ASTR/ATOC-5410: Fluid Instabilities, Waves, and Turbulence

Project description November 11, 2016, Axel Brandenburg

Project on alignment of structures in turbulence

Background

Numerical simulations have shown conclusively that ω aligns itself with the intermediate eigenvector of the rate-of-strain matrix (Vincent & Meneguzzi, 1991). In MHD, on the other hand, it turns out that, the magnetic field vector aligns itself with the direction of shear, which is at 45^{∘} angles with the directions of both stretching and compression (Brandenburg et al., 1995). This project will focus mainly on hydrodynamic turbulence, but the application to MHD is a natural extension.

Project details

You will be provided with data of high-resolution simulations of decaying hydrodynamic and MHD turbulence.

1. Study the local alignment of vorticity ω with the intermediate eigenvector of the rate-of-strain matrix, e_{2}. How does it correlate with local increases of the dissipation rate, for example?

2. How big is the volume over which the alignment of ω with e_{2} persists?

3. Are there locations where ω aligns itself with e_{1} and e_{3}?

4. Are there corresponding alignment properties in the magnetic field? How big are they? How does it depend on the magnetic Prandtl number, Pr_{M}? [You will have access to data with Pr_{M} = 0.01, 1, and 100.]

5. Verify locally that B aligns itself with the direction of shear. Determine a corresponding characteristic vector from the velocity gradient matrix u_{i,j}.

References

Brandenburg, A., Nordlund, Å., Stein, R. F., & Torkelsson, U., “Dynamo generated turbulence and large scale magnetic fields in a Keplerian shear flow,” Astrophys. J. 446, 741-754 (1995).

Vincent, A. & Meneguzzi, M., “The spatial structure and statistical properties of homogeneous turbulence,” J. Fluid Mech. 225, 1-20 (1991).