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This article provides a comprehensive analysis of geostrophic and real winds, including the physics of geostrophic wind, pressure gradient field, and prediction of wind patterns. It also discusses the nature of geostrophic wind and the variation of wind profiles at lower altitudes.
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Analysis of Geostrophic & Real Winds P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Description of Wind Generated & Finally Available…
Physics of Geostrophic Wind • Winds result from any influence that creates differences in atmospheric pressure. • On Earth, global pressure field are influenced by several factors: • First, the Coriolis effect. • Second, the warming influence of ocean currents and atmospheric capture of solar heat. • The earth receives 1.74 1017watts of power from Sun. • About 1 to 2 per cent of the energy coming from the sun is converted into wind energy. • This is about 50 to 100 times more than the energy converted into biomass by all plants on earth. • Third, convection cells : the Hadley cell, the Ferrel cell, and the Polar cell.
The Pressure Gradient Field Primary Wind is the horizontal movement of air in response to differences in pressure. Primary wind is defined as,
GDEs for Geostrophic Winds Low Pressure High Pressure
Geostrophic Wind Component form: Vector form: with the Coriolis parameter f = 2 sin. The geostrophic wind describes the dominant balance between the pressure gradient force and the Coriois force.
Prediction of Simple Wind Patterns • The knowledge of the pressure distribution at any time determines the geostrophic wind. • This is very true for large-scale motions away from the equator. • The geostrophic wind becomes the total horizontal velocity to earth surface within 10–15% in mid latitudes.
Nature of Geostrophic Wind : Final Remarks • The direction of the geostrophic wind is parallel to the isobars. • The closer the isobars are together, the stronger the magnitude of the geostrophic wind | vg | (isotachs increase). • The geostrophic wind vg is a good approximation of the real horizontal wind vector, especially over oceans and at upper levels. • Why?
Wind at Lower Altitudes • At heights in excess of 500m or so above the earth ‘s surface , horizontal air motions proceed in a largely geostrophic maner. • These motions are essentially unretarded by friction known as planetary boundary layer. • Between an altitude of around 50m and the surface , the speed of the wind reduces more and more rapidly towards zero . • This sub-region is often termed the ‘Surface Boundary Layer ‘. • The region between 500m and 50m is in effect a zone of transition between the smooth geostrophic flow in the free atmosphere and flow of an essentially turbulent nature near the ground.
Variation of Wind Profiles @ Lower Altitudes At lower altitudes the thickness of boundary layer is a strong function of surface roughness. Urban locale Sub-urban locale Rural locale
Development of Models of Mean Wind Velocity Profile • Develop simple experimental test rigs. • Measure wall shear stress. • Define wall friction velocity using the wall shear stress by the relation Define non-dimensional boundary layer coordinates.
Approximation of velocity distribution for a fully turbulent 2D Boundary Layer
Approximation of velocity distribution for a fully turbulent 2D Boundary Layer The vertical wind shear ( 𝜕𝑢/𝜕𝑧 ) is found to be largest near the surface itself and to decrease progressively at higher altitudes
Inverse Law of Wind Shear • Plotting of 𝜕u/𝜕𝑧 against 1/z invariably produces a straight line relationship , so that in general : Where the parameter A , although independent of z , is a function of wind speed and of the nature of the surface in question. On integration of equation Where B is the appropriate constant of integration . This relationship is of the form found , in the laboratory , to describe the shape of the wind profile in a fully developed turbulent boundary layer .
Aerodynamic Roughness Length • The nature and characteristics of airflow close to the earth‘s surface is described in terms of turbulent boundary layer theory • The aerodynamic rourghness length , z0 , is defined as the height where the wind speed becomes zero. • The word aerodynamic comes because the only true determination of this parameter is from measurement of the wind speed at various heights. • Given observations of wind speed at two or more heights , it is easy to solve for z0 and friction velocity u*. • z0 is a fuction of roughness elements on the earth’s surface. • Such as caused by changes in the height and coverage of vegetation, manufacture of fences , construction of houses , deforestationetc.
A Model for Mean Wind Speed Profile U* = friction velocity (m/s) = von Karman constant, approximately equal to 0.4 z = elevation above ground level (m) z0= empirical surface roughness length (m)
