Physics-based models for large-eddy simulations of (un)steady magnetohydrodynamic turbulence

Asif Nawaz (University of Edinburgh)

Wednesday 15th October 15:00-16:00
Maths 311B

Abstract

For Navier-Stokes turbulence, contributions to the energy cascade from e.g. vortex stretching can be identified by an exact decomposition of the energy flux. This results in a quantification of the relative contributions of such effects to the kinetic energy cascade by direct numerical simulation, and provides guidance for physics-informed LES modelling. LES modelling is of particular importance for magnetohydrodynamic (MHD) turbulence due to the extreme Reynolds numbers typical for plasma flows in astrophysics and nuclear fusion. The provision of better models that capture the main physical mechanisms that govern MHD cascades would therefore be a major advance for computational research in the field. For MHD LES, difficulties arise due to interactions between flow and magnetic field, and the unsteady nature of many fundamental problems in MHD, such as the kinematic and nonlinear dynamo. A key issue is that LES models typically underestimate the magnetic field amplification by a turbulent flow, for instance, the turbulent small-scale dynamo is not captured adequately by current LES models in neither its kinematic, nonlinear or saturated (i.e. statistically steady) phases.
The decomposition formalism was recently extended to MHD, which led to the identification and quantifcation of the physical processes governing the energy cascade. Here, we follow up on this work and formulate fundamental requirements of physical consistency that MHD LES model must have. Moreover, we devise and test LES models based thereon to provide new physics informed modelling approaches for MHD turbulence and in particular the small-scale dynamo. We find that LES models that explicitly incorporate terms representative of current-sheet thinning and its back-reaction on the flow result in higher dynamo growth rates and nonlinear magnetic energy saturation levels.

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