Contact

Mohammad Farazmand
PhD Student
Institute for Mechanical Systems | ETH Zurich, CLA, G 26
Tannenstrasse 3 | 8092 Zurich | Switzerland

T. +41 44 632 7750
Email Mohammad Farazmand

Publications

  1. Farazmand M. and Haller G., The Maxey-Riley Equation: Existence, Uniqueness and Regularity of Solutions, submitted to SIAM J. of Appl. Dyn. Syst., 2013
  2. Farazmand M., Blazevski D. and Haller G., Shearless transport barriers in unsteady two-dimensional flows and maps, submitted to Physica D, 2013
  3. Farazmand M., Haller G., Attracting and repelling Lagrangian coherent structures from a single computation, Chaos, vol. 23, pp. 023101, 2013
  4. Hadjighasem A., Farazmand M., Haller G., Detecting invariant manifolds, attractors and generalized KAM tori in aperiodically forced mechanical systems, Nonlinear Dynamics, vol. 73, pp. 689-704, 2013 
  5. Farazmand M., Haller G., Computing Lagrangian Coherent Structures from Their Variational Theory, Chaos, vol. 22, pp. 013128, 2012 . 
  6. Farazmand M., Haller G., Erratum and Addendum to "A variational theory of hyperbolic Lagrangian Coherent Structures, Physica D 240 (2011) 574-598.", Physica D, vol. 241, pp. 439-441, 2012. 
  7. Farazmand M., Kevlahan N., Protas B., Controlling the Dual Cascade of Two-dimensional Turbulence, J. Fluid Mech., vol. 668, pp. 202-222, 2011. 

 

Mohammad Farazmand

My main area of research lies in the intersection of dynamical systems and fluid dynamics with an emphasis on differential geometric methods. Please see bellow for a sample of my work.

 

 

 

Current Projects

Lagrangian vorticesLagrangian vortices
We conduct the first fully Lagrangian study of coherent vorticies in a direct numerical simulation of 2D Navier-Stokes turbulence. The coherent vortices (red) preserve their shape over a long period of time as opposed to a non-coherent vortex (blue). The gray curves show the instantaneous vorticity contours.

We find that Eulerian techniques, e.g. Okubo-Weiss criterion, all underestimate the extent of the coherent vortices.

*Collaborator: G. Haller

 

Non-twist KAM tori
Numerical simulations have shown that non-twist KAM tori are the most robust tori under steady or time-periodic perturbations. Their counterparts in unsteady real-life flows are the cores of oceanic and atmospheric jets.

We develop a variational theory for extending the notion of non-twist tori from steady and time-periodic to general unsteady 2D flows. This theory results in an automatic detection algorithm for shearless (non-twist) jet cores.

*Collaborators: D. Blazevski and G. Haller

Non-twist KAM tori

 

 

 

Controlling the dual cascadeControlling the dual cascade*
The numerical simulations of forced Navier-Stokes turbulence in 2D do not reproduce the energy spectrum predicted by Kraichnan. There is numerical evidence that Kraichnan's scaling holds only in the limit of infinite Re number.

The forcing that is used in a typical DNS of turbulence is ad hoc with random phase and amplitude tuned to inject certain amounts of energy and enstrophy into the system.

We were able to find a forcing that reproduces Kraichnan's scaling laws even for moderate Re numbers. An adjoint-based optimal control method was used to find this particular forcing.

*Collaborators: N. Kevlahan and B. Protas