# Accession Number:

## ADA018013

# Title:

## A Semi-Spectral Numerical Model for Forced, Vertically Propagating Planetary Waves. Part I. Application of the Model to Linear Diurnal and Semi-Diurnal Atmospheric Thermal Tides.

# Descriptive Note:

## Memorandum rept.,

# Corporate Author:

## NAVAL RESEARCH LAB WASHINGTON D C

# Personal Author(s):

# Report Date:

## 1975-10-01

# Pagination or Media Count:

## 44.0

# Abstract:

A three dimensional, semi-spectral, numerical model is developed for forced, vertically propagating planetary waves and is used to simulate atmospheric diurnal and semi-diurnal thermal tides. The physical model is the same as the one developed by Lindzen 1971 for tides, except that the equation normally used for height is used as the vertical coordinate instead, and an initial value approach is used to obtain the steady state instead of the eigen-value approach used by Lindzen 1971. In the semi-spectral method all the variables are expanded in Fourier series in the E-W direction, and are specified on a mesh of equally spaced grid points in N-S direction. The vertical direction is divided into a number of layers with variable thicknesses. The free modes generated by inperfect initial conditions are dissipated by using a transient Rayleigh friction decaying in time. Reflections of the vertically propagating waves from the top boundary are avoided by absorbing them in a sponge layer, in which Rayleigh friction increase exponentially with height. The model is integrated by using a two step predicted-corrector leapfrog-trapezoidal time integration scheme, and is driven by the diurnal and semi-diurnal heating function given by Lindzen 1971. Comparision of the numerical results with the analytical solutions of Lindzen 1971 show that the model reproduced the tidal oscillations very well.

# Descriptors:

# Subject Categories:

- Atmospheric Physics
- Numerical Mathematics