Wind and atmospheric air currents

The wind is the horizontal movement of air relative to the ground. In the earth’s atmosphere, air can move in any direction, but only the vertical movement is in equilibrium, while other approaches are affected by the gas difference pressure.

The direct cause of wind formation is the uneven atmospheric pressure distribution on the earth’s surface. Air in a region of higher pressure, i.e. more mass, will move to an area of ​​lower pressure, i.e. less mass.

The uneven air temperature distribution is the root cause of the variable pressure distribution. Where the air temperature is high, the density of the air will be low, and with it, the pressure will also be soft and vice versa. Thus, the air temperature difference creates a pressure difference.

The surface on which the pressure is equal at all points is called the isobaric surface. The intersection of the isobaric surface with a horizontal plane is the isobar, i.e. the line of the same pressure.

The barometric pressure from one isometric line to another on the same plane can decrease and increase, creating a pressure difference, the horizontal barometric balance is broken, and the air begins to move from a region of higher pressure to a lower part of lower pressure.

The notion of gradients: the gradient of any physical quantity is its variation in space towards the smallest values ​​per unit distance. The gradient is determined by the amount and by the direction. It is a vector quantity.

Components of the barometric gradient. If the isobaric surfaces are horizontal, the barometric rise will have an upward vertical direction. If they are inclined below α certain angle concerning the horizontal plane, in this case, the barometric gradient vector, OA can be broken down into two components, the vertical component OB and the horizontal component OC. At this moment:

and OB = OA.cosα, OC = OA.Sinα

Since in the authentic atmosphere, the angle α of inclination at isobaric planes is very small, the vertical component OB of the barometric gradient is thousands and tens of thousands of times greater than the component horizontal OC.

But the vertical feature is close and does not affect the horizontal movement of air. Horizontal air movements are caused by the flat part of the barometric gradient and are called horizontal pressure gradients or barometric gradients.

The actual barometric gradient is determined according to isometric maps; its direction is perpendicular to the isobars, from the upper pressure to the lower isobar. Each unit of distance generally corresponds to 100 km or the length of 1° arc of longitude.

The barometric gradient usually does not exceed 1 to 3 mb over 1° meridians, but in extreme storms, it can reach 30 mb over 1° meridians.

Near the equator, the barometric field is vast, and there, the average gradient is only 0.14 mb over 1° meridians; according to him, the winds are very weak.

According to the international system of units (SI), the barometric difference ∆P is usually calculated as N per square meter, and the unit of distance – ∆n is the meter. From there, the barometric gradient:

 

and in CGS                           

 

So the barometric gradient is the force of 1N or applied to a unit volume of 1m³.

All movement occurs under the action of a particular force.

The force that moves air is produced when there is a pressure difference between two points in the air time. This force is called the barometric force gradient.

Barometric force gradient: symbol: G . As mentioned in the section, the barometric angle is the force acting on a unit volume of air (1N/1m³) or (1din/1cm³).

However, in most cases, for convenience of calculation, it is often assumed that the force of the barometric gradient acting on a unit mass rather than a unit volume is considered. Therefore the unit volume of air should be multiplied by its degree (P); from here, we have:

Inside ∆P is the difference in barometric pressure between the two points’ direction of the force gradient toward the reduced pressure.

Dimensional level of

Is the acceleration. The gradient force acting on a gas molecule constantly increases its motion. However, this does not happen because when the air element begins to move, it also begins to be stressed by other forces, such as the force of deflection due to the earth’s rotation, the air’s friction strength, and the centrifugal force.

The deflecting force due to the earth’s rotation is called the Coriolis force. This force is denoted A. Its quantity:

A = 2ωvsinϕ

Inside ω is the angular speed of the earth, v is the wind speed, and ϕ is the geographic latitude. The coriolis force is proportional to the sine ϕ. At the equator, the force A is minimum, equal to 0.

And at the two poles, the force A is maximum, equivalent to 2ω v. It can be understood as follows: in the region close to the equator, the action of the contraction force Coriolis is insignificant, but at high latitudes, especially near the two poles, this force significantly affects the movement of air.

The direction of the force is perpendicular to the direction of air movement. It deviates to the right for the northern hemisphere and the left – for the southern hemisphere.

Centrifugal force, symbol C. If air moves in curved orbits, there is always centrifugal force. For a

gaseous element:

Inside V is the speed of displacement of the gas,
r is the radius of the curved trajectory.

The direction of the centrifugal force is perpendicular to the direction of motion of the gas particles and from the center of the orbit outward.

The airflows moving in the orbit have a microscopic curvature, so the centrifugal force is tiny; sometimes, it can be ignored.

The force of friction, symbol R, restricts the forward motion of gas particles. A magic force is determined by the formula:

Inside k – coefficient of friction, V – air flow, the sign “-” represents the direction of the friction force opposite to the law of air movement. In the free atmosphere, where the density is very low, the friction force = 0.

The geotropic wind is the air movement in the absence of friction in straight and parallel isobars. This is the case of air movement at altitudes above 1000 km, where the density of the air is low, and the force of friction is negligible. In this case, the centrifugal force is 0.

The remaining 2 forces are the pressure gradient and the driving force deviation due to the earth’s rotation. At the initial moment of movement, for the gas molecule to be in equilibrium, the two forces are equal and opposite in direction, ie:

From this, we get the geospatial wind speed: 

If the wind speed calculation: m/s and ∆p/∆l is: , then: 

The wind direction OV is such that it is perpendicular to the deflection force A and leaves it to the right for the northern hemisphere. Thus, the tropical wind has a direction parallel to the isobaric line and goes low pressure on the left in the northern hemisphere and on the right – in the southern hemisphere.

Wind gradientis air movement in curved isobars at altitudes above 1000 m, also known as turbulent geotropic wind. In this case, an element is subjected to three forces: the gradient force, the Coriolis force, and the centrifugal force.

a) – in a cyclone
b) – in the reverse vortex

In the northern hemisphere cyclone, the gradient force is directed in the radial direction towards the center of the low pressure. The remaining two forces: deflection and centrifugal force, are directed outwards. At the initial time for the state of motion of the gas particles to be balanced, we have:

G = A + C(1)

So the wind direction OV should be counterclockwise around the center.

In the counter-vortex (the region of maximum barometric pressure) by analogous analysis, we have:

A = G + C(2)

Wind direction OV is clockwise.

Briefly, in curved isobars, the wind gradient has a tangential direction to the isobar and always leaves low pressure on the left for the northern hemisphere and on the right – the southern hemisphere.

To determine the wind speed in cyclonic and anticyclonic, when substituting the values of the forces: G, A, and C into the above two formulas, we have the following system of quadratic equations according to V:

After solving 2 quadratic equations according to V, we have:

and

From (1′), we see that while the barometric gradient (∆P/∆l) in a cyclone can be infinitely large, the wind speed  is also infinitely large.

And from (2′) – the wind speed in the anticyclone must be finite since the pressure gradient in the anticyclone is limited by a certain amount. Indeed, the elements under the radical sign must be positive, that is:

 infer 

The actual observations show that the above theoretical calculation results are correct, even for the air near the ground.

The movement of air at altitudes below 1000 m is influenced by friction. In the barometric field are straight and parallel isobaric lines, directed, not perpendicular to the barometric gradient (such as at altitudes above 1000 m), which deviates an angle α <90° (Figure 5) from the triangle OBR, we have:

So the angle of deviation depends mainly on the geographical latitude. For winds near the ground, that dependence is calculated as follows:

ϕ	0°	5°	10°	20°	40°	60°	80°
α	0°	32°	52°	68°	78°	81°	82°

The motion of air close to the ground in curved isobars. Figure 6 shows the wind direction in the barometric maximum (reverse vortex) and the barometric minimum (cyclonic) region in the northern hemisphere.

In an anticyclone, the angle of inclination a is between the direction of air movement relative to the gradient direction.

In the vortex, we see that the deflection angle a in cyclonic is more extensive, and in the counter vortex is smaller than the angle a in straight isobars.

From the analysis results, we see that in the vortex, the air currents form spirals that converge to the center near the center, where the barometric gradient is maximal, angle α ~ 90°, the direction of air movement follows the tangent to the isobaric line (innermost) counterclockwise around the center concerning the northern hemisphere and in the same order – the southern hemisphere.