Note: Wind can be exact geostrophic motion only if the height contours are parallel to the latitude circle.
The following picture shows how the forces balance out in geostrophic flow at 500mb in the northern hemisphere. Imagine the flow is moving from west to east, thereby not changing latitude.
PGF
f0
Vg
fo + Df
coriolis
Notice that the flow is parallel to the lines of constant geopotential height, as they should be by the definition of the geostrophic wind equation. To reiterate, since there is no friction, there is no cross-contour flow, and therefore, no acceleration of the flow.
Question: If the geopotential hight counters are parallel to longitude circle, does geostrophic approximation is valid?. ( Instructor can give introduction about β-effect)
The geostrophic wind is generally a good approximation to the actual wind in extra tropical synoptic-scale disturbances. However, in some of the special cases discussed later, this is not true.
Note that although the actual speed V must always be positive in the natural coordinates, Vg, which is proportional to the height gradient normal to the direction of flow, may be negative, as in the “anomalous low”. The instructor can recall this while discussing Gradient Wind equation…
Thermal Wind
Jet Stream and Vorticity
The continuity Equation
The continuity equation of fluid mechanics states that the rate at which density decreases (increases) in each infinitesimal volume element of fluid is proportional to the mass flux of fluid parcels flowing away from (into) the element, written as
Dines compensation Principle and Vertical Motion
The net mass convergence into a column of air (from the surface to the tropopause) is generally much smaller than the convergence at any particular level. This is because convergence at one level tends to be offset by divergence at another. This is known as Dines compensation. Mathematically this principle is explained by the continuity of air:
r (¶ u/¶ x + ¶ v/¶ y) = ¶ (rw)/¶ z kg m-3 s-1
Where (u,v,w) are the 3D velocity components in directions (x,y,z) and r(z) is the air density. The term (¶u/¶ x + ¶ v/¶ y) is the horizontal divergence; convergence occurs when this term is negative. An integration of this equation with height, subject to zero vertical motion as boundary condition at the top and bottom, yields:
ò r (¶ u/¶ x + ¶ v/¶ y) dz = 0
i.e. mass divergence at some levels must be offset by convergence at others
Physically, compensation occurs because convergence in the lower troposphere implies that air in the atmospheric column must ascend. However, very little air escapes through the tropopause into the stratosphere, and the height of the tropopause does not change much. Therefore the uplifted air must spread out somewhere below the tropopause. Therefore, low-level convergence implies divergence somewhere aloft in the troposphere, i.e. Dines compensation
Various configurations are possible, but the two most relevant ones are shown below. Low-level convergence (divergence) and atmospheric ascent (subsidence) occur along with the counterpart at a higher level. This principle applies to the convective scale: thunderstorm updrafts gather air in the boundary layer and rapidly lift it into the upper troposphere. A thunderstorm anvil dramatically displays the divergence aloft.
Dines compensation implies a relationship between convergence (assessed from surface winds) and vertical motion. Synoptic vertical motion is far too slow to measure directly (it is around 0.01 m/s, up to 0.1 m/s in vigorous frontal disturbances), yet it is essential to weather, since ascent leads to clouds and precipitation, whereas descent leads to clear skies.
Trajectories and Streamlines
The natural coordinate system used in balanced flow, s(x,y,t) was defined as the distance along the curve in the horizontal plane traced out by the path of an air parcel. The path followed by a particular air parcel over a finite period of time is called the trajectory of the parcel. Thus the radius of curvature R of the path ‘s’ referred to in the gradient wind equation is the radius of curvature of a parcel trajectory. In practice, R is often estimated by using the radius of curvature of a geopotential height contour, as this can be estimated easily from the synoptic chart. However the height contour are actually streamlines of the gradient wind (ie., lines that are everywhere parallel to the instantaneous wind velocity).
Instructor can show some of the real time stream line data from IMD website to the trainees.
Deepening and Intensification of Cyclone
Although deepening and intensification of systems are often considered as synonyms, but they are different. A cyclone may be deepening while weakening (cyclolysis), or it may be intensifying (cyclogenesis) and filling (Fig below). While deepening refers only to change of pressure height, intensification refers to the increase of the height gradient or the increase of circulation with time. Maximum values and the time of occurrence for these parameters characterize cyclones and their life cycles.
Deepening refers to geopotential height drop at the center of the systems. Therefore, negative values are expected gpm per 6 h (the time resolution). On the other hand, intensification is expressed by positive values, which are expressed in gpm per 100 km and 6 h
(Instructor can give some examples of cyclones such as Aila or Orisa Super cyclones to understand the difference b/w deepening and intensification of cyclones.)