Explicit solution of atmospheric Ekman flows with some types of eddy viscosity (Q2070996)

The authors consider atmospheric Ekman flows with classical boundary conditions. As in earlier work [\textit{M. Fečkan} et al., Monatsh. Math. 193, No. 3, 623--636 (2020; Zbl 1453.34027)], the eddy viscosity \(k(z)\) denotes the perturbation of the atmospheric reference value. In that work, the authors used a variable change and get a linear nonhomogeneous second order differential equation. They obtain the existence and uniqueness of solutions and certain smooth results. In the present paper, the authors transform the original equation to a first order linear nonhomogeneous differential equation to compute the explicit solution. For a two layer with uniform eddy viscosity in the upper layer and continuous eddy viscosity in the lower layer, they transform the system to a Riccati equation with a initial value on a finite interval. Further, they construct the solution for piecewise-constant eddy viscosity.