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Equations of Motion Hydrostatic Approximation. September 22. Recall:. x-momentum. y-momentum. z-momentum. continuity. where:. Dissipation/ Turb Mixing Horiz Vert. Total Accel. Pressure Gradient. Coriolis Accel. x-momentum. y-momentum. z-momentum. continuity.
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Equations of MotionHydrostatic Approximation September 22
Recall: x-momentum y-momentum z-momentum continuity where:
Dissipation/ Turb Mixing Horiz Vert Total Accel Pressure Gradient Coriolis Accel x-momentum y-momentum z-momentum continuity
Hydrostatic Equilibrium Typical Scales: with these we can “scale” the equations of motion
The momentum equation for vertical velocity is therefore: and the only important balance in the vertical is hydrostatic: Correct to 1:106
The momentum equation for horizontal velocity in the x direction is
The momentum equation for horizontal velocity in the x direction is The Coriolis balances the pressure gradient, known as the geostrophic balance – similarly for y-direction
Steady Geostrophic Flow:Another way to state equations Steady – No acceleration X (eastward) momentum balance Y (northward) momentum balance Z (vertical) momentum balance - Hydrostatic Continuity – Conservation of Mass or Volume
Hi P Lo P Lo P cf pgf pgf cf ρ=const u,v=const w/z
Pressure Gradient c c fc Pressure Gradient fc fc fc c c Pressure Gradient Lo Pressure Hi Pressure Pressure Gradient Lo Pressure
Dissipation/ Turb Mixing Horiz Vert Total Accel Pressure Gradient Coriolis Accel x-momentum y-momentum z-momentum hydrostatic continuity
Inertial Motion Total Accel Coriolis Accel balances x-momentum y-momentum z-momentum hydrostatic continuity
Dissipation/ Turb Mixing Vertical Coriolis Accel balances x-momentum y-momentum z-momentum hydrostatic continuity Ekman Flow
Geostrophic Motion Pressure Gradient Coriolis Accel balances x-momentum y-momentum z-momentum hydrostatic continuity