Studies of inertio‐gravity waves on midlatitude beta‐plane without the traditional approximation

Abstract

AbstractThe role of the Rossby parameter β due to the meridional variation of the Coriolis parameter f is investigated for inertio‐gravity waves in midlatitudes based on a linear Boussinesq model without the traditional approximation, namely including the role of the horizontal component of the Coriolis vector of the Earth's rotation. Without the β‐effect, it is well established that the non‐traditional Coriolis effects give rise to an additional mode of inertio‐gravity (IG) waves whose frequencies are slightly smaller than the local Coriolis frequency f unlike the traditional IG‐mode whose frequencies are larger than f. The addition of the β‐effect modifies the properties of the sub‐inertial and super‐inertial IG‐modes. These modifications are examined by calculating the model normal modes for a given vertical profile of the buoyancy frequency N. Inclusion of the β‐effect yields the external and internal Rossby modes in addition to the IG‐modes. Presence of the external Rossby mode in this model is a new result, since it does not occur in the traditional version with β nor in the non‐traditional version without β. The normal‐mode properties, including wave frequencies and eigenfunctions, are presented for various values of N. The normal‐mode analysis is complemented by the initial‐value approach to study the evolution of waves generated by forcing. The results of numerical time‐integrations of wave generation in the ocean forced by atmospheric disturbances and by the interaction of tidal flows with bottom topography are presented to reveal a notable role of β for the IG‐waves. Application to atmospheric problems is proposed. Copyright © 2010 Royal Meteorological Society