Baroclinic velocity

An analysis of the recent observation data [30,31] shows that baroclinic Rossby waves that are generated off the eastern coasts in the northern parts of the Pacific and Atlantic oceans in a period of about a year represent their dominant non-stationary dynamical response to the annual cycle of the atmospheric forcing in the latitudinal range from 10-15° to 45-50°N. In so doing, their mean phase velocities (0.02-0.03 ms 1 at 40-45°N) are higher than the theoretical values (about 0.01 ms-1). A similar situation is observed in the Black Sea as well [27]. In [32], several reasons of this phenomenon were listed such as the interaction with more large-scale non-stationary processes, topographic and nonlinear effects, and insufficient duration and spatiotemporal resolution of the observation data. 

A large long-living anticydonic eddy centered at 43°N and 34°E, in the area between the western and eastern cyclonic gyres (approximately abeam the southern extreme of the Crimea), was detected by the hydrographic survey of 1984 [6]. It was formed in September 1984 as a result of coalescence of two other anticyclones formed owing to baroclinic instability of the RC and to detachment of its meanders in the north (from the Crimean coast) and in the south (from the Turkish coast near Sinop). Its diameter exceeded 100 km, the maximum of the orbital geostrophic velocity was 25-45 cm/s, and the rate of the westward displacement was about 1 cm/s. Density and salinity anomalies related to this eddy were traced down to a depth of 1000 m and temperature anomalies were followed down to 300 m. 

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. 

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. 

---