Intrinsic flow structure and multifractality in two-dimensional bacterial turbulence

Turbulent lithosphere deformation in the Tibetan Plateau

In this work, we show that the Tibetan Plateau deformation demonstrates turbulence-like statistics, e.g., spatial invariance across continuous scales. A dual-power-law behavior is evident to show the existence of two possible conservation laws for the enstrophy-like cascade in the range 500≲r≲2000km and kinetic-energy-like cascade in the range 50≲r≲500km. The measured second-order structure-function scaling exponents ζ(2) are similar to their counterparts in the Fourier scaling exponents observed in the atmosphere, where in the latter case the earth's rotation is relevant. The turbulent statistics observed here for nearly zero-Reynolds-number flow can be interpreted by the geostrophic turbulence theory. Moreover, the intermittency correction is recognized with an intensity close to that of the hydrodynamic turbulence of high-Reynolds-number turbulent flows, implying a universal scaling feature of very different turbulent flows. Our results not only shed new light on the debate regarding the mechanism of the Tibetan Plateau deformation but also lead to new challenges for the geodynamic modeling using Newton or non-Newtonian models because the observed turbulence-like features have to be taken into account.