The paper is concerned with the vanishing viscosity limit of the
two-dimensional degenerate viscous lake equations when the Navier slip
conditions are prescribed on the impermeable boundary of a simply connected
bounded regular domain. When the initial vorticity is in the Lebesgue space
Lq with 2<q≤∞, we show the degenerate viscous lake equations
possess a unique global solution and the solution converges to a corresponding
weak solution of the inviscid lake equations. In the special case when the
vorticity is in L∞, an explicit convergence rate is obtained