Isotropic two-dimensional turbulence

 

We derive and investigate exact expressions for third-order structure functions in stationary isotropic two-dimensional turbulence, assuming a statistical balance between random forcing and dissipation both at small and large scales. Our results extend previously derived asymptotic expressions in the enstrophy and energy inertial ranges by providing uniformly valid expressions that apply across the entire non-dissipative range, which, importantly, includes the forcing scales. In the special case of white noise in time forcing this leads to explicit predictions for the third-order structure functions, which are successfully tested against previously published high-resolution numerical simulations. We also consider spectral energy transfer rates and suggest and test a simple robust diagnostic formula that is useful when forcing is applied at more than one scale.

 

Figure on the right shows the comparison of predicted structure function (blue curve) with the data from Figure 3 of Boffetta & Musacchio (2010) (red circles), where the associated high-resolution numerical simulation (run E) used 327682^2 grid points. The axis labels have been chosen for easy comparison with Boffetta & Musacchio (2010). The horizontal dashed lines mark the constant 3/2, the inset enlarges the rectangular transition region, and kf = 1/lf .

 

 

(Work with Prof. Oliver Bühler.)