1. Monteverdi, John. Advanced Weather Analysis Lectures, Spring 2005.
“Dynamical Effects of Convection” Kathryn Saussy Meteorology 515: Analysis & Pred. of Severe Storms March
Bluestein, Howard: Synoptic-Dynamic Meteorology in Midlatitudes, Vol. II. Oxford Press, 594 pp.
Johnson, Richard H., Mapes, Brian E, 2001: Mesoscale Processes and Severe Convective Weather. Meteor. Mon. 28 (50), Amer. Meteor. Soc., Boston.
Monteverdi, John. Advanced Weather Analysis Lectures, Spring 2005.

2. Dynamical Effects of Convection
Development & dynamical consequences of rotation
II. Cold pool-shear interactions
Johnson and Mapes write that dynamical effects of convection are “numerous” – and that an important process is the development of mesoscale pressure fields through buoyancy and dynamic effects.
I’ll talk a bit today about some of the recent work involved in dynamical consequences, as well as touching on some insight into cold pool-shear interactions.

3. I. Development & dynamical consequences of rotation
Pressure perturbation forces develop.
2 perturbation dynamic pressures are associated with the wind field:
The linear, p´L , and the nonlinear part, p´NL .
( p´  perturbation upward-directed pressure gradient force that adds to the synoptic-scale upwards directed force…or subtracts from the perturbation pressure change that would occur at that level. )
(What is the effect of an updraft on the pressure field in an environment of vertical shear?)
From the boussinesq approximation, in which density decreases in the vertical (-RHOg) – the pressure forces are partitioned into a base state & then perturbed from that state.
In fluid dynamics, the Boussinesq approximation is used in the field of buoyancy-driven flow. It states that density differences are sufficiently small to be neglected, except where they appear in terms multiplied by g, the acceleration due to gravity. The essence of the Boussinesq approximation is that the difference in inertia is negligible but gravity is sufficiently strong to make the specific weight appreciably different between the two fluids.
Boussinesq flows are common in nature (such as atmospheric fronts, oceanic circulation, katabatic winds), industry (dense gas dispersion, fume cupboard ventilation), and the built environment (natural ventilation, central heating). The approximation is extremely accurate for many such flows, and makes the mathematics and physics simpler.
The approximation's advantage arises because when considering a flow of, say, warm and cold water of density ρ1 and ρ2 one needs only consider a single density ρ: the difference δρ = ρ1 − ρ2 is negligible. Dimensional analysis shows that, under these circumstances, the only sensible way that acceleration due to gravity g should enter into the equations of motion is in the reduced gravity g' where .
(Note that the denominator may be either density without affecting the result because the change would be of order g(δρ / ρ)2). The most generally used dimensionless number would be the Richardson number.
The flow is therefore simpler because the density ratio (ρ1 / ρ2---a dimensionless number) does not affect the flow: the Boussinesq approximation states that it may be assumed to be exactly one.
p´ is the TOTAL perturbation pressure.
Laplacian involved with linear part –
a nonlinear system is one whose behavior is not simply the sum of its parts. MOST PHYSICAL SYSTEMS ARE NONLINEAR. Eg, NAVIER-STOKES EQNS.
Linearity of a system allows investigators to make certain mathematical assumptions and approximations, allowing for easier computation of results. In nonlinear systems these assumptions cannot be made. Since nonlinear systems are not equal to the sum of their parts, they are often difficult (or impossible) to model, and their behavior with respect to a given variable (for example, time) is extremely difficult to predict.
In nonlinear systems one encounters such phenomena as chaos effects, strange attractors, and freak waves. Whilst some nonlinear systems and equations of general interest have been extensively studied, the vast majority are at best poorly understood.

4. Nonlinear pressure perturbation, p´NL
This says that pressure falls are proportional & opposite in sign to the square of the vertical vorticity.
It doesn’t matter if this is cyclonic or anticyclonic – it’s squared!
The vertical pressure gradient increases – (no longer hydrostatic) –
In the non-linear equation, the perturbation vertical vorticity is the new vorticity that’s produced when mesoscale and microscale tilting occurs.

5. Nonlinear pressure perturbation, p´NL (con’d)
Unidirectional shear  Initial stage shows pressure falls (on either flank) that augment the updraft.
The pNL contributes to updraft evolution in a straight (unidirectional) hodograph case, if the deep later shear is favorable. The evolution of updraft is clear in a straight hodograph –
This figure shows tilting streamwise vorticity in the horizontal flow upwards.

6. Nonlinear pressure perturbation, p´NL (con’d)
Unidirectional shear  Splitting stage shows downdraft forming; equal preference for R and L-moving storms.

7. Nonlinear pressure perturbation, p´NL (con’d)
On radar, it appears that the storm splits into mirror images.
Note the unidirectional shear on the hodograph.

8. Linear pressure perturbation, p´L
p´L  v/z  2w´
Unidirectional shear 
If the wind shear vector (v/z) lies transverse a buoyant updraft, then pressures rise on the upshear side and fall on the downshear side.
This results in no preferential growth to either of the flanks lying across the shear.

9. Linear pressure perturbation, p´L (con’d)
Clockwise shear vector 
Leads to pressure falls on the right flank of the storm…and pressure rises on the left.
New growth is favored on the right.

10. Linear pressure perturbation, p´L (con’d)
On radar, it appears that new storm growth favors the right flank.
Note the clockwise shear indicated on the hodograph.

11. II. Cold pool-shear interactions
Vertical shear  enhances ability of outflow (or cold pool) to trigger new storms
Increasing shear  interaction between shear and cold pool enhances lifting on preferred storm flank.
Vertical wind shear influences storm organization by enhancing the ability of a thunderstorm outflow (or cold pool) to trigger new storms. By itself, a cold pool can only trigger new cells if the upward motion at its leading edge can lift the warm air to its LFC. In a uniform environment, when the vertical wind shear is weak, no one portion of the gust front especially favors new cell growth. Of course, since the atmosphere is generally NOT uniform, there are usually areas along the outflow boundary where lifted warmer air may more easily reach the LFC.
As vertical wind shear increases, the interaction between the shear and the cold pool becomes an additional factor that can enhance the lifting on a preferred storm flank. This enhanced lifting occurs even in a relatively uniform environment. We can describe this shear/cold pool interaction through the concept of horizontal vorticity.
Horizontal buoyancy gradients generate horizontal vorticity. In this example of a spreading cold pool, negative horizontal vorticity is generated along the right edge of the spreading cold pool, and positive horizontal vorticity is generated on the left edge

12. Evolution of a Convective System: Stage 1
The initial updraft leans downshear in response to the surrounding vertical shear.
(C is the strength of the cold pool; Du is the strength of surrounding vertical shear. Circular arrows show the most significant horizontal vorticity.)
If the shear contributions are larger than the cold pool contributions, then the air ahead of the cold pool will be dragged up and then back downshear. The scenario produces less lift than the optimal case of balanced shear and cold pool vorticity.

13. Evolution of a Convective System: Stage 2
The circulation generated by the storm-induced cold pool balances the surrounding shear, and the system becomes upright.
If the cold pool vorticity and shear contributions are nearly balanced, then a vertical jet of air is produced that lifts both the environmental air and cold pool air much higher than the height of the cold pool. This is the optimal case for deep lifting.

14. Evolution of a Convective System: Stage 3
The cold pool dominates the surrounding shear and the system tilts upshear, producing a rear-inflow jet. (The rear-inflow jet is indicated by the thick, black arrow.)
If the cold pool vorticity is much stronger than the shear contribution, then the environmental air will be lifted just to the height of the cold pool and then dragged to the rear.

15. Thank you.