# Adiabatic Invariant in Large-Scale Atmospheric Dynamics by Michael V.Kurgansky

By Michael V.Kurgansky

This booklet offers with the most ideas of large-scale atmospheric dynamics at the foundation of adiabatic movement constants. it may be regarded as an creation to the idea of quasi two-dimensional fluid movement concentrating totally on approximately horizontal fluid parcel displacements in a stably stratified compressible fluid. a radical mathematical remedy of the governing equations is coupled with a transparent interpretation of the phenomena studied and followed via examples of genuine meteorological facts research. subject matters comprise an entire set of compressible fluid dynamic equations besides a survey on fluid dynamical conservation legislation utilized in meteorology and atmospheric physics; the derivation of two-dimensional atmospheric types; large-scale flows; isentropic research of large-scale atmospheric tactics; and the foundations of kinetic power sinks and their relation to the strength stability within the surroundings.

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It is the angular momentum conservation law. Dealing with this topic, we arrive at the necessity to use the explicit form of atmospheric governing equations written in spherical coordinates. We start from the mathematical expression for the specific kinetic energy of atmospheric motions relative to the rotation of a spherical coordinate system at a constant angular velocity with the poles situated in the Earth’s geographic poles and with the origin of coordinates in the solid Earth’s center: (1) Here r is the radius, υ is the co-latitude, λ is the longitude and the wellknown expression for spherical metrics (the squared distance between two infinitely closely spaced points) is used (1′) (dl)2=(dr)2+r2(dυ)2+r2 sin2υ(dλ)2 The point above the variables in Equation (1) denotes the material timederivative.

It is assumed that frictional stresses vanish at the top of the atmosphere. The second integral in the right-hand side of Equation (4) can be approximately taken at z=0 and is used in the form −∫∫Tλdσ, where Tλ is the zonal component of frictional stresses on the Earth’s surface. It is usually assumed that where the numerical coefficient cD is determined on the basis of both empirical and experimental data processing and is of the order of 10−3. The values of cD depend on both the stratification of the atmospheric boundary layer and underlying physical surface properties.

1991) which, on the whole, confirm the accuracy of Kurgansky’s (1981) estimate. As it was stated above, in order for the atmosphere to keep positive values of the excessive angular momentum it should have a permanent supply of power W. Based on general physical arguments, Sidorenkov with x>0. (1976) suggested the use of the functional dependence We can try to make the exponent x value concrete based on the concept of unavailable kinetic energy. We estimate its viscous dissipation rate which results from the law of quadratic surface by the formula friction resistance.