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There are no acoustic waves in a hydrostatic model of the atmosphere. Among the other waves, the most fast ones are the Lamb waves that propagate horizontally. Their speed is comparable with the speed of sound. Its exact value depends on the choice of the basic state of the atmosphere which is used to linearize the hydrothermodynamic equations. It is a state with a polytropic stratification where the temperature decreases linearly with altitude at a constant lapse-rate G that corresponds to the actual conditions of the Earth's troposphere. It is assumed that all the atmosphere has a politropic stratification, i.e., it is finite with altitude because G >0. We suppose also that the stratification is statically stable or neutral . The vertical profile of the eigenmodes in the polytropic model is described with the help of the Bessel functions. Therefore, the dispersion equation that determines the eigenvalues of the problem, and consequently an oscillation spectrum, is transcendental. The highest propagation speed (the front speed) corresponds to the minimum solution of this equation, i.e., the minimum eigenvalue. When , the minimum eigenvalue can be calculated using the development of the solution into the series by powers of the small difference . It is proved that a simple analytical formula, obtained by keeping in the series only the two first terms, gives a good approximation not only of this limit but of the opposite limit when G=0 , too. A comparison of the results obtained by the analytical formula and using the complete dispersion equation shows a good precision of the formula in the whole range of .

Velocidade de propagação da frente de distúrbios no modelo hidrostático da atmosfera politrópica