Inducing intermittency in the inverse cascade of two-dimensional turbulence by a fractal forcing

We demonstrate that, as in the forward cascade of three-dimensional turbulence that dis-plays intermittency (a lack of self-similarity) 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 a 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. The present model thus provides a unique example that intermittency is controlled and can thus shed light and provide test beds for multifractal models of turbulence.

Automated summary

We show that the inverse cascade of two-dimensional turbulence can exhibit a lack of self-similarity and intermittency when the energy injection is constrained within a fractal set of dimension less than two. Numerical simulations of two-dimensional turbulence with different forcing functions and fractal dimensions are conducted, demonstrating the loss of self-similarity and the emergence of intermittency as the fractal dimension decreases. This model serves as a valuable example to understand and test multifractal models of turbulence.