Rossby length scale

Generally, the appropriate representation of baroclinic flows in the model requires the resolution of the baroclinic Rossby radius as the typical horizontal length scale. If this resolution is not achieved, baroclinic processes are governed by friction and advection, while the important contribution of barotropic waves is hidden in parameterizations. 

Rossby radius of deformation Length scale that is equal to c/l/l, where c is the wave speed in the absence of rotation effects and / is the Coriolis parameter caused by Earth s rotation. 

Rossby radius of deformation Fundamental parameter for rotating fluids subject to gravitational restoring forces. It is defined as the gravity-wave phase speed divided by the Coriolis parameter. When a disturbance displaces the atmosphere away from an equilibrium state, the ratio of the Rossby radius to the horizontal length scale of the disturbance determines the character of the adjustment toward equilibrium. 

To motivate the geostrophic approximation, we invoke a scale analysis approach. Assume frictional forces can be neglected, and the atmospheric motions have a characteristic horizontal length-scale, L, and velocity scale, U. Recalling the definition of the advective derivative operator D/Dt, we find that the magnitude of the acceleration terms, Dw/Dt and Du/Dt in Eqs. (9.2.20) and (9.2.21), is 17 /L, provided the magnitude of the time scale of the motion is greater than or equal to the advective time, L/U. The terms proportional to tan 0 are of order U /a, and the Coriolis terms are of order /(/. If L < a, then the ratio of each of the terms to the Coriolis term is less than or comparable to the Rossby number, defined as... 

U, L, H are the characteristic velocity, length and layer thickness scales. L/j is the Rossby deformation radius. The Rossby number measures the importance of rotation on the flow, the Burger number measures the stratification in the atmosphere via the Brunt-Vaisala frequency. As it is known, the atmospheric structure in the giant planets in the solar system is in bands. This structure evolves from shallow-water turbulence. Two dimensional turbulence is characterized by an inverse energy cascade—this means a transfer from small to large scales. 

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