atmospheric motion soee1400: lecture 7. plan of lecture 1.forces on the air 2.pressure gradient...

Atmospheric Motion

SOEE1400: Lecture 7

Plan of lecture

1. Forces on the air

2. Pressure gradient force

3. Coriolis force

4. Geostrophic wind

5. Effects of curvature

6. Effects of friction

7. Upper level charts.

SOEE1400 : Meteorology and Forecasting 2


Isobars at 4mb intervals

Steady flow• The air is subject to Newton’s second law

of motion: it accelerates when there is an unbalanced force.

• When the forces are balanced, the airflow is steady.

• There are 3 forces which influence horizontal airflow:– Pressure gradient force (p.g.f.)– Coriolis force– Frictional drag



The Pressure Gradient Force

Horizontal pressure gradients are the main driving force for winds.

where P is pressure, is air density, and x is distance. The force is thus inversely proportional to the spacing of isobars (closer spacing stronger force), and is directed perpendicular to them, from high pressure to low.

The pressure force acts to accelerate the air towards the low pressure.

Pressure gradient force = - 1 dP dx

1000 mb

1004 mb

pressureforce


The coriolis force is an apparent force, introduced to account for the apparent deflection of a moving object observed from within a rotating frame of reference – such as the Earth.

The coriolis force acts at right angles to both the direction of motion and the spin axis of the rotating reference frame.

V

Coriolis Force

Axis of spin


Movies … see web page.


VFc

1 2 3

4 5 6

Coriolis Force on a Flat Disk


Earth is a sphere – more complex than disk: horizontal and vertical components to the coriolis force.In the atmosphere, we are concerned only with the horizontal component of the coriolis force. It has a magnitude (per unit mass) of:

2Ω V sin = f VΩ = angular velocity of the earthV = wind speed = latitude

f = 2Ω V sin = “Coriolis parameter”

This is a maximum at the poles and zero at the equator, and results in a deflection to the right in the northern hemisphere, and to the left in the southern hemisphere.


Geostrophic Balance

1000 mb

1004 mb

Vg

FP

Fc

Steady flow tends to lie parallel to the isobars, so that the pressure and coriolis forces balance. This is termed

geostrophic balance, and Vg is the geostrophic wind speed.


Steady flow in the absence of friction

Since the coriolis force balances the pressure force we have:

N.B. air density changes very little at a fixed altitude, and is usually assumed constant, but decreases significantly with increasing altitude pressure gradient force for a

given pressure gradient increases with altitude geostrophic wind speed increases with altitude.

Pressure gradient force = coriolis force

1 dP dx

= 2Ω Vg sin

Geostrophic wind speed is directly proportional to the pressure gradient, and inversely dependent on latitude.

For a fixed pressure gradient, the geostrophic wind speed

decreases towards the poles.


Geostrophic wind scale (knots)


Geostrophic flow is a close approximation to observed winds throughout most of the free atmosphere, except near the equator where the coriolis force approaches zero.

Departures from geostrophic balance arise due to:

– constant changes in the pressure field

– curvature in the isobars

Significant departure from geostrophic flow occurs near the surface due to the effects of friction.


Centripetal Acceleration

Motion around a curved path requires an acceleration towards the centre of curvature: the centripetal acceleration.

LOW

V

FP

Fc

Centripetalacceleration

The required centripetal acceleration is provided by an imbalance between the pressure and coriolis forces.

V is here called the gradient wind

For a low, the coriolis force is less than the pressure force; for a high it is greater than pressure force. This results in:

LOW: V < geostrophic (subgeostrophic)

HIGH: V > geostrophic (supergeostrophic)

HIGH

V

FP

Fc

Centripetalacceleration


Effect of friction

1000 mb

1004 mb

V

FP

Fc

The direction of the drag force (Fd) is approximately opposite to the wind direction.

The drag force exactly balances the coriolis and pressure gradient forces.

The wind speed is lower than the geostrophic wind.

FP

VgFd


Effect of FrictionFriction at the surface slows the wind. Turbulent mixing extends effects of friction up to ~100 m to ~1.5 km above surface.

Lower wind speed results in a smaller coriolis force, hence reduced turning to right.

Wind vector describes a spiral: the Ekman Spiral. Surface wind lies to left of geostrophic wind

• 10-20 over ocean• 25-35 over landThe wind speed a few metres above the surface is ~70% of geostrophic wind over the ocean, even less over land (depending on surface conditions)

Geostrophic flow away from surface

Vg

Ekman Spiral


Surface winds cross isobars at 10-35

Upper-level charts


Ground level

1000m

2000m

3000m

4000m

700 hPa surface

850 hPa surface

On a 2000 m chart, the pressure here is lower than to each side.

The height of the 850 hPa surface is also low.

Higher pressure

Lower pressure

“Height of a pressure surface Pressure on a height surface”

Example500 hPa height is

shaded (with black contour). 500hPa winds circulate around the low.

Surface pressure is the white lines.


500 hPa geostrophic wind


Global Circulation


For a non-rotating Earth, convection could form simple symmetric cells in each hemisphere.


Coriolis force turns the air flow. Stable mean circulation has 6 counter-rotating cells – 3 in each hemisphere.Within each cell, coriolis forces turn winds to east or west. Exact boundaries between cells varies with season.This is a grossly simplified model, circulations are not continuous in space or time. Notably the Ferrel cell is highly irregular in reality.

Ferrel Cell

Polar Cell


Summary• Balance of pressure and

coriolis forces results in geostrophic flow parallel to isobars

• Curvature of isobars around centres of high and low pressure requires additional acceleration to turn the flow, so the resulting gradient wind is:– supergeostrophic around

HIGH– subgeostrophic around

LOW

• Friction reduces wind speed near surface

• Lower wind speed reduced coriolis turning, wind vector describes an Ekman Spiral between surface and level of geostrophic flow

• Surface wind lies 10-35 to left of geostrophic wind, crossing isobars from high to low pressure.


• Difference in solar heating between tropics and poles requires a compensating flow of heat

• Coriolis turning interacts with large scale convective circulation to form 3 cells in each hemisphere

• This 6-cell model is a crude over-simplification of reality, but accounts for major features of mean surface winds, and the Hadley circulation is a robust feature which is well observed.