By

Gp Capt (Dr) B Nandi

Simplified horizontal/ two dimensional motion can be described by the following equation.

Where **V** is the wind velocity, f Coriolis parameter, ρ air density, P pressure. **k** vertical unit vector. First term is acceleration of air parcel, second term is Coriolis force and third term is pressure gradient force.

For diagnostic purpose, a balanced flow is assumed. That is acceleration is zero. In mathematical term

In this case wind is termed as geostrophic wind **V**_{g}. It gives first guess of wind given a pressure gradient. The cross product of k vector indicate that Coriolis force is perpendicular to geostrophic wind and is to the right of wind in northern hemisphere and pressure gradient force is to the left of wind to balance the Coriolis force.

The equation (1) of motion can be rewritten with the help of equation(3) as

The deviation of actual wind **V** from geostrophic wind **V**_{g} is called **ageostrophic **wind (**V**_{a})

It ca be seen that acceleration is perpendicular to ageostrphic wind **V**_{a} . this means that acceleration cannot change the magnitude of ageostrophic wind but can change the direction. While changing the direction it can change the magnitude of actual **V**

**V**_{a }will rotate as long as wind is accelerated. So the wind is expected to be minimum at A and Maximum at B. A motion which is a combination of translation and rotation will follow a cycloid. Since the geostrophic wind is larger than its **ageostrophic** component, the trajectory will be like a contracted cycloid.

The period of rotation is 2π/f ,which happens to be known as inertial period. The value is approximately 24 hours at 30 degree latitude and 16.5 hours at 45 degree latitude.

During daytime there is a constant contact between the air nearest the ground and higher up, through turbulent exchange. For a steady wind regime, there is a balance amongst the Pressure Gradient Force, Coriolis force and Frictional Force. This balance is possible at the** ageostorphic** wind circle when wind vector is tangent to the circle (t=0, in Fig ) so that acceleration of **ageostrophic** wind and frictional force is opposite to each other. This balance state is mostly observed for steady wind regime.

At sunset, when the temperature in the lowest 100m or so falls, a thermally stable layer, called an inversion, is created. This cuts off the contact between the wind nearest to the ground and the wind above the inversion. It leaves just the pressure gradient force and the Coriolis force, to work. In the absence of frictional force acceleration becomes imbalanced and starts rotaing the ageostrophic wind. Ageostrophic wind starts rotating trying to achieve balance. Wind speed starts increasing till the rotation reaches B (in Fig 2) when wind is maximum. This takes little more than **one quarter of inertial period** that is little more than 6 hours at 30 degree latitude. More time is needed at 20 degree latitude. This maximum wind is supergeostrophic and happens during small hours over tropical region leading to nocturnal jet.

To get nocturnal jet it is necessary that there is a creation of inversion layer after sun set. This happens most of the time after sunset and more so when there is warm advection little over ground.

Over the coastal area where the wind is parallel to coast there is another effect to augment the wind. The thermal gradient increases at coast due fall in temperature over land. So a channel of wind close to coast increases above ground at some level due increase in thermal wind. Few examples