The images on this year's t-shirt are a mixture of both techniques.
Despite what your grade-school science teacher told you, air is a fluid.
At a macroscopic level, at least, air behaves very much like a low-viscosity
(i.e. not very sticky) fluid and it is typically modelled
mathematically by the same equations that govern all fluid flow: the
Navier-Stokes (NS) equations. These are partial differential equations
(PDEs) that describe conservation of momentum via Newton's 2nd Law of Motion.
They are normally non-dimensionalised, by writing all variables in
terms of "typical" scales of length, time, etc., so that phenomena
can be described in terms of a few dimensionless parameters rather than a
host of variables of varying units (and thereby revealing, for example, that
massive cyclonic weather patterns are simply large-scale forms of similar
motions in your cup of coffee).
Thus, a great deal of atmospheric and oceanic phenomena can be comprehended with an understanding of fluid dynamics and the NS equations. Unfortunately, the full NS equations are nonlinear and generally fairly complicated. As with many mathematical problems that live in the "nonlinear" (and, therefore, "hard") category, there are two basic approaches mathematicians take: 1) use approximate analytical techniques (either exactly solve approximate equations or approximately solve the exact equations), and 2) find ways to calculate quick and accurate numerical solutions. Within fluid dynamics, this latter approach is glorified by the title Computational Fluid Dynamics (CFD).
CFD is a fairly new field since the necessary computing power is a recent development. The simplest approach to solving fluid dynamics problems numerically is Direct Numerical Simulation, i.e. apply your favourite PDE-solving algorithm to the NS equations and solve to required accuracy. In general, however, this brute force approach is extremely sub-optimal because of the astronomical computing cost.
One of the classical examples of technique 1 (above) is Linear Stability Analysis. The complicated feature of the NS equations is their nonlinearity. It is this that allows turbulence (i.e. the phenomenon of a flow becoming extremely "mixed up" and complicated). It is well known that some laminar (i.e. smooth) flows can become turbulent with a slight perturbation or "kick" (such as is invariably supplied by "real world" imperfections in any experiment). But some set-ups are much more resistant to small perturbations. Why? The classical way to answer this question is to split the features of the flow into the sum of their laminar background states and a small noise perturbation. Since the noise is small, it should (approximately) satisfy the linear version of the NS equations. Since linear equations are easier to work with, it is then possible to find when the noise will grow (until it causes the flow to become turbulent) or decay away (leaving the flow laminar).
The images on this year's t-shirt are a mixture of both techniques.
A classical stability problem is the Kelvin-Helmholtz (KH) instability. Take a light fluid sitting on top of a heavy fluid and induce a shear by moving the heavy fluid one way and the lighter fluid the other way. This situation is always unstable, i.e. a slight wave on the interface between the fluids will grow and develop "rolls" which mix the light fluid into the heavy fluid, leading to a turbulent mess in between the two.
In the atmosphere and ocean, however, fluid is often continuously stratified, with density decreasing smoothly with height, rather than a sharp jump as in the "true" KH instability. Nevertheless, a strong, but smooth, shear can induce a similar instability as in the simple KH problem and produce layers of turbulence, which are important meterological features. Whether or not the small disturbance triggers instability depends on the value of the Richardson number. This is a dimensionless parameter which measures the ratio of stratification (i.e. how fast the density changes with height) to shearing. For a flow with sufficiently small Richardson number, the noise will produce "rolls" (known as KH billows) as in the simple KH problem, leading to turbulent mixing.
This year's t-shirt images are visualisations of a direct
numerical simulation of a KH-type instability in 2 dimensions.
The main difference in the two images is the size of domain
-- the side "stripe" being a flow in a "box"
twice as long as that used for the pocket logo image.
In order to see a fluid flow, it is often useful to look at
the magnitude of the flow's vorticity.
Mathematically, voticity is the curl of the flow velocity. For a 2-D flow,
this has only one non-zero component. Physically, the magnitude of vorticity
is a measure of the amount of local twisting at each point in the flow.
Vorticity plots, such as those on the t-shirts, therefore, show where there
is the greatest amount of local velocity shear. The magnitude of vorticity
in these images is shown as a scaled, colourmapped image in physical space
with black corresponding to zero vorticity and white corresponding to maximum
vorticity. Use of different colourmaps not only generates asthetically
pleasing images, but can also show different details of the flow.
Direct numerical simulation, while inefficient in most situations, is useful in research situations to guide, motivate and/or verify theoretical results. One goal of this current research is to find a simple parametrisation of the depth of the turbulent layer in terms of the Richardson number (and, possibly, other such basic flow parameters). One useful benefit of such a result would be in finding ways to avoid direct numerical simulation in larger CFD problems (such as weather prediction) by predicting, a priori, the extent of turbulent shear layers. There are other possible applications to aircraft safety and radar imaging.