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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