some axisymmetric simulations of a buoyant blob

Here are numerical (computer) simulations of a buoyant blob in a "can". The simulations are axisymmetric.

The purpose of the simulations is to demonstrate (to undergraduate meteorology students) the partitioning of buoyancy between driving vertical motion and sustaining a hydrostatic pressure deficit at the surface.

The can has a diameter equal to the height. The simulations are axisymmetric, meaning the variables in the (r,z) plane are forecasted. These variables are represented at 181 grid points in the vertical and 91 in the radial, uniformly distributed. The plotted fields are thus very smoothly varying.

There are links to three animations below. Here is an example of what a frame looks like:

For those unfamiliar with axisymmetric simulations, what is shown here is the (r,z) plane. In a real "can", you would probably view the complete cross-section and see the blob at the center. Here we only need to show half of the cross-section, and the viewer should understand the mirror image also exists.

You may be unfamiliar with leaving units unspecified in simulations. One possible interpretation (among many) is to assume:

The symbols:

The labels:

Explanation of β

The pressure in all simulations is initialized as hydrostatic, with the pressure constant at the top boundary. Thus puts a low pressure anomaly beneath the blob. A cyclostrophic v can be calculated that allows for a steady balance with the horizontal component of the pressure gradient force. β is a multiplier imposed on the calculated cyclostrophic v at the time of the initialization. Thus β=0 sets v=0, for which the hydrostatic initialization of pressure vanishes very quickly (after the first time step) because the speed of sound in the model is essentially infinite. The pressure in the model is calculated to keep the velocity field non-divergent. With β=1, the hydrostatic and cyclostrophic balance is perfectly compatible, and the initial fields can exist forever. With β=0.5 the initial cyclostrophic balance is weakened. This is the most interesting simulation.

animations of the simulations

There are many features to be seen in the simulations, that are probably best explained in a lecture.