Rossby parameter

Abstract: The 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

Abstract: In this paper, we study the problem of the change of Rossby parameter and the topography in a two-layer fluid. Based on the traveling wave method and the perturbation method, the Rossby wave amplitude is obtained to satisfy the homogeneous KdV equation and the homogeneous mKdV equation, which describe the evolution of the amplitude of solitary Rossby waves. The efiects of Rossby parameters and topography on Rossby wave are generalized.

Abstract: For the stratified fluids, based on the quasi-geostrophic potential vorticity equation, an inhomogeneous modified Korteweg-de Vried (mKdV) equation including topographic forcing is derived by employing the perturbation method and stretching transforms of time and space. With inspection of the evolution of the amplitude of Rossby waves, it is found that Coridis effect, topography effect and Vaisala-Brunt frequency are the important factors, that induce the solitary Rossby wave, and it is induced even though the basic stream function has not a shear. Assuming that there is a balance between nonlinear and topographic effects, an inhomogeneous mKdV equation is derived, the results show that the topography and Rossby waves interact in the stratified flows. The inhomogeneous mKdV equation describing the evolution of the amplitude of solitary Rossby waves as a function of the change of Rossby parameter β ( y ) with latitude y , topographic forcing and the Vaisala-Brunt frequency is obtained.

Abstract: Applying the scale analysis method, analysis of the Rossby parameter β effect which couldn't be neglected in the strong vortex is presented. It is shown that the action of Rossby parameter β can generate the vortex Rossby waves in strong cyclonic vortices with the constant basic-state angular wind. The presence of the vortex Rossby waves generates the asymmetry of the vortex weakening the vortex axisymmetric structure. If one considers the radial variation of the basic-state angular wind, then the dispersion relation of the vortex Rossby waves contains the radial gradient term of the basic-state angular wind's vorticity and β term. The vortex Rossby waves always propagate outward in the presence of the radial shear of the basic-state angular wind, while the effect of the β term, which varies with the azimuthal angel θ, disperses the energy of the vortex system asymmetrically.