Vorticity production and turbulent cooling of "hot channels" in gases: Three dimensions versus two dimensions

Hot channels (HCs), created in a gas by a rapid energy release in the quasi-cylindric geometry, cool anomalously fast by turbulent flow. Picone and Boris [Phys. Fluids 26, 365 (1983)] suggested that turbulent mixing results from the vorticity generation by the baroclinic mechanism during the early, shock-wave dominated stage of the dynamics. This scenario was confirmed, with important modifications, in a recent series of two-dimensional (2D) hydrodynamic simulations. This work reports three-dimensional (3D) hydrodynamic simulations of the HC evolution, and compares the results with those of 2D simulations. Assuming a small perturbation of the cylindric shape of the energy release region, we followed a typical HC up to 200 acoustic times. The simulations capture well the phenomenology of the HC cooling. The details of vorticity production, that results in a fast mixing of the cold ambient gas into the HC, are clearly identified. The cooling process can be interpreted as turbulent diffusion. The empiric diffusion coefficient and cooling time agree with experiment. The late-time morphology of the HC and the empiric turbulent diffusion coefficient are dimension-dependent, the 3D cooling being faster than 2D cooling.