Turbulence

Turbulence is the last great unsolved problem of classical physics. Although temporarily abandoned by much of the community in favor of particle physics, the current popularity of chaos and dynamical systems theory (as well as funding problems in particle physics) is now drawing the physicists back. During the interim and up to the present, turbulence has been avidly pursued by engineers.

Turbulence has enormous intellectual fascination for physicists, engineers, and mathematicians alike. This scientific appeal stems in part from its inherent difficulty – most of the approaches that can be used on other problems in fluid mechanics are useless in turbulence. Turbulence is usually approached as a stochastic problem, yet the simplifications that can be used in statistical mechanics are not applicable – turbulence is characterized by strong dependency in space and in time, so that not much can be modeled usefully as a simple Markov process, for example. The nonlinearity of turbulence is essential – linearization destroys the problem. Many problems in fluid mechanics can be approached by supposing that the flow is irrotational – that is, that the vorticity is zero everywhere. In turbulence, the presence of vorticity is essential to the dynamics. In fact, the nonlinearity, rotationality, and the dimensionality interact dynamically to feed the turbulence – hence, to suppose that a realization of the flow is two-dimensional also destroys the problem. There is more, but this is enough to make it clear that one faces the turbulence problem stripped of the usual arsenal of techniques, reduced to hand-to-hand combat. One is forced to find unexpected chinks in its armor almost by necromancy, and to fabricate new approaches from whole cloth. This is its fascination.