Calculation of steady turbulent flow of an electrically conducting fluid in a channel in a transverse magnetic field.

*(English. Russian original)*Zbl 0538.76116
Sov. Phys., Dokl. 28, 320-322 (1983); translation from Dokl. Akad. Nauk SSSR 269, 1336-1340 (1983).

The Hartmann channel flow problem is analyzed for turbulent MHD flow. The classical Kármán similarity hypothesis is used to define an eddy diffusivity as:\(\nu_ T/\nu =[0.53[Re| du/dy|^ 3/(du/dy)]^ 2]^{3/4}\). Calculations are carried out for the two-dimensional Hartmann flow under this assumption and velocity profiles and wall shear stresses obtained and compared to experiment. It is concluded from the results that the classical Kármán theory works well for this type of MHD flow. This is a surprising result and contrary to the customarily held belief that MHD turbulence must be treated differently. However, the comparison with experiment is striking and the conclusion of this work appears to be important and any worker in the field of MHD turbulence should find it interesting and worthy of consideration. However, the effect of the magnetic field on the critical Reynolds number is not investigated but it is explained that the suppression of the critical number by magnetic effects is not contradicted by their results.

Reviewer: W.Hughes