Small viscosity asymptotics for the inertial range of local structure and for the wall region of wall-bounded turbulent shear flow.

The small viscosity asymptotics of the inertial range of local structure and of the wall region in wallbounded turbulent shear flow are compared. The comparison leads to a sharpening of the dichotomy between Reynolds number dependent scaling (power-type) laws and the universal Reynolds number independent logarithmic law in wall turbulence. It further leads to a quantitative prediction of an essential difference between them, which is confirmed by the results of a recent experimental investigation. These results lend support to recent work on the zero viscosity limit of the inertial range in turbulence.

The influence of the flow of the reacting gas on the conditions for a thermal explosion

The classical problem of thermal explosion is modified so that the chemically active gas is not at rest but is flowing in a long cylindrical pipe. Up to a certain section the heat-conducting walls of the pipe are held at low temperature so that the reaction rate is small and there is no heat release; at that section the ambient temperature is increased and an exothermic reaction begins. The question is whether a slow reaction regime will be established or a thermal explosion will occur. The mathematical formulation of the problem is presented. It is shown that when the pipe radius is larger than a critical value, the solution of the new problem exists only up to a certain distance along the axis. The critical radius is determined by conditions in a problem with a uniform axial temperature. The loss of existence is interpreted as a thermal explosion; the critical distance is the safe reactor’s length. Both laminar and developed turbulent flow regimes are considered. In a computational experiment the loss of the existence appears as a divergence of a numerical procedure; numerical calculations reveal asymptotic scaling laws with simple powers for the critical distance.