Dynamics Exam 2

Gradient Wind Balance

PGF, Coriolis, Centrifugal Balance, (ex: low pressure troughs, high pressure ridges)

Cyclostrophic Balance

PGF & Centrifugal Balance, only supports low pressure system with CW or CCW flow, R » 1 (ex: tornado)

Geostrophic Balance

PGF & Coriolis Balance, R « 1 (ex: jet stream)

Inertial Balance

Coriolis & Centrifugal Balance, R ~ 1

PGF force

due to pressure differences, always flows from high to low

Coriolis Force

due to Earth’s rotation

NH: f>0 to right of motion

SH: f<0 to left of motion

Centrifugal Force

due to the rotating flow, outward always

Rossby Number

ratio of the centrifugal force to the Coriolis force = v/fr or u/fl

subgeostrophic

the flow around a regular gradient low, when the actual wind speed v is less than the geostrophic wind speed

supergeostrophic

the flow around a gradient high, when the actual wind speed v is faster than the geostrophic wind speed

for the same pressure perturbation and radius, there are _____ winds around a gradient _____ than a gradient ____.

stronger, higher, low

for the same wind speed, a gradient low is _____ (larger pressure perturbation) than a gradient high

deeper (trough steeper than a ridge)

Gradient low pressure systems can in theory have counterclockwise or clockwise flow (in NH).

true

Gradient high pressure systems can only have clockwise flow (in NH).

true

In Northern Hemisphere…

Air flows counterclockwise around a low, clockwise around a high

surface friction

reduces wind speed and messing with balance so that flow becomes cross-isobaric (CCW and inward around a low, CW and outward around a high)

Circulation

macroscopic measure of rotation of a flow field; always CCW

Stokes Theorem

circulation is equivalent to the area integral of the vorticity normal to the surface enclosed by the path S

*For the simple case of a circular ring of fluid where |~dl| = Rdθ and the wind is in the same direction as ~dl, the circulation about the circular path is C = integral from 0 to 2π |~u|Rdθ, which, according to Stokes theorem, is equal to the average vorticity within the circle * πR² (the area enclosed by the circular path)

The (Bjerknes) Circulation Theorem

governs the evolution of circulation of the flow relative to Earth’s rotation, first term on the right hand side of the equation is the Coriolis term and the second term on the right hand side of the equation is the pressure gradient term

A_E

= Asinφ, the projection of the area enclosed by the material circuit onto the equatorial plane; changes in A_E are a unified interpretation of divergence and beta terms

if s and A are in xy plane

n = k

if s and A are in yz plane

n = i

if s and A are in the xz plane

n = -j

The Coriolis Term of the Bjerknes

can generate circulation through changes in area (because of divergence/convergence of flow) and through changes in latitude and thus the projection of the area of the circuit in the equatorial plane, by changing the orientation of the circuit relative to omega via meridional motion

The Pressure Gradient Term (aka baroclinic term or solenoidal term)

generates circulation if the pressure gradient force is non-uniform in space, does NOT generate circulation if atmosphere is barotropic (density is only a function of pressure)

barotropic state

surface or contours of pressure are parallel to contours of density (or temp) and that the pressure gradient is parallel to density (or temp) gradient, no vertical wind shear

∇ρ × ∇p = 0

baroclinic state

density (or temp) varies on a pressure surface

∇ρ × ∇p does not = 0

continuity equation in pressure and height coordinates

Divergence Term

coriolis deflects the flow

In NH:

Area Dec, Circ Inc —> Convergent Flow

Area Inc, Circ Dec —> Divergent Flow

Beta Term

meridional motion changes orientation of the circuit relative to Earth’s axis of rotation, changing strength of coriolis

potential vorticity

A measure of fluid particle spin that is conserved following adiabatic, frictionless flow, PV conservation can be used to understand the generation of vorticity when a column of air shrinks and stretches as it moves over topography

vertical contribution to isentropic Ertel PV

simple term of PV

incompressible fluid of PV