Pressure Fluctuations Associated with Deep Moist Convection

1. Pressure Fluctuations Associated with Deep Moist Convection

2. 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

3. 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

4. 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

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

6. Dynamic and buoyancy pressure perturbations Thus, we have Using , we obtain And after evaluating and , we obtain

7. Dynamic and buoyancy pressure perturbations relatively unimportant on convective scales very small on all scales dominates on the synoptic scale . . . when p’ is reasonably “well-behaved,”

8. Dynamic and buoyancy pressure perturbations Define vorticity (w) and deformation (D) vectors… Then the pressure equation can be written as

9. 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

10. Dynamic and buoyancy pressure perturbations “buoyancy pressure” “dynamic pressure” remainder of + part of

11. Dynamic and buoyancy pressure perturbations high pressure upshear, low pressure downshear of an updraft

14. Courtesy of Matt Parker

15. Courtesy of Matt Parker

16. Courtesy of Matt Parker

17. Results: 2D, no upper-level shear Courtesy of Mike Coniglio

18. Results: 2D, 10 m s-1 upper-level shear Courtesy of Mike Coniglio