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

The Basics R. A. Brown 2003 U. ConcepciÓn

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

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

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

Atmospheric Flow --- the basic equations F = ma (Is there an eddy-turbulent continuum?); F = 0 (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

TURBULENCE & Approximations in the boundary layer Required MODEL # Layers Comment Analytic PBL 0 U = f(UG, , Ta - Ts, Ta) K-Theory for small eddies Equator, Inversion, Explicit Large eddies limitations Numerical PBL LES 50 Equator, Inversion, limited K-Theory for small eddies Re #, Domain Limited Explicit Large eddies GCM PBL 5 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