Viscous Boundary Layer For Transonic Equilibrium

Transonic equilibria have been studied in the past in a number of papers, see e.g. [1-4]. They occur in tokamak geometry when the core region of the plasma has slow (with respect to the poloidal sound speed, C_sp = C_sB_p/B) poloidal rotation, while the edge has supersonic (v_p > C_sp) rotation, a realistic condition in H-mode tokamak plasmas. In the single-fluid MHD model transonic equilibria are characterized by a radial discontinuity in density, pressure and velocity. Physical intuition dictates that including fluid viscosity in the problem will relax the discontinuity to a sharp-gradient layer between the slow- and fast-flowing regions. In this work, we start examining the properties of the viscous boundary layer at the flow transition in transonic equilibria. We observe that the system is similar to a fluid-dynamic viscous flow between two rigid plates. We point out analogies and differences with the classical Blasius and Falkner-Skan solutions for viscous boundary layers and investigate the effect of compressibility.

[1] L. Guazzotto, R. Betti, J. Manickam, S. Kaye, Physics of Plasmas 11 2, 604-614

[2] L. Guazzotto, R. Betti, Physics of plasmas 12 5, 056107

[3] L. Guazzotto, E. Hameiri, Physics of Plasmas 21 2, 022512

[4] L. Guazzotto, R. Betti, S.C. Jardin, Physics of Plasmas 20 4, 042502