Initial-value approach to study the inertio-gravity waves without the ‘traditional approximation’

An initial-value problem is formulated with linear Boussinesq equations to study the inertio-gravity waves without the “traditional approximation” that is to include a complete effect of rotation. Motions are assumed to be horizontally periodic, but bounded vertically at the top and bottom. The evolution of the vertical structure of wave motions can be calculated from given initial conditions with a one-dimensional finite-difference version of the model with or without forcing/dissipation under a variable thermal buoyancy condition in height.This program is intended to use as a simple numerical laboratory to study the time-evolution of inertio-gravity waves. Examples show for (1) the free oscillations using the normal mode solutions as initial conditions, and (2) the forced oscillations as a simulation of near-inertial currents in the oceans generated by atmospheric storms. An emphasis is made to asses the role of the horizontal component of the earth’s rotation which has been traditionally neglected in the study of inertio-gravity waves.