Ocean Modeling EAS 8803

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Ocean Modeling - EAS 8803
Geostrophy and Shallow-water model

• Further scaling of the primitive equations of
  motion
• Dimensionless number and active dynamics
• Steady and homogenous flows (geostrophic flow)
• Properties of geostrophic flows
• Unsteady and homogenous flows (shallow water
  model)

Chapter 7
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Primitive Equations describing motions of
geophysical flows
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Primitive Equations describing motions of
geophysical flows
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Important Dimensionless Numbers
measuring the sizes of the terms in the equations
Typical Scales
inertial terms
rotation
frictional forces
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Important Dimensionless Numbers
measuring the sizes of the terms in the equations
high turbulent flows
inertial terms
frictional forces
frictional forces
inertial terms
rotation
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Important Dimensionless Numbers
measuring the sizes of the terms in the equations
frictional forces
inertial terms
rotation
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Geostrophic flows or steady state solution
frictional forces
inertial terms
rotation
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Geostrophic flows or steady state solution
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Geostrophic flows or steady state solution
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Geostrophic flows or steady state solution
homogeneous flow
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Properties of Geostrophic homogeneous flows
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Properties of Geostrophic homogeneous flows
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Properties of Geostrophic homogeneous flows
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Properties of Geostrophic homogeneous flows
non-divergent
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Properties of Geostrophic homogeneous flows
if
therefore flow is permittedonly along isobaths
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Properties of Geostrophic homogeneous flows
homogeneous flow
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Properties of Geostrophic homogeneous flows
if pressure only a function of the sea level
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Properties of Geostrophic homogeneous flows
re-write the continuity equation for the layer
velocity
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Properties of Geostrophic homogeneous flows
re-write the continuity equation for the layer
velocity
integrate from bottom to surface
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Properties of Geostrophic homogeneous flows
boundary conditions
where
re-write the continuity equation for the layer
velocity
NEW continuity equation!
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Equations of Geostrophic homogeneous flows
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Equations of Geostrophic homogeneous flows
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Equations of Geostrophic homogeneous flows
describe unsteady motions of a 2D uniform density
layer or of the depth average motion