Method of Infinitetesmal Disturbances

Reading, Bluestein, Volume II, pp. 62-82 (Long Waves and Short Waves)

pp. 82-111 (Climatology of Waves)

pp. 112-130 (Baroclinic Instability)

Assume one air parcel is accelerated out of a balanced state.. Acceleration may be due to a mountain, an island, local turbulence etc. If air parcel finds itself in a situation where the acceleration acting upon it increases, than an imbalance of forces must have taken place.

“Restoring” force is the force that “attempts” to bring the air parcel back to its base state. (Another way of viewing instability is if restoring force does NOT bring the air parcel to an stable state. For example, if air parcel brought back to its initial position continues to accelerate past that point).

Meteorologically-significant Waves

Meteorologically-signficant waves at the mesoscale or larger may be put into the following categories:

1. Vertical Transverse

Waves that can be understood on the basis of hydrostatic stability where gravity is the “restoring” force.

· Lee Waves (generally stable)

· Absolute Instability (unstable)

2. Horizontal Transverse

Waves that can be understood on the basis of hydrodynamic instability (restoring forces vary)

A. Long Waves

Rossby Waves (stable waves) -->restoring force is Coriolis.

B. Short Waves

i. Barotropic Waves--no solenoids, no thermal wind (winds at every level roughly same speed), winds are geostrophic.

· Solberg Inertial (Centrifugal or symmetric instabilty) Waves--> Deviating force is centrifugal (or centripetal), restoring force is pressure gradient (criterion, where absolute vorticity is zero or negative)

· Barotropic Instability-->Deviating force is related to conservation of absolute angular momentum, restoring force is pressure gradient force (criterion, where the gradient of absolute vorticity changes sign

ii. Baroclinic Waves--solenoids, strong vertical shear. These waves are actually both vertically and horizontall transverse and are in a special category. Signficant divergence and vertical accelerations.

· Baroclinic instability-->temperature advection amplifies troughs and ridges and therefore “produces” vorticity. Vertical temperature advection tends to weakn troughs and ridges and therefore “destroys” vorticity. Production or destruction of vorticity is measured by ∂/z∂t and is what is often referred to as “development” term in equations.

· Conditional symmetric instabilty (CSI)-->slantwise convection. Baroclinically-unstable waves that are also horizontally transverse because northward moving air parcels find themselves in different environment with respect to hydrostatic instability.

· Conditional Instability of the Second Kind (CISK)--combination of baroclinic instability and hydrostatic instability with respect to parcel theory.