In the Eyewall of Katrina,

Pretty dramatic footage.

GOES East Infrared Hurricane Sector - June thru July 2007,

No hurricanes here but note the baroclinic wave that develops over Florida in the beginning. Seems pretty far south for this, especially this time of year. Mid-latitude westerlies seem to weaken as June goes into July. Easterlies closer to the equator.

2005 GOES Hurricane Season,

This was a very active season with quite a few hurricanes. There are also many other interesting aspects. Note how earlier in the video, in June, cold fronts penetrate deeply into the Caribbean. I would assume that this dry air inhibits hurricane development at this time. Another factor is that SST's are not as high as they are in July and August. Note that, in July, Florida starts to blink with deep convection due to the preferential development of deep convection in the afternoon. Whether this blinking occurs or not on a given day is of course dependent on the large scale synoptic context, which can overwhelm local effects, but it is pretty regular.

Heuristic Derivation of h proportional to V*V*L/H ... (NOT REQUIRED FOR EXAM)

Horizontal Pressure Gradient Acceleration = g*h/L: The fan is pushing the water in the bathtub to the left. This gives rise to a slope in the water dh/dx. By hydrostatic balance, the water pressure at any depth is proportional to the total weight of the fluid above that height. So for places where h is higher, the water pressure tends to be higher, relative to the pressure at a different place in the fluid at the same height. There is therefore a horizontal pressure gradient acceleration (1/rho)*dp/dx pushing water parcels to the right. It is easy to show that if p is proportional to the depth of the overhead water column, and h is the change in the height of the surface at any point, then dp/dx = rho*g*dh/dx. The horizontal force pushing water parcels to the right is therefore equal to g*dh/dx. Assume that the slope is constant, in which case dh/dx = h/L, where L is the length of the bathtub. The horizontal downslope pressure gradient acceleration then become g*h/L.

Acceleration from the wind (fan): Remember that the power dissipated by the surface wind goes as the surface wind speed to the third power (multiplied by the drag coefficient CD). The drag coefficient is a function of the surface roughness (which over the ocean is also a function of the wind speed ... its complicated). The momentum flux going into the water goes as CD*V*V. This is given in (9.19c) of Wallace and Hobbs . (Note that this is consistent with power going to the third power of the wind since power goes as applied force times speed.) CD is dimensionless, so the momentum flux has units m*m/s*s. The momentum flux is a momentum (kg*m/s), per unit area (m*m), per unit time (s), normalized by the density of the medium (kg/m*m*m). This works out to m*m/s*s. The medium here refers to air. The density of the air matters because if the density of the air goes up, more momentum would go into the fluid for a given wind speed. You need to have some mass to push another mass. The non density normalized momentum flux going into the water is then rho(air)*CD*V*V. This momentum flux at the top must counteract a reverse pressure gradient acceleration that exists at every depth of the fluid. This means that rho(air)*CD*V*V must be divided by H. To convert this to an acceleration of water, divide this force by the density of water Therefore, the acceleration of the water parcels to the left from the surface wind forcing equals (rho(air)/rho(water))*CD*V*V/H.

Setting the two accelerations equal to each other gives h = (rho(air)/rho(water))*(CD/g)*V*V*L/H. It makes sense that the change in the elevation of the fluid would scale as the ratio of the densities of the fluids. This reflects the fact that it is hard for a wind speed to change the elevation of the ocean much since water is about a thousand times more dense then air. It also makes sense h would be inversely proportional to g, since gravity opposes a any deviation of the ocean surface from a flat geopotential surface. h should scale with CD since it is the non-zero drag coefficient that allows a momentum transfer between the two fluids. This is a force balance. However, as mentioned in class, one must also think about the kinetic energy budget. When I first turn on the fan, the kinetic energy being input at the top is used to spin up a circulation. However, there soon reaches a steady state whereby the kinetic energy going in is balanced by friction dissipation. Most of this dissipation would occur at the bottom of the bathtub. This frictional force would slow the fluid at the bottom of the bathtub.