Redistribution of kinetic energy by pressure forces in turbulence

In statistically homogeneous turbulent flows, pressure forces provide the main mechanism to redistribute kinetic energy among fluid elements, without net contribution to the overall energy budget. This holds true in both two-dimensional (2D) and three-dimensional (3D) flows, which show fundamentally different physics. As I will demonstrate, pressure forces act on fluid elements very differently in these two cases. Numerical simulations demonstrate that in 3D pressure forces strongly accelerate the fastest fluid elements, an effect which is absent in 2D. In 3D turbulence, these findings suggest a mechanism for a possibly singular build-up of energy, and thus may shed new light on the smoothness problem of the solution of the Navier-Stokes equation in 3D.