Spectral modeling of turbulent flows and the role of helicity

Abstract

We present a new version of a dynamical spectral model for Large Eddy Simulation based on the Eddy Damped Quasi Normal Markovian approximation [1,2]. Three distinct modifications are implemented and tested. On the one hand, whereas in current approaches, a Kolmogorov-like energy spectrum is usually assumed in order to evaluate the nonlocal transfer, in our method the energy spectrum of the subgrid scales adapts itself dynamically to the large-scale resolved spectrum; this first modification allows in particular for a better treatment of transient phases and instabilities, as shown on one specific example. Moreover, the model takes into account the phase relationships of the small-scales, embodied for example in strong localized structures such as vortex filaments. To that effect, phase information is implemented in the treatment of the so-called eddy noise in the closure model. Finally, we also consider the role that helical small scales may play in the evaluation of the transfer of energy and helicity, the two invariants of the primitive equations in the inviscid case; this leads as well to intrinsic variations in the development of helicity spectra. Therefore, our model allows for simulations of flows for a variety of circumstances and a priori at any given Reynolds number. Comparisons with Direct Numerical Simulations of the three-dimensional Navier-Stokes equation are performed on fluids driven by an ABC (Beltrami) flow which is a prototype of fully helical flows. Good agreements are obtained for physical and spectral behavior of the large scales.

Lack of universality in decaying magnetohydrodynamic turbulence

“…Akin to the one presented here, insofar as implementing a reduction of modes at a given Reynolds number, is the numerical algorithm that decimates modes (somewhat arbitrarily) in the dissipation range [57]. Another possibility is the use of large-eddy simulations that compare well against high-resolution direct numerical simulations, such as in [58]. Of a different nature is the Lagrangian averaging approach, or alpha model, which can be viewed as a sort of direct numerical simulation methodology imposing a filter to the small scales by means of a closure consistent with preserving the Hamiltonian nature of the flow, although these averaged equations conserve the ideal invariants using a different norm than L 2 [59].…”

Bayesian inversion for the filtered flow at the Earth's core‐mantle boundary

“…Therefore, focusing on the large scales, and their dynamics, is probably the best solution to study such systems. This approach has been widely followed in the context of hydrodynamic (HD) and magnetohydrodynamic (MHD) turbulence [see Sagaut, 2006;Lesieur, 2008;Baerenzung et al, 2008aBaerenzung et al, , 2008b; Fabre and Balarac, 2011]. To extract the large scales from a given field, one has to filter it.…”

Helical Turbulence in Fluids and MHD

“…Other helical models have been devised recently [21][22][23][24]. For example, in [23], it is shown by assuming a Kolmogorov spectrum valid in the absence of rotation that the classical Smagorinsky model underestimates energy and helicity dissipation by 40 %, although numerically the effect seems smaller.…”

“…In [21,22], the modeling is done based on the EDQNM (Eddy Damped Quasi Normal Markovian) closure. One arrives at a formulation of eddy viscosity and eddy noise which, in addition to the traditional expressions, specify contributions, stemming from the helicity of the flow, for the eddy viscosity and for the eddy noise.…”