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SUMMARY:The absence of bottleneck in the Lagrangian-averaged model for inc
 ompressible magnetohydrodynamics - Pouquet\, A (NCAR)
DTSTART:20081001T090000Z
DTEND:20081001T093000Z
UID:TALK13858@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:In order to better understand the small scale dynamics of geop
 hysical and astrophysical flows with huge Reynolds numbers\, numerical mod
 eling is an invaluable tool but it needs to be assessed against experiment
 al and observational data as well as direct numerical simulations (DNS) at
  high resolution. In this context\, we study the properties of the Lagrang
 ian-averaged magnetohydrodynamics (MHD) $lpha-$model\, LAMHD hereafter\; 
 this model can be viewed as a norm-preserving filtering of the primitive M
 HD equations. Among its advantages is the fact that the LAMHD formulation 
 preserves the basic properties of MHD\, e.g. the Alfv'en theorem of flux c
 onservation\, and invariants such as the total energy\, the cross-correlat
 ion between the velocity and magnetic field and magnetic helicity\, albeit
  in a modified (H_1) form.\n\nLAMHD has been tested in two and three space
  dimensions and is found to behave satisfactorily\, for example reproducin
 g the threshold for dynamo action at moderately low magnetic Prandtl numbe
 rs P_M\, as encountered in the liquid core of the Earth\, the solar convec
 tion zone or in liquid metals in the laboratory (where P_M is the ratio of
  viscosity to magnetic diffusivity). Here we demonstrate that\, for the ca
 se when there is initially quasi-equipartition between the velocity and th
 e magnetic field and with a magnetic Prandtl number equal to unity\, the m
 odel reproduces well both the large-scale and small-scale properties of tu
 rbulent flows\; in particular\, it displays no increased (super-filter) bo
 ttleneck effect with its ensuing enhanced energy spectrum at the onset of 
 the sub-filter-scales. This is in contrast to the case of the neutral flui
 d in which the Lagrangian-averaged Navier-Stokes $lpha-$model is somewhat
  more limited in its applications because of the formation of spatial regi
 ons with no internal degrees of freedom and subsequent contamination of su
 per-filter-scale spectral properties.\n\nThe LAMHD model is thus shown to 
 be capable of leading to large reductions in required numerical degrees of
  freedom for a given set of kinetic and magnetic Reynolds number. Specific
 ally\, we find a reduction factor of approx 200 when compared to a direct 
 numerical simulation on a large grid of 1536^3 points at the same Taylor R
 eynolds number approx 1700. The DNS having been stopped at the peak of dis
 sipation of total energy\, the run was pursued using LAMHD. We thus also r
 eport on preliminary explorations of the decaying dynamics of that high Re
 ynolds number MHD flow at late times using the LAMHD model. 
LOCATION:Seminar Room 1\, Newton Institute
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