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The evolution of unforced and weakly damped two-dimensional turbulence over random rough topography presents two extreme states. If the initial kinetic energy E is sufficiently high, then the topography is a weak perturbation, and evolution is determined by the spontaneous formation and mutual interaction of coherent axisymmetric vortices. High-energy vortices roam throughout the domain and mix the background potential vorticity (PV) to homogeneity, i.e., in the region between vortices, which is most of the domain, the relative vorticity largely cancels the topographic PV. If E is low, then vortices still form but they soon become locked to topographic features: Anticyclones sit above topographic depressions and cyclones above elevated regions. In the low-energy case, with topographically locked vortices, the background PV retains some spatial variation. We develop a unified framework of topographic turbulence spanning these two extreme states of low and high energy. A main organizing concept is that PV homogenization demands a particular kinetic energy level E#. E# is the separator between high-energy evolution and low-energy evolution. [ABSTRACT FROM AUTHOR]

The Liutex vector is new quantity introduced to represent the rigid-body rotation part of fluid motion and thus to define and identify vortices in various flows. In this work, the intermittency and power-law similarity of the Liutex vector in homogeneous, isotropic turbulence and a turbulent channel are explored. First, we found that the Liutex vector is more intermittent than the vorticity vector in the considered turbulent flows, which indicates that an iso-surface of a Liutex magnitude with an appropriate threshold could capture the major rotating motions or vortical motions of the flow. Second, the three-dimensional energy spectrums of velocity, vorticity (enstrophy spectrum) and the Liutex vector in homogeneous isotropic turbulence are shown to exhibit power laws of −5/3, 1/3 and 1/3 in the inertial subrange, respectively, whilst the Liutex energy spectrum particularly satisfies an additional −10/3 power law in the viscous subrange. This viscous similarity of the Liutex vector is the only power law that survived from the wall presence and is argued to originate from the fact that the Liutex vector represents the rigid part of fluid motion and is free from any shear contamination. The existence of such a viscous similarity law indicates a certain coherence of the small scales of turbulence and could possibly help understand and model turbulence. [ABSTRACT FROM AUTHOR]