HW 3 - Q1a. Normally P > 0 in the northern hemisphere. Instabilities result if P < 0. Discuss the two types of instability releases that may occur when P < 0 in a table. Indicate in this table, for each type, • the force that destabilizes the air (units m s-2) (equation only)• the flow direction that results to restore stability• the time scale of oscillation (if the atmosphere is stable), expressed as an equation • the magnitude of this time scale, using typical values in the troposphere. • the typical length scale (distance) of the unstable flow, if instability is present (hint:

think about regions where the instability occurs, in the convective BL, in the troposphere, on the equatorward side of the jet … Note that to a first order, the width of the eddies scales with this length scale)

Homework 3, question 1b:

P is generally conserved, at least in inviscid, adiabatic conditions. Focusing on the effect of friction,

(1)Here d/dt is the total derivative, k the unit vector normal to an isentropic surface, and F the friction vector. Demonstrate how P can be created by friction in the schematic below showing a series of gap currents (e.g. northeasterly wind in the Appalachians). At points 1, 2, and 3 on the isentropic surface (shown with dashed lines), show the friction vector, the P tendency, and the resulting P anomalies.

effect of friction on PV

)(1)(

~

v

FkP

Pvt

P

dt

Pdr

curl of friction force

PV banners in lee of complex terrain

example: PV banners in Idaho under NW wind

290 K potential vorticity(filled colors: PVU)

288 K potential vorticity

26 Nov 2005, 18 Z. Source: Andretta and Geerts 20xx

300 mbpvu

PVU

Note the shear vorticity, suggesting that the PV is generated by friction along orography

Some PV is not generated but advected down from UL in downslope wind storm (note slope of isentropes)

PV banners in the lee of the Alps

Q1.c

• If the P anomaly resulting from terrain interaction in the boundary layer (schematic above) is negative, and larger in magnitude than the background P, then what kind of instability (of the two mentioned in (a)) would be released in this case? Explain