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.
Highlights
Two-dimensional (2-D) and quasi-2-D flows occur at the macro- and mesoscale in a variety of physical systems
By means of direct numerical simulations we show that the nature of the transition depends on the type of driving: it is supercritical for random forcing and subcritical if the driving is given by a small-scale linear instability
A similar transition in the energy spectra in statistically stationary 2-D turbulence occurs if the condensate is avoided through a strong drag term (Tsang & Young 2009), in the sense that the extent of the −5/3 scaling range decreases with increasing large-scale friction and a power law with positive exponent appears at low wavenumbers
Summary
Two-dimensional (2-D) and quasi-2-D flows occur at the macro- and mesoscale in a variety of physical systems. By means of direct numerical simulations we show that the nature of the transition depends on the type of driving: it is supercritical for random forcing and subcritical if the driving is given by a small-scale linear instability In the former case we explore the effect of large-scale friction on the location of the critical point and the value of the critical exponent
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