Amplification of Slow Magnetosonic Waves by Shear Flow: Heating and
  Friction Mechanisms of Accretion Disks
  Propagation of three dimensional magnetosonic waves is considered for a
homogeneous shear flow of an incompressible fluid. The analytical solutions for
all magnetohydrodynamic variables are presented by confluent Heun functions.
The problem is reduced to finding a solution of an effective Schroedinger
equation. The amplification of slow magnetosonic waves is analyzed in great
details. A simple formula for the amplification coefficient is derived. The
velocity shear primarily affects the incompressible limit of slow magnetosonic
waves. The amplification is very strong for slow magnetosonic waves in the
long-wavelength limit. It is demonstrated that the amplification of those waves
leads to amplification of turbulence. The phenomenology of Shakura-Sunyaev for
the friction in accretion disks is derived in the framework of the Kolmogorov
turbulence. The presented findings may be the key to explaining the anomalous
plasma heating responsible for the luminosity of quasars. It is suggested that
wave amplification is the keystone of the self-sustained turbulence in
accretion disks.
