THREE-DIMENSIONAL MODEL OF GENERATION OF ATMOSPHERIC INTERNAL GRAVITY WAVES INDUCED BY INHOMOGENEITIES IN GRAVITATIONAL FIELD

Abstract

In modern models of geophysical fluid dynamics, the gravitational field is usually taken uniform and defined by the single parameter. It is known, however, that the average gravitational force at the earth’s surface is superimposed upon by a broad spectrum of gravitational force anomalies (GFAs). This is due mainly to inhomogeneities of the distribution of mass in the Earth’s crust. Variations in the gravitational force are certainly very small in magnitude compared to the average value. It is important, however, that such inhomogeneities generate a gravitational-force component tangential to earth's ellipsoid. In plane mesoscale models using Cartesian coordinates (an f-plane or a β-plane), this means that additional volume inhomogeneous forces with a horizontal component have to be taken into account. The dynamics of the atmosphere is quite sensitive to such components. Recently we showed that in the highly anomalous regions GFAs, in principle, can lead to appreciable dynamic effects, in particular, the generation of regular currents and internal gravity waves (IGW). But this analysis has so far been limited to two-dimensional problems (that is, the effects of two-dimensional GFAs were considered). In this paper, the next step is taken: in the linear approximation, IGW generation in the atmosphere is analytically studied under the action of three-dimensional GFAs on the atmospheric flow above a flat horizontal underlying surface. The terms in the expressions obtained for velocity components and pressure perturbations can be divided into two categories. One of them directly describes flow around equipotential surfaces. These terms do not contain waves propagating with vertical component and slowly decay with altitude on the same scales as the gravity anomaly. Other terms describe internal gravity waves, whose phase velocity is directed downward and the group velocity, upward. The amplitude of these waves in the velocity field exponentially increases with altitude. Taking into account the three-dimensional geometry of GFAs in the three-dimensional formulation can lead to a noticeable change in results in comparison with the two-dimensional model considered earlier. In addition to the appearance of horizontal motions perpendicular to the background flow, the wavelength and the vertical flux of wave energy can markedly vary: GFAs elongated along the stream can lead to smaller perturbations in amplitude than the “ridge” oriented perpendicular to the background flow. The analytical expression is derived; it shows that the mentioned energy flow is proportional to the background buoyancy frequency, to the squares of the GFAs amplitudes, and to the background flow velocity. According to numerical estimates, this flow can be noticeable, although it is usually much inferior to IGW sources associated with the relief.