Geostrophic winds

This describes the geostrophic wind (f = 2a sin 0, where u) is the angular velocity of the Earth and 0 is the latitude). The air moves parallel to the isobars (lines of constant pressure). The geostrophic wind blows counterdockwise around low pressure systems in the northern hemisphere, clockwise in the southern. 

At sea level, for 30°N and S, and a pressure gradient of 1 mbar per 100 km (or 1 x 10 Pa/m), Pg = 15 m/s. In many instances, the observed wind is indeed dose to the geostrophic wind and it is often useful to have maps of isobars so that the transport trajectory can be approximated from V. For a complete derivation and explanation of the geostrophic wind, departures from it, and related topics, the reader is referred to textbooks on meteorology (e.g. Wallace and Hobbs, 1977). 

In the mid-latitude region depicted in Fig, 10-5, the motion is characterized by large-scale eddy transport . Here the eddies are recognizable as ordinary high- and low-pressure weather systems, typically about 10 km in horizontal dimension. These eddies actually mix air from the polar regions with air from nearer the equator. At times, air parcels with different water content, different chemical composition, and different thermodynamic characteristics are brought into contact. When cold, dry air is mixed with warm moist air, clouds and precipitation occur. A frontal system is said to exist. Two such frontal systems are depicted in Fig. 10-5 (heavy lines in the midwest and southeast). 

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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. 

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... 

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 ... 

Figure 2.1 Characteristic features of canopy flows (especially urban canopies). Lo is outer-or meso- (regional) scale on which the canopy affects the dispersion. Lc and L/ are the canopy and inner length scales, respectively. Note that UG is the approach geostrophic wind speed above the boundary layer, UB is the typical wind speed associated with local buoyancy effects, e.g. downslope winds from nearby mountains. Hc is the canopy height and Hc is the standard deviation of building height.

This locally observed climatic behavior of winds at Warnemunde is well reflected (even quantitatively) by coiTesponding geostrophic winds on the regional scale, as shown in... 

Retaining only the Coriolis and pressure gradient terms in (3.23a) and (3.23b), we obtain the geostrophic wind equations ... 

Taking the p derivative of the x component of the geostrophic wind in pressure coordinates, we have... 

This relation shows that horizontal temperature gradients must be accompanied by vertical gradients of geostrophic wind speed. 

Now the thermal wind relation will allow us to calculate the change in geostrophic wind over this layer. The only temperature gradient is in the eastward (x) direction. From (21.22), there is no change ug with altitude. From (21.22), we can express... 

Spatial and Temporal Scales of Atmospheric Processes 40 Appendix 1 Derivation of the Geostrophic Wind Speed 43 References 47... 

Ageostrophic wind Vector difference between measured wind and assumed geostrophic wind. 

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

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