Recitation Geostrophic Balance Thermal Wind Effect of Friction

Geostrophic Balance Pressure gradient force balances Coriolis force L H Flow is counterclockwise around low pressure systems (cyclones) and clockwise around high pressure systems (anticyclones) In Northern Hemisphere

Geostrophic Balance Valid for small Rossby number: R o = U/fL <<1 Coriolis term exactly balances pressure gradient term Also can be written in pressure coordinates relating the Coriolis term to height gradients on a constant pressure surface

Addition of Friction Friction slows the speed of the flow The Coriolis force depends on the speed of the flow, so this reduces the strength of the Coriolis force L In Northern Hemisphere

Flow around Highs and Lows Low Pressure: flow is counter clockwise and toward the low High Pressure: flow is clockwise and away from the high L H In Northern Hemisphere

Terminology Cyclonic : flow around low pressure (or low height) systems Anticyclonic: flow around high pressure (or high height systems) Northern Hemisphere – cyclonic flow (flow around Lows) is counterclockwise. – anticyclonic flow (flow around Highs) is clockwise Southern Hemisphere – cyclonic flow (flow around Lows) is clockwise. – anticyclonic flow (flow around Highs) is counterclockwise

Mass Conservation Since the surface flow converges towards lows and diverges from highs, by mass conservation this induces vertical motions. L H z RISING AIR SINKING AIR

Thermal Wind: Geostrophic Balance + Hydrostatic Balance Temp decreases as go North => zonal wind must decrease with pressure => zonal wind increases with height Temp increases as go East => meridional wind must decrease with pressure => meridional wind increases with height This is thermal wind balance for an ideal gas in pressure coordinates.

Forms of Thermal Wind Equation General Form For ideal gas atmosphere in pressure coordinates For ocean with equation of state

Sfc wind 500 hPa wind Sfc pressure 500 hPa heights Motion of surface low In Northern Hemisphere