Anisotropic viscous dissipation in three-dimensional magnetic merging solutions

Department of Mathematics, University of Waikato, PB 3105, Hamilton, New Zealand

Received: 4 February 2009
Accepted: 23 April 2009

Abstract

Aims. We consider viscous and resistive energy dissipation in the flaring solar corona.

Methods. We compute energy dissipation rates, associated with magnetic merging in three dimensions. We examine an exact 3D solution for steady magnetic merging in a viscous resistive incompressible plasma. We use the Braginskii stress tensor to model viscous effects and derive scalings for the resistive and viscous dissipation rates. We evaluate the dissipation rates for typical parameters of solar active regions.

Results. Large-scale advective flows required to sustain resistive current sheets are shown to be associated with significant viscous losses. For plausible dimensionless resistivities (inverse Lundquist numbers), whether classical η ≤ 10^-14 or anomalous η ≤ 10^-8, viscous loss rates greatly exceed the resistive loss rates of the current layer and can approach flare-like rates of 10²⁸ erg s^-1 .