Much of the current work is concerned with waves in a variable-depth regime, in both two and three dimensions. A fundamental problem in the mathematical physical and engineering sciences is why a fluid becomes unstable and turbulent when it moves at sufficiently high speed. For example, if you gently open the tap of water in the kitchen you will see that the jet of water is at first smooth and laminar, and then, if you open the tap more, it becomes unstable, irregular and the turbulent. This general problem is tackled in a number of contexts. Stationary fluid heated from below becomes unstable and convects when the adverse temperature gradient is sufficiently large.
Further heating increases the vigour of the motion, which itself becomes unstable.
The description of the finite amplitude convection, and the nature of the secondary instabilities which follow, require the numerical solution of partial differential equations. This problem has much impact on the issue of geophysical and astrophysical fluid dynamics. A recent discovery is that turbulence in a fluid is not random mess, but contains coherent structures called vortex tubes. Vortex tubes, vortex lines and their properties are much studied at the moment.