Pressure Fluctuations Associated with Deep Moist Convection

Introduction• pressure perturbations may arise

from density anomalies or from wind speed gradients, and perturbation pressure gradients may, in turn, influence the wind in important ways– reduction of vertical velocity

(generally the case)– enhancement of vertical velocity in

some special cases (may intensify storms or rotation within storms)

– forced lifting of air to the LFC (critical to storm maintenance and propagation)

• nonhydrostatic vs hydrostatic pressure

• dynamic vs buoyancy pressure

Review of the origins of pressure perturbations

Describe the pressure and density as the sum of a horizontally homogeneous base state pressure and density, respectively, and a deviation from this base state, i.e.,

The base state is in hydrostatic balance, i.e.,

The inviscid vertical momentum equation then can be written as

Hydrostatic and nonhydrostatic pressure perturbations

We can represent the perturbation pressure as the sum of a hydrostatic pressure perturbation (p’h) and a nonhydrostatic pressure perturbation (p’nh), i.e.,

arises from density perturbations by way of the relation

Thus we can rewrite the vertical momentum equation as

Where is the velocity vector, is a constant specific volume, and f is the Coriolis parameter (the Coriolis force has been approximated as ).

Dynamic and buoyancy pressure perturbations

Another common approach undertaken to decompose the perturbation pressure is to form a diagnostic pressure equation by taking the divergence of the three-dimensional momentum equation,

Dynamic and buoyancy pressure perturbations

Thus, we have

Using , we obtain

And after evaluating and , we obtain

Dynamic and buoyancy pressure perturbations

very small on all scalesdominates on the synoptic scale

when p’ is reasonably “well-behaved,”

. ..

relatively unimportant on convective scales

Dynamic and buoyancy pressure perturbations

Define vorticity () and deformation (D) vectors…

Then the pressure equation can be written as

Dynamic and buoyancy pressure perturbations

Again, when p’ is reasonably “well-behaved,” such that , then

• Rotation (of any sense) is associated with low pressure

• Convergence and divergence (fluid extension terms) are associated with high pressure

• Deformation is associated with high pressure

• Low (high) pressure is found below (above) the level of maximum buoyancy

Dynamic and buoyancy pressure perturbations

“dynamic pressure” “buoyancy pressure”

+ part of remainder of

Dynamic and buoyancy pressure perturbations

high pressure upshear, low pressure downshear of an updraft

Courtesy of Matt Parker

Courtesy of Matt Parker

Courtesy of Matt Parker

Results: 2D, no upper-level shear

Courtesy of Mike Coniglio

Results: 2D, 10 m s-1 upper-level shear

Courtesy of Mike Coniglio