Non-universal transitions to two-dimensional turbulence

Abstract

The occurrence of system-scale coherent structures, so-called condensates, is a well-known phenomenon in two-dimensional turbulence and is a consequence of the inverse energy cascade - the energy transfer from small to large scales that is a characteristic of two-dimensional turbulence. Here, the onset of the inverse energy cascade and the ensuing condensate formation are investigated as a function of the magnitude of the force and for different types of forcing. Random forces with constant mean energy input lead to a supercritical transition, while forcing through a small-scale linear instability results in a subcritical transition with bistability and hysteresis. That is, the transition to two-dimensional turbulence is non-universal. For the supercritical case we quantify the effect of large-scale friction on the value of the critical exponent and the location of the critical point.