Lecture 7 Forces (gravity, pressure gradient force)

Lecture 7

• Forces (gravity, pressure gradient force)• Imaginary forces (Coriolis, centrifugal)• Force balance and resulting horiz. wind• Geostrophic wind• Gradient wind• Adjustment to balance• The thermal “wind” (change in geostrophic

wind in the vertical)

Wind direction is the direction from which the wind is blowing. Wind direction is expressed in

degrees

Wind speed is expressed in terms of the flagpole

Units: m/s or knots

1 knot = 0.5 m/s

1knot ~ 1 mile/hr

Newton’s law of motion

• A body at rest tends to stay at rest; a body in motion tends to stay in motion, traveling at a constant speed in a straight line.

• A force exerted on a body of mass m causes the body to accelerate in the direction of the applied force.

Force = mass x acceleration

A force has direction and magnitude (it is a vector). Adding two forces is vector addition.

Forces that move the air

• Gravitational force (g=9.8 m/s2)• Pressure gradient force (-1/rho x dp/dx or

--1/rho x dp/dy). It points toward lower p. The pressure gradients causing the wind are horizontal.

• Coriolis force• Centrifugal force• Frictional force

Pressure gradient force pushes from higher to lower pressures

Magnitude depends on value of pressure gradient

PGF

Isobaric chart (height contours on a constant pressure surface)

Pressure (p) as a function of height

Vertical structure in the atmosphere

• What about pressure?• Hydrostatic equation: balance between pressure gradient

force and gravity.– dp/dz = - rho g

• Ideal gas law:– p = rho R T

Let’s go to the board!

z = - H ln (p/p0), where H is scale height and is only constant if T is constant.In other words, p = p0 exp(- z/H)

Next: Coriolis forceEarth’s rotational speed is greatest at the

equator and exactly zero at the poles

Coriolis deflection

Coriolis force deflects moving air to the right in the Northern Hemisp.

Coriolis force deflects moving air to the left in the S. Hemisphere

The magnitude of the Coriolis force (CF) is proportional to the wind speed and sine of latitude

CF= f x V,Where f is2xEarth’s rotation rate xsin(latitude)

Centrifugal force: arises because the trajectory is curved. CENTF= V^2/R, where R (radius of curvature) is positive for cyclones,

negative for anticyclones

Frictional force is proportional to the wind- speed and directed opposite to the wind dir.

FF = -k V (where k describes the roughness)

Summary: The Forces

• Gravity – the strong silent type• PGF arises from pressure gradients

generated by differential solar heating –leads to wind. Only then do the other forces start acting.

• CF, CENTF, FF all depend of V, wind speed.

Atmospheric force balancesSum of forces = mass x acceleration

Balance when the forces add up to zero• Hydrostatic balance in the vertical (gravity

does not cause wind).• Strong horizontal PGF means strong wind• CF changes wind direction not speed• CENTF only acts on curved flow• FF slows down the wind (regardless of

direction).

Geostrophic wind, geostrophic balancePGF + CF = 0

Wind blows counterclockwise around lows (cyclonic wind in cyclones), clockwise

around highs (anticyclones)

Force balance not quite right since we have curved flows

Add centrifugal force

Gradient balance and the gradient wind

Gradient balance results in gradient wind

• Represents balance of three forces• It is an excellent approximation to free

atmospheric flow.• Around highs it is supergeostrophic• Around lows it is subgeostrophic

Adjustment to balance

• The atmosphere tries hard to stay in balance, but it is constantly being pushed away from it.

• The atmosphere adjusts very quickly (in a matter of minutes) to imbalance.

Adjustment to balance with 3 forces: