HOW THE VISCOUS SUBRANGE DETERMINES INERTIAL RANGE PROPERTIES IN TURBULENCE SHELL MODELS

We calculate static solutions of the 'GOY' shell model of turbulence a nd do a linear stability analysis. The asymptotic limit of large Reyno lds numbers is analyzed. A phase diagram is presented which shows the range of stability of the static solution. We see an unexpected oscill atory dependence of the stability range upon lg nu, where nu is the vi scosity. This effect depends upon the discrete structure of the shell model and goes to zero as the separation between the shells is brought to zero. These findings show how viscous effects play a role in deter mining inertial properties of shell models and give some hints for und erstanding the effects of viscous dissipation upon real turbulence.