Rossby radius

In the zone of the MRC, the proportions of the contributions of the mean motion and of the synoptic and inertial variabilities to the total kinetic energy were 50 40 10, which is close to the estimates based on the data of moored buoy observations (see above). Thus, in the Black Sea, the relative contribution of the kinetic energy of synoptic fluctuations is sixfold lower than in the World Ocean. In the opinion of the authors of [25], this may be related to the small sizes of the sea and to the correspondingly high ratio R /L, where llL is the baroclinic Rossby radius and L is the half-width of the basin. In the Black Sea, R /L = 0.1, while in the World Ocean R /L = 0.01. At R /L > 1, no baroclinic mechanism for eddy formation cross section be implemented. 

The arbitrary longshore shape of the wave described by G x — ci) remains unchanged while propagating along the coast and can be of a localized or a sinusoidal pattern. The Kelvin wave is trapped in a coastal wave guide along the coast and is not felt offshore of this guide with the width determined by the Rossby radius. Barotropic Kelvin waves have a wide Rossby radius of the order of = 0(100 km) and baroclinic waves a Rossby radius of the order of R = 0(5 km) in the Baltic Sea. 

Moreover, the Kelvin wave can control the water exchange between two basins connected by a channel. The basic physics of this process can be reduced to the Rossby adjustment process in a channel of uniform depth and uniform width. This problem was considered theoretically by Gill (1976) as an initial problem with a steplike sea level distribution in the channel. The results are similar for abarotropic and a baroclinic two-layer flow however, the sea level elevation must be replaced by the elevation of the interface and the barotropic long wave phase velocity by the baroclinic phase velocity, which is much smaller than the barotropic velocity. This implies that the baroclinic Rossby radius is more than one order of magnitude smaller than the barotropic radius. 

In case of a channel with a width 2W much larger than a Rossby radius, the sea level equals the initial high sea level of the areax < 0 along the shore aty = W/2 and the initial low sea... 

Kelvin waves require a flat-bottomed ocean, so the coastal boundary needs to be a vertical cliff. In a real ocean, there is a topographic transition from the coastline to the central plain areas of the basin. We denote this transition region as shelf. If the horizontal scale of the shelf is small compared with the internal Rossby radius, the Kelvin wave is the most important... 

When the shelf scale is comparable with the internal Rossby radius, wave motions normal to the shelf induce vertical motions due to the inclined bottom that generate internal pressure gradients. Therefore, a separation between barotropic and baroclinic modes is not possible anymore and these modes are denoted as mixed or hybrid modes that have been called coastally trapped waves. To evaluate their dispersion relations with respect to frequency and longshore wave number and their modal structure in the vertical plain normal to the coast, a two-dimensional eigenvalue problem must be solved numerically (Brink, 1991). The nodal lines of the velocity modes of these hybrid modes are inclined with respect to the sea surface in contrast to the baroclinic modes in case of a flat-bottomed ocean. 

When the width of the shelf is much larger than the baroclinic Rossby radius, the mixed modes become quasi-barotropic (Huthnance, 1978) and stratification follows the barotropic motions of the waves passively without having an impact on the properties of these waves, which are denoted as Continental Shelf Waves (CWS). 

In the Baltic Sea, the offshore scale for the transition of topography from the coast to the plain areas of the basins is commonly much larger than the baroclinic Rossby radius. Therefore, CTW can be used to analyze the dispersion and modal structure of sea level variations and quasi-geostrophic currents trapped at the basin rim. Some basins do not have well established plains, therefore, in these basins, the eigenvalue problem must be solved for the whole basin diameter, for example, the Eastern Gotland Basin. The CTW structures of both coasts splice each other in the center of the basin. Hence, CTWs are an effective mechanism for the communication between the rim and the center of the corresponding (e.g., Gotland) basin. 

A critical issue is the proper choice of the horizontal and vertical model resolution. The baroclinic Rossby Radius is a typical horizontal scale for eddies and wavelike processes. If this scale, that varies in the Baltic from less than 1 km to 7 km (Fennel et al., 1991), is not resolved, adjustment processes by waves are filtered out and the model dynamics is... 

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. 

FIGURE 3 Dispersion diagram for the midlatitude )0-plane (a) inertia-gravity waves, (b) Rossby waves. (Note different scales along the ordinates.) The frequency a and zonal wavenumber k are nondimensionalized by fo and the Rossby radius Lr, respectively. Curves are labeled by the index n corresponding to meridional wavenumbers In = for n = 0, 1, 2, 3. See text for additional details. 

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