Nonlinear theory of slow dissipative layers in anisotropic plasmas

The solar coronal plasma is a well-known example of a plasma with strongly anisotropic dissipative coefficients. The main dissipative processes in the solar corona are strongly anisotropic thermal conductivity and viscosity. Ruderman and Goossens [Astrophys. J. 471, 1015 (1996)] developed a linear theory of driven slow resonant waves in plasmas with strongly anisotropic viscosity and thermal conductivity. Linear theory shows that in the slow dissipative layer the amplitudes of oscillations become very large for high Reynolds and Pecklet numbers, so that nonlinearity may be important. In the present paper the nonlinear behavior of driven magnetohydrodynamic waves in the slow dissipative layer in plasmas with strongly anisotropic viscosity and thermal conductivity is studied. The nonlinear governing equation for wave variables in the dissipative layer is derived. The nonlinear connection formulae, which are extensions of the linear connection formulae first introduced in the theory of resonant magnetohydrodynamic waves by Sakurai, Goossens, and Hollweg [Solar Phys. 133, 127 (1991)], are derived.