Cancellation exponent in isotropic turbulence and MHD turbulence

Small scale characteristics of turbulence, such as velocity gradients and vorticity, fluctuate in magnitude and oscillate in sign rapidly in space and time. At high Reynolds number, the oscillatory character can be characterized by a cancellation exponent, which measures the propensity of the quantity considered to cancel out when averaged over a region of space or interval of time. Past experimental work suggests that the exponents depend on the dimensionality considered. We compute cancellation exponents of vorticity and longitudinal as well as transverse velocity gradients in isotropic turbulence up to R_λ of 1300 on 8192³grids. The 2D and 3D results for the cancellation exponent are the same, while the 1D data are smaller for transverse velocity gradients and vorticity. We show that the increased degree of spatial coherency, for example in elongated vortex structures along the magnetic field in MHD turbulence (Zhai & Yeung, PRF 2018), results in substantially smaller cancellation exponents in one dimension. Likewise, the presence of vortical filaments in isotropic turbulence leads to smaller cancellation exponents in 1D. Our results suggest that cancellation exponents in higher dimensions tend to be more reliable.