Geostrophic forces

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... 

When the isobars are essentially straight, the balance between the pressure gradient force and the coriolis force results in a geostrophic wind parallel to the isobars. 

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. 

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. 

Fig. 12.20 Results of a steady-state simulation with a coupled model for ocean circulation, water chemistry and sediment diagenesis. Major control parameters and forcings comprise a large-scale geostrophic flow field, primary productivity controlled by nutrient advection, export production and sediment accumulation, as well as CO input by weathering and CO -exchange with the atmosphere, a) Export production (mol m yr ), b) CaCO export production (both mol m yr ), c) wt% CaCOj, d) CaCO mass accumulation rate (g cm kyr ) (from Archer et al. 1998).

The approach to the geostrophic equilibrium for an air parcel starting from rest, accelerated by the pressure gradient and then affected by the Coriolis force, is shown in Figure 21.5,... 

From the standpoint of air motion, the atmosphere can be segmented vertically into two layers. Extending from the ground up to about 1000 m is the planetary boundary layer, the zone in which the effect of the surface is felt and in which the wind speed and direction are governed by horizontal pressure gradients, shear stresses, and Coriolis forces. Above the planetary boundary layer is the geostrophic layer, in which only horizontal pressure gradients and Coriolis forces influence the flow. 

The direction of winds in the geostrophic layer is determined by horizontal pressure gradients and Coriolis forces. As we have discussed, an air parcel moving southward in the Northern Hemisphere as a result of pressure gradients is accelerated toward the west by the Coriolis force. We can actually compute the wind speed and direction at any latitude as a function of the prevailing pressure gradient if we assume that only pressure and Coriolis forces influence the flow. 

Geostrophic wind Horizontal wind in which the Coriolis and pressure-gradient forces are balanced. 

For most meteorologically significant motions in the extratropical stratosphere, the Coriolis force is nearly balanced by the pressure gradient. This type of flow is called geostrophic. Under such conditions, the longitudinally averaged east-west wind is given by (10). With the aid of the hydrostatic equation (7), this can also be written as... 

Geostrophic wind Wind resulting from a balance between the horizontal components of the pressure gradient and Coriolis forces. 

The geostrophic wind considers a balance between the horizontal pressure gradient and Coriolis forces. A less restrictive balance is one that includes the centripetal acceleration terms in the horizontal momentum equations. The balance that follows is not obtainable by a rigorous... 

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