Pressure Gradient Force

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Pressure Gradient Force

• Remember from Physics

Calculate the pressure at a depth of 10m. Assume
a density of s35.
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Use of Hydrostatic Equation

• P ?gZ
• Size of x-dir pressure gradient force 1 dp
• 
  ? dx
• How can we get a horizontal PGF in a 1-layer
  fluid?

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How do you get a pressure gradient in the water?
If h110m, ?h1m and ?x10km, what is the
Fp? Assume s35.
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1 layer model
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1)Balance of Forces in the x,y - dir

• Geostrophic Balance
• Pressure Gradient Coriolis
• 0 fv - 1 dp 0 - fu - 1 dp
• ? dx ? dy

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Equations of Motion (4)

• Coming back to the equations of motion

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Geostrophic Balance

• If
• Only important forces are Pressure Gradient and
  Coriolis
• Ocean is in Steady State (no acceleration)

So Find the difference in pressure between two
level points. How do you do that?
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How do you measure ?P?
(i is the surface slope)
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Along the Hill
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1)Balance of Forces in the x,y - dir

• 0 fv - 1 dp 0 - fu - 1 dp
• ? dx ? dy

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Concept Problem

• Which way does the current flow if height is
  increasing towards the South?
• West?
• North?

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Gulf Stream
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SeaSat data
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Sea Surface Height
(NASA JPL)
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Geostrophic Balance (2)
Back to
and since
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Geostrophic Currents

• In x-dir
• fv 1 dp
• ??dx
• Assuming the current is uniform density (1
  layer)
• fv gi

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Geostrophy Problem

• A certain ocean current has a height change of
  1.1 m over 100 km when measured from N to S at
  40S. How fast and in what direction is the
  current flowing?

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Gulf Stream Temperature
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Gulf Stream Density
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Two Layer Geostrophic Flow

• Velocity of lower layer (2), where i1 is the
  surface slope, i2 is the interface slope, and r1
  and r2 are the upper and lower densities,
  respectively.

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Total PGF in bottom layer is the combination of
both surface and isopycnal slopes. There are 2
PGFs acting in the bottom layer

• P.G.F. due to Surface Slope gtgt g i
• P.G.F. due to Isopycnal Slope gtgt g(r2-r1)i2
• r2

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The 2 PGFs acting in the bottom layer are
opposing each other since the slopes are opposite

• In the bottom layer
• fv g i1 - g i2

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What if we had 3 layers?

• In the bottom layer
• fv g i1 - g i2 - g i3
• g g(r3-r2)
• r3

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Looking downstream H pressure on the right
(N.Hemi.)
Low Pressure

• High Pressure

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Cyclonic Anticyclonic
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Geostrophic flow
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Pressure Map
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Dynamic Topography