1 research outputs found
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.Comment: Comments on the paper by R.I.Nigmatulin: The equations of hydro- and
thermodynamics of the atmosphere with low inertia forces compared with
gravity, published in Journal of Applied Mathematics and Mechanics, 82,
472-484, 2018. link.springer.com/article/10.1134/S0015462818040201, (also in
Russian dx.doi.org/10.31857/S003282350000205-5). Submitted to the same
journa