Lecture 3: the equations of motion, the Coriolis force, and

the geostrophic balanceAtmosphere, Ocean, Climate

DynamicsEESS 146B/246B

Equations of motion and the basic force balances

• Review of the equations of motion• The physics behind the Coriolis force• The geostrophic balance

The equations of motion

Acceleration = (Sum of forces)/mass

Coriolisforce

Pressure gradient

force

Friction

•Vertical momentum equations: hydrostatic balance

•Horizontal momentum equations in a frame rotating about the vertical at angular velocity

latitude

•Flow in the ocean isnearly incompressible

CONTINUITY EQUATION

The Coriolis Force•Northern Hemisphere

•Southern Hemisphere

•The Coriolis force causes moving objects to veer to the right (left) in the Northern (Southern) Hemisphere.

The physics behind the Coriolis force

Viewed in non-rotating frame, water is moving in solid body rotation

HIGHHIGH LOW

Surface circulation in the Pacific

L=3500 km

~400 days

Geostrophic balance

The effect of the Earth’s rotation: the generation of geostrophic currents

Northern Hemisphere

Floats on the sea-surface

The effect of the Earth’s rotation: the generation of geostrophic currents

Northern Hemisphere

•In the Northern Hemisphere, water moves in a clockwise direction around highs in the free surface.

ANTICYCLONE

Floats on the sea-surface

The effect of the Earth’s rotation: the generation of geostrophic currents

Northern Hemisphere

•In the Northern Hemisphere, water moves in a counter-clockwise direction around lows in the free surface.

CYCLONE

The effect of the Earth’s rotation: the generation of geostrophic currents

Southern Hemisphere

•In the Southern Hemisphere, water moves in a counter-clockwise direction around highs and clockwise around lows in the free surface.

ANTICYCLONE CYCLONE

Thermal wind balance at the subpolar front of the Japan/East Sea

Thermal wind balance at the subpolar front of the Japan/East Sea

density zonal geostrophic flow

Thermal wind balance at the subpolar front of the Japan/East Sea

zonal geostrophic flowmeasured zonal flow