Physics of Climate
Romps Group at the University of California, Berkeley
|Jeevanjee and Romps, Effective buoyancy at the surface and aloft, QJRMS, 2016|
Stationary buoyant parcels of fluid do not accelerate at a rate equal to their buoyancy. Instead, they accelerate at a smaller rate, which is called the effective buoyancy. This smaller rate of acceleration is caused by the fact that the buoyancy must accelerate not just the buoyant parcel, but also some of the surrounding fluid. Qualitatively, the ratio of effective buoyancy to buoyancy is a function of the parcel's aspect ratio. Parcels whose widths are much greater than their heights have a very small effective-buoyancy-to-buoyancy ratio; these parcels approach the hydrostatic limit. Parcels whose widths are much smaller than their heights have effective buoyancies that nearly equal their buoyancies.
Here, we explore how the relationship between effective buoyancy and buoyancy is affected by the proximity of the parcel to the surface. This is an important question because new thermals (and, therefore, new convecting clouds) are born from near-surface air parcels. By finding an analytical solution to the simple system a buoyant cylinder, we show that wide parcels have a significantly smaller effective buoyancy at the surface than aloft. This is then demonstrated using large-eddy simulations.
Figure 16. For a buoyant, cylindrical parcel (black), contours of upward acceleration (red) and downward acceleration (blue).