Scales of a fluid

The flow of a viscous fluid is perturbed by its internal friction which generates heat and leads to a small temperature change. This does not occur for an ideal fluid. We would like to resolve this picture as a function of the dynamical macroscopic scales of both problems. In order to do this we will study the evolution of the Navier-Stokes Hamiltonian with the classical similarity renormalization group in the region of small viscosity. The connection between the Euler and Navier-Stokes fluids will be pursued, but also the viscous structures that arise will be studied in their own right to determine the low-order velocity correlators of realistic fluids such as single-component air and water. The canonical coordinate of the Navier-Stokes Hamiltonian is a vector field that stores the initial position of all the fluid particles. Thus these appear to be natural coordinates for studying arbitrary separations of fluid particles over time. This connection will be pursued and the region where the classic 1926 Richardson 4/3 scaling law holds will be determined. The evolution of the Euler Hamiltonian will also be studied and we will attempt to map its singular structures to those of the small-viscosity Navier-Stokes fluid.