1. Cursos Internacionales
de Postgrado en
Sensoramiento Remoto
Remote Sensing
of Winds
R. A. Brown 2003 U. ConcepciÓn

2. The Basics
R. A. Brown 2003 U. ConcepciÓn

3. Newton’s Parcel m a F  V v/t F = The Fluid Parcel  V v/t F = o
V v/ s
V v/ s
 V v/t
F =
R. A. Brown 2003 U. ConcepciÓn

4. Young’s Modulus for a Solid Parcel
Strain, s
Stress,  
Stress is proportional to strain
  G s
Navier-Stokes Hypothesis for Fluids
Strain, s
Stress  
Stress is proportional to rate of strain
  c s/ t = c u
R. A. Brown 2003 U. ConcepciÓn

5. In order for the parcel to behave well (like a Newton Parcel), one must have a Newtonian Fluid
In a static fluid, there are only normal (pressure) forces
The forces on a face are independent of heat flux
There are no preferred directions
The stress is proportional to the velocity gradient
R. A. Brown 2003 U. ConcepciÓn

6. Atmospheric Flow --- the basic equations
F = ma (Is there an eddy-turbulent continuum?);
F = (Is there steady-state?);
F = P -  f VG = 0 (Virtual Coriolis Force, f VG)
This Inviscid, Barotropic model makes a decent GCM. …….
F = P -  f VG + Fviscous = 0 (Add the PBL)
Winds
GCM (freestream): VG = P / ( f )
w/PBL: V = P / ( f ) - Fviscous / ( f )
Surface Layer: V/u* = k [ ln z/zo +  ] ( Stratification ,
roughness, zo, von Karman k)
R. A. Brown 2003 U. ConcepciÓn

7. TURBULENCE & Approximations in the boundary layer
Required
MODEL # Layers Comment
Analytic PBL U = f(UG, , Ta - Ts, Ta)
K-Theory for small eddies Equator, Inversion,
Explicit Large eddies limitations
Numerical PBL LES Equator, Inversion, limited
K-Theory for small eddies Re #, Domain Limited Explicit Large eddies
GCM PBL Bad Physics (no OLE,LES)
K-Theory for all eddies
All Fluxes (u*) depend on
Bulk Coefficients for Flux land empirical formulas
Surface Layer Approx.
R. A. Brown 2003 U. ConcepciÓn