On the leading-order dynamics of viscous tropospheric flows

We construct a family of solutions to the leading-order equations governing stratified tropospheric flows, showcasing height-dependent density and height-dependent viscosity. Starting from the compressible Navier–Stokes equations for a viscous fluid in rotating spherical coordinates, coupled with the equation of mass conservation, the equation of state and the first law of thermodynamics, we non-dimensionalize the system. By introducing physically motivated parameters, we identify an asymptotic regime in which the existence of solutions can be established via a global bifurcation approach. The resulting three-dimensional traveling-wave solutions capture key tropospheric features, including the observed decrease in density and temperature with altitude. We present our solutions using spherical coordinates, thereby avoiding simplifications such as the flat geometry assumptions of the $f$-plane or $\beta$-plane approximations, which fail to capture key aspects of large-scale flows.