GEOPHYSICAL RESEARCH, 2019, vol. 20, no. 3, pp. 36-44. https://doi.org/10.21455/gr2019.3-3

UDC 532.51: 551.511.3: 551.513: 551.558

Abstract  References   Full text (in Russian)

ON ANALOGY BETWEEN THERMAL AND “GRAVITY” MESOSCALE ATMOSPHERIC CIRCULATIONS

L.Kh. Ingel(1,2,3), A.A. Makosko(2,3)

(1) RPA “Typhoon”, Obninsk, Russia

(2) Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Moscow, Russia

(3) Interdepartment Center of Analytical Research in Physics, Chemistry and Biology at the Presidium of the Russian Academy of Sciences, Moscow, Russia

Abstract. In a number of previous papers by the authors, it has been shown that inhomogeneities of gravity field can, generally speaking, affect the wind field, leading to the occurrence of currents in the atmosphere. In this paper, the authors compare linear stationary models of mesoscale flows associated with thermal inhomogeneities of the underlying surface and with inhomogeneities of gravity field. For both types of problems, linear perturbations are considered in a stably stratified semi-bounded volume of a medium rotating around a vertical axis. The Boussinesq approximation is used; it is assumed that the medium density depends linearly on the perturbations of the potential temperature. The defining parameters of the problems under consideration are analogues of the Rayleigh and Taylor numbers: , . Here N is the buoyancy frequency; ν, κ are the coefficients of kinematic viscosity and thermal diffusivity respectively; f is the Coriolis parameter (double angular velocity of background rotation); k is the horizontal wave number of disturbance (inverse horizontal scale of inhomogeneities). There is considered the limiting case that is characteristic for mesoscale disturbances in the atmosphere: . The solutions found transparently demonstrate the similarity of flows caused in the stratified atmosphere by inhomogeneities of the gravity field and circulations over thermal inhomogeneities of the underlying surface. The ratio between the amplitudes of such flows is found. Inhomogeneities of the gravitational field with amplitude G () lead to the emergence of flows with approximately the same amplitude and structure as the horizontal heterogeneities of the heat flux on the underlying surface () with the amplitude . Here ρ0, c are the background density and heat capacity respectively, γ>0 is the background vertical gradient of the potential temperature, g is the mean gravity.

Keywords: mesoscale atmospheric flows, thermal inhomogeneities of the underlying surface, inhomogeneities of the gravitational field, linear disturbances, analytical model.

References

Gershuni G.Z., Zhukhovitskii E.M., Konvektivnaya ustoichivost' neszhimaemoi zhidkosti (Convective stability of incompressible fluid), Moscow: Nauka, 1972.

Gill A.E. Atmosphere-Ocean Dynamics, New York: Academic Press, 1982.

Ingel L.Kh. and Makosko A.A., Generation of the vortex movement in the atmosphere due to gravity inhomogeneities, Izv. Atmos. Ocean Phys., 2018, vol. 54, no. 6, pp. 536-541.

Lin Y.-L., Mesoscale Dynamics. Cambridge: Cambridge University Press, 2007.

Makosko A.A. and Panin B.D., Dinamika atmosphery v neodnorodnom pole sily tyazhesti (Dynamics of the Atmosphere in the Inhomogeneous Field of Gravity), St. Petersburg: RGGMU, 2002.

Pedlosky J. Geophysical Fluid Dynamics. Springer-Verlag, 1987.

Perestenko O.V. and Ingel L.Kh., Linear theory of nonsteady-state convection in a stably stratified rotating medium above a thermally nonuniform surface, Izv. Atmos. Ocean Phys., 1990, vol. 26, no. 9, pp. 666-673.