The dynamics of a plasma with magnetized electrons is studied in the t
wo-dimensional approximation. The problem is substantially simplified
by equalizing the Lagrange invariants in a turbulent plasma. This appr
oach makes it possible to generalize the set of Davydov-Zakharov equat
ions in order to describe the plasma ion dynamics with allowance for q
uasisteady electron motion and a nonzero curl of the generalized elect
ron momentum equalized by plasma turbulence. Steady-state self-consist
ent equilibrium spectra of plasma turbulence are obtained. A decrease
in vorticity of electron motion at the front of a shock wave is analyz
ed.