1112.2037 (Mikhail I. Ivanov)
Mikhail I. Ivanov
Free internal waves in polytropic atmospheres are studied (polytropic
atmosphere is such one that the temperature of gas linearly depends on
altitude). We suppose gas to be ideal and incompressible. Also, we regard the
atmosphere of constant height with the "rigid lid" condition on its top to
filter internal waves. If temperature, density and pressure of such undisturbed
atmosphere do not depend on latitude and longitude then the internal waves are
harmonic with apriori unknown eigenfrequencies, the problem permits separation
of variables and reduces to the system of two ODE's. The first ODE (the
Laplace's tidal equation) is analyzed by author earlier. The second ODE
determines the vertical structure of the waves to be considered and has
analytical solution for polytropic atmospheres. There are 6 dimensionless
numbers, 2 for the Laplace's tidal equation and 4 for the vertical structure
equation. The solution is a countable set of the eigenfrequencies and
eigenfunctions of the vertical structure equation; every
eigenfrequency/eigenfunction corresponds to its own countable set of the
eigenfrequencies and eigenfunctions of the Laplace's tidal equation. Parametric
analysis of the problem has been done. It shows that there exists the solution
weakly depending on altitude-temperature variations and the atmosphere's height
for parameters modelling the Earth's troposphere (with the "rigid lid" between
the troposphere and the tropopause). The natural periods of internal waves have
been obtained for this case.
View original:
http://arxiv.org/abs/1112.2037
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