NON-NEWTONIAN EFFECTS ON THE TURBULENT ENERGY SPECTRUM FUNCTION.

Working with the isotropic homogeneous flow of second order fluids and assuming the turbulence Reynolds number to be very large, some features of the turbulent energy spectrum are investigated theoretically. Instead of working with the equation for the fluctuating energy of the turbulent flow, the fluctuating velocity is split into a macro component and a micro component associated respectively with eddies larger and smaller than a given size, and the energy equation for the micro component of velocity is derived. Terms representing interation between large and small eddies are then simplified by assuming that the departure from isotropy of the small eddies depends on the history of deformation of the large eddies. This equation is further simplified by assuming the existence of an equilibrium range. A change of variable converts this into an integral equation whose approximate solution is found by the method of iteration. The results present an extension of the energy spectrum form due to Heisenberg and mark three divisions of the whole range of wave numbers, which may be called the inelastic range, resonance range and elastic range. Author