Convergence is defined as

the increase of mass within a given layer of the

atmosphere

divergence is

the decrease of mass within a given layer of the atmosphere

conditions for convergence to take place

the winds must result in a net inflow of, air into that layer

For convergence to take place, the winds must result in a net inflow of, air into that layer. This type of convergence is generally associated with

low‐pressure area

where convergence of winds toward the center of the low results in

an increase of mass into the low and an upward motion

Divergence

Winds in this situation produce

a net flow of air outward from the layer

Winds in this situation produce a net flow of air outward from the layer. We

associate this type of divergence with

high‐pressure cells

Winds in this situation produce a net flow of air outward from the layer. We associate this type of divergence with high‐pressure cells, where the flow of air is directed

outward from the center, causing a downward motion

The natural coordinate system describes

motion as normal or tangential to the radius of curvature of the flow

how is the natural coordinate system represented

Rather than isobars,

flow is depicted as streamlines, which represent the instantaneous direction of the wind, and isotachs, the instantaneous wind speed

We can construct natural coordinates with

unit vectors

We can construct natural coordinates with unit vectors

n and , where

n is the normal vector and

s is the tangential vector

k is directed vertically upward

Ψ (angle) as the angle that the tangent of the curve makes with a fixed direction, and

the radius of curvature of the flow

Note thatΨis defined as

positive in the counterclockwise direction and R > 0 for counterclockwise flow

In the natural coordinate system the direction of the unit vectors is

not constant as in the Cartesian system

In the natural coordinate system the direction of the unit vectors is not constant as in the Cartesian system, but is determined by

the direction of the wind

In natural coordinate system, the horizontal divergence can be expressed as:

explain the components

(the first term)

The first term, the directional divergence(convergence),represents the change in

angle with movement (or change in isobar spacing) across the flow.

explain the components

(the first term)

The first term, thedirectional divergence(convergence),representsthechangein

angle with movement (or change in isobar spacing) across the flow. occures when

winds spreading outward (inward) at a constant speed, which represents a net

outflow (diffluence), or inflow (confluence)ofair.

what is the condition of directional divergence and convergence

speed is constant in both cases

show directional divergence and convergence

the second term

thespeed divergence(convergence), occurs when downstream winds are faster (slower) than upstream winds for the same isobar spacing. More air is moving out (in) this area than moving in (out).

condition of speed convergence and divergence

same isobar spacing

show speed divergence and convergence

According to the geostrophic relationship, which shows that

if the isobar spacing Δx remains constant, the wind speed doesn’t change

Divergence of geostrophic winds equation and graph

Also, if the isobar spacing becomes wider downstream (...................), the wind

speed should

divergence

decrease (convergence)

if the winds are purely geostrophic, the two terms

cancel each other out exactly and there will be no vertical motions.

Thus, if the winds are purely geostrophic, the two terms cancel each other out exactly and there will be no vertical motions.

This shows that

the divergence of geostrophic winds is always zero, which can be proven mathematically also.

Divergence of ageostrophic winds

where ....................................... the winds are described as ageostrophic

there are vertical motions

In areas, where there is ascent or descent, there is

mass being added to (or removed from) the airflow from some other level, which results in convergence (or divergence).