scostep 2010 (stp12) - Leibniz-Institut für Atmosphärenphysik an der ...

STP12 Abstracts
Berlin, 12 - 16 July 2010
SCOSTEP Symposium 2010
A Review on Lamb`s Atmospheric Oscillations Using Initial Value Problem Approach
De Andrea González Angel
Departamento de Física. Escuela Politécnica Superior. Universidad Carlos III de Madrid. Av.
Universidad 30. 28911 Leganés (Madrid)
Waves at a surface of discontinuity in the atmosphere is analysed in 1910 by Lamb, who derived,
using normal mode approach, an analytical dispersion relation for a discrete mode (surface mode).
Lamb examined the case of waves propagated along a horizontal plane where the equilibrium
temperature is discontinuous. For simplicity, the upper region and the lower region are considered
incompressible.
In this work, in order to show how the modes appear in the response of a surface discontinuity to an
initial perturbation, we consider the initial value problem (IPV). The main difference from the
standard analysis is that solutions to the linearized equations of motion which satisfy general
conditions are obtained in terms of Fourier-Laplace transform of the hydrodynamics variables .
These transforms can be inverted explicitly to express the fluid variables as integrals of Green´s
functions multiplied by initial data. In addition to discrete mode (surface mode), a set of continuum
modes due to a branch cut in the complex plane, not treated explicitly in the literature, appears.