arXiv subjects

Alban Pothérat

Publications and source records attributed to Alban Pothérat.

40 records · Page 3Linked to original sources

arXiv2014

Spectral Direct Numerical Simulations of low Rm MHD channel flows based on the least dissipative modes

We put forward a new type of spectral method for the direct numerical simulation of flows where anisotropy or very fine boundary layers are present. The mean idea is to take advantage of the fact that such structures are dissipative and that their presence should reduce the number of degrees of freedom of the flow, when paradoxically, their fine resolution incurs extra computational cost in most current methods. The principle of this method is to use a functional basis with elements that already include these fine structure so as to avoid these extra costs. This leads us to develop an algorithm to implement a spectral method for arbitrary functional bases, and in particular, non-orthogonal ones. We construct a basic implementation of this algorithm to simulate Magnetohydrodynamic (MHD) channel flows with an externally imposed, transverse magnetic field, where very thin boundary layers are known to develop along the channel walls. In this case, the sought functional basis can be built out of the eigenfunctions of the dissipation operator, which incorporate these boundary layers, and it turns out to be non-orthogonal. We validate this new scheme against numerical simulations of freely decaying MHD turbulence based on a Finite Volume code and it is found to provide accurate results. Its ability to fully resolve wall-bounded turbulence with a number of modes close to that required by the dynamics is demonstrated on a simple example. This opens the way to full blown simulations of MHD turbulence under very high magnetic fields, which were until now too computationally expensive, as the computational cost of the proposed method, in contrast to traditional methods, does not depend on the intensity of the magnetic field.

physics.flu-dyn↗

arXiv2012

Three-dimensionality in quasi-two dimensional flows: recirculations and barrel effects

A scenario is put forward for the appearance of three-dimensionality both in quasi-2D rotating flows and quasi-2D magnetohydrodynamic (MHD) flows. We show that 3D recirculating flows and currents originate in wall boundary layers and that, unlike in ordinary hydrodynamic flows, they cannot be ignited by confinement alone. They also induce a second form of three-dimensionality with quadratic variations of velocities and current across the channel. This scenario explains both the common tendency of these flows to two-dimensionality and the mechanisms of the recirculations through a single formal analogy covering a wide class of flow including rotating and MHD flows. These trans-disciplinary effects are thus active in atmospheres, oceans or the cooling blankets of nuclear fusion reactors.

physics.flu-dyn↗

arXiv2010

Formation mechanism of hairpin vortices in the wake of a truncated square cylinder in a duct

We investigate the laminar shedding of hairpin vortices in the wake of a truncated square cylinder placed in a duct, for Reynolds numbers around the critical threshold of the onset of vortex shedding. We single out the formation mechanism of the hairpin vortices by means of a detailed analysis of the flow patterns in the steady regime. We show that unlike in previous studies of similar structures, the dynamics of the hairpin vortices is entwined with that of the counter-rotating pair of streamwise vortices, which we found to be generated in the bottom part of the near wake (these are usually referred to as base vortices). In particular, once the hairpin structure is released, the base vortices attach to it, forming its legs, so these are streamwise, and not spanwise as previously observed in unconfined wakes or behind cylinders of lower aspect ratios. We also single out a trail of Omega-shaped vortices, generated between successive hairpin vortices through a mechanism that is analogous to that active in near-wall turbulence. Finally, we show how the dynamics of the structures we identified determine the evolution of the drag coefficients and Strouhal numbers when the Reynolds number varies.

physics.flu-dyn↗

arXiv2010

Direct Numerical Simulations of Low-$Rm$ MHD turbulence based on the least dissipative modes

We present a new spectral method for the Direct Numerical Simulation of Magnetohydrodynamic turbulence at low Magnetic Reynolds number. The originality of our approach is that instead of using traditional bases of functions, it relies on the basis of eigenmodes of the dissipation operator, which represents viscous and Joule dissipation. We apply this idea to the simple case of a periodic domain in the three directions of space, with an homogeneous magnetic field in the $\mathbf e_z$ direction. The basis is then still as subset of the Fourier space, but ordered by growing linear decay rate $|λ|$ (\emph{i.e} according to the \emph{least dissipative modes}). We show that because the lines of constant energy tend to follow those of constant $|λ|$ in the Fourier space, the scaling for the the smallest scales $|λ^{\rm max}|$ in a forced flow can be expressed using this single parameter, as a function of the Reynolds number as $\sqrt{|λ^{\rm max}|}/(2πk_f)\simeq 0.5\Rey^{1/2}$, where $k_f$ is the forcing wavelength, or as a function of the Grashof number $\Gr_f$, which gives a non-dimensional measure of the forcing, as $|λ^{\rm max}|^{1/2}/(2πk_f)\simeq 0.47\Gr_f^{0.20}$. This scaling is also found consistent with heuristic scalings, and which we are able to numerically quantify as $k_\perp^{\rm max}/k_f\simeq 0.5 \Rey^{1/2}$ and $k_z^{\rm max}/k_f\simeq 0.8k_f \Rey/Ha$. Finally, we show that the set of least dissipative modes gives a relevant prediction for the scale of the first three-dimensional structure to appear in a forced, initially two-dimensional turbulent flow. This completes our numerical demonstration that the least dissipative modes can be used to simulate both two- and three-dimensional low-Rm MHD flows.

physics.flu-dyn↗