Geostrophic velocity

The estimates of the climatic mean annual parameters of the MRC in the sections normal to the northeastern coast of the Black Sea presented in [17] yielded a distance of its core from the shore about 40 km, a full width of the current (with respect to velocity values of 0.02 m s-1) of 75 km, a penetration depth of 275 m, a maximal geostrophic velocity of 0.31 ms-1, and a volume transport of 1.3 x 106 m3 s x. These estimates are of the same order of magnitude as shown in Fig. 4a within the velocity interval to 0.20 m s x. This allows us to suggest a certain geographical universality (self-similarity) of the MRC profile normal to the coast. 

In July 1992, off the Turkish coast, a slightly meandering MRC stream was observed its core was approximately 30 km wide and had maximal velocities in the upper layer 50-75 m thick up to 0.50 ms-1 [22], In the layer from 75 to 125 m, the most rapid velocity drop was observed (by 0.25 ms-1). At a depth of 200 m, the values decreased down to 0.05-0.10 m s-1. Toward the coast, the velocities decreased by 0.20 m s 1 per 10 km, the rate of their decrease in the seaward direction was fourfold lower. The maximal geostrophic velocities with respect to the 500-dbar level were 0.20 ms-1 lower than the ADCP velocities, which points to significant ageostrophic effects in the MRC dynamics. 

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. 

Although the vertical features of Figure 15 were common during our sampling period, they rarely persisted for more than 1 or 2 days. They were then replaced by totally different vertical structures and concentrations of both copepods and chlorophyll by as much as an order of magnitude. Such variability was consistent with the observed variability of the geostrophic velocity estimates. 

The section inverse method is based on the geo-strophic principle, which for a given pair of hydro-graphic stations allows calculating the geostrophic velocity Vg(z) perpendicular to the connecting line between the two stations as function of depth A reference velocity b has to be added to the geostrophic velocity to obtain the absolute flow velocity... 

This describes the geostrophic wind f- 2co sin 4>, where oj is the angular velocity due to the rotation of the Earth and 0 is the latitude). The air moves parallel to the isobars (lines of constant pressure). The geostrophic wind blows counterclockwise around low-pressure systems in the northern hemisphere, clockwise in the southern. 

For typical meteorological conditions the maximum diffusivity can be expected to be in the range 0.5-5 m sec". The magnitude is considerably smaller than the equivalent values encountered under strongly unstable conditions. A limitation of the above formulation is the need for knowledge of the geostrophic wind velocity Vg. If the assumption Vg == 8m., discussed in the previous section, is employed, then Eq. (9.25) can be written in the form... 

Because Earth does rotate, however, another set of forces also acts on the fluids these geostrophic forces are the consequence of the fact that Earth s surface forms an accelerating reference frame. Relative to Earth s surface, all fluid motions are deflected perpendicular to their velocity by the Coriolis force in the Northern Hemisphere, fluid motions are deflected to the right, and in the Southern Hemisphere, to the left. A parcel of fluid in motion in the Northern Hemisphere, under the influence of only the Coriolis force, experiences acceleration equal to... 

Here, U and V are horizontal flow velocity components of the geostrophic wind Ug directed, respectively, along Ox and Oy axes, and W is its vertical Oz-component. Nothing is changed in Oy-direction in the two-dimensional case (1.5) and also in Oz-direction in the one-dimensional case (1.4). vr is the effective kinematical turbulence viscosity that varies over Oz and Ox in the general case, vT = vT(x,z). The Coriolis force f = k- V,Ug-U] linearly depends on the local velocity but needs to be accounted for only in tall forest canopies. 

Boundary conditions for the one-dimensional (1.4) and two-dimensional (1.5) models are evident. They are the no-slip condition on the surface and a prescribed velocity value (often, the geostrophic wind velocity Ug) sufficiently far away of the surface ... 

It is illuminating to study the time evolution of a river plume as an initial value problem. It can be shown that the current pattern is governed by a geostrophically adjusted eddy confined to the buoyancy patch (near field) and a coastally trapped flow that develops in the wake of a Kelvin wave (far field). Behind the front of the first Kelvin wave mode, undercurrents are set up. Although the velocities of the flow forced by the momenrnm of the river mnoff are small enough to justify a linear treatment, there are important nonlinear effects owing to the advection of density, which limits the validity of the linear analytical models. In particular, the structure of the near field in front of the river mouth is dominated by the response to the buoyancy flux associated with the river discharge. 

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