMs. At Re=Re_m=100 the zeroth order ADM-MHD provides results, which agree with the DNS. Finally, at Re=Re_m=10000 the ADM-MHD created the data for the following movie.