Title: Ocean Modeling EAS 8803
1Ocean 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
2Primitive Equations describing motions of
geophysical flows
3Primitive Equations describing motions of
geophysical flows
4Important Dimensionless Numbers
measuring the sizes of the terms in the equations
Typical Scales
inertial terms
rotation
frictional forces
5Important Dimensionless Numbers
measuring the sizes of the terms in the equations
high turbulent flows
inertial terms
frictional forces
frictional forces
inertial terms
rotation
6Important Dimensionless Numbers
measuring the sizes of the terms in the equations
frictional forces
inertial terms
rotation
7Geostrophic flows or steady state solution
frictional forces
inertial terms
rotation
8Geostrophic flows or steady state solution
9Geostrophic flows or steady state solution
10Geostrophic flows or steady state solution
homogeneous flow
11Properties of Geostrophic homogeneous flows
12Properties of Geostrophic homogeneous flows
13Properties of Geostrophic homogeneous flows
14Properties of Geostrophic homogeneous flows
non-divergent
15Properties of Geostrophic homogeneous flows
if
therefore flow is permittedonly along isobaths
16Properties of Geostrophic homogeneous flows
homogeneous flow
17Properties of Geostrophic homogeneous flows
if pressure only a function of the sea level
18Properties of Geostrophic homogeneous flows
re-write the continuity equation for the layer
velocity
19Properties of Geostrophic homogeneous flows
re-write the continuity equation for the layer
velocity
integrate from bottom to surface
20Properties of Geostrophic homogeneous flows
boundary conditions
where
re-write the continuity equation for the layer
velocity
NEW continuity equation!
21Equations of Geostrophic homogeneous flows
22Equations of Geostrophic homogeneous flows
23Equations of Geostrophic homogeneous flows
describe unsteady motions of a 2D uniform density
layer or of the depth average motion