Intermittency in the inverse cascade of two dimensional turbulence
Abstract: One of the most puzzling properties of three dimensional turbulence is intermittency: the breaking of self-similarity as smaller scales are examined. This property is in general absent in the inverse cascade of two dimensional turbulence. In this talk I will present results demonstrating that like the forward three dimensional turbulence that displays intermittency due to the concentration of energy dissipation in a small set of fractal dimension less than three, the inverse cascade of two-dimensional turbulence can also display lack of self-similarity and intermittency if the energy injection is constrained in a fractal set of dimension less than two. A series of numerical simulations of two dimensional turbulence are examined, using different forcing functions of the same forcing length-scale but different fractal dimension D that varies from the classical D=2 case to the point vortex case D=0. It is shown that as the fractal dimension of the forcing is decreased from D=2, the self-similarity is lost and intermittency appears, with the scaling of the different structure functions differs from the dimensional analysis prediction. The present model thus provides a unique example that intermittency is controlled and can thus shed light and provide test beds for multi-fractal models of turbulence.
