Linda Vahala

Using the Madelung transformation on a generalized scalar Gross–Pitaevski equation, a nonlinear continuum fluid equations are derived for a classical fluid. A unitary quantum lattice algorithm is then determined as a second order discrete representation of this Gross–Pitaevski equation and the simulations are compared to those using classical fluid dynamic techniques.

Turbulence is of vital interest and importance to the study of fluid dynamics Pope (1990). In classical physics, turbulence was first studied carefully for incompressible flows whose evolution was given by the Navier-Stokes equations. One of the most celebrated results of incompressible classical turbulence (CT) is the existence of an inertial range with the cascade of kinetic energy from large to small spatial scales until one reaches scale lengths on the order of the dissipationwave length and the eddies/vortices are destroyed. The Kolmogorov kinetic energy spectrum in this inertial range follows the power law in wave number space.