Paper detail

On hydrostatic approximation by R.I. Nigmatulin and L.F. Richardson's equation

The theorem given in 'Equations of Hydro-and Thermodynamics of the Atmosphere when Inertial Forces Are Small in Comparison with Gravity' (2018) is wrong, since the solutions of the system of Navier-Stokes equations do not converge to the solutions of the system of hydrostatic approximation equations, when the vertical acceleration approaches zero. The main consequence is that the scales given in the paper are not suitable for application of hydrostatic approximation. The correct asymptotics should be given by the traditional hydrostatic parameter H/L, where H and L are the vertical and horizontal scales of motion. Also scale analysis of the L.F. Richardson's equation for vertical velocity in hydrostatic approximation is not correct.