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Two common definitions of the spatially local rate of kinetic energy cascade at some scale
in turbulent flows are (i) the cubic velocity difference term appearing in the ‘scaleintegrated local Kolmogorov–Hill’ equation (structurefunction approach), and (ii) the subfilterscale energy flux term in the transport equation for subgridscale kinetic energy (filtering approach). We perform a comparative study of both quantities based on direct numerical simulation data of isotropic turbulence at Taylorscale Reynolds number 1250. While in the past observations of negative subfilterscale energy flux (backscatter) have led to debates regarding interpretation and relevance of such observations, we argue that the interpretation of the local structurefunctionbased cascade rate definition is unambiguous since it arises from a divergence term in scale space. Conditional averaging is used to explore the relationship between the local cascade rate and the local filtered viscous dissipation rate as well as filtered velocity gradient tensor properties such as its invariants. We find statistically robust evidence of inverse cascade when both the largescale rotation rate is strong and the largescale strain rate is weak. Even stronger net inverse cascading is observed in the ‘vortex compression’$\ell$ ,$R>0$ quadrant, where$Q>0$ and$R$ are velocity gradient invariants. Qualitatively similar but quantitatively much weaker trends are observed for the conditionally averaged subfilterscale energy flux. Flow visualizations show consistent trends, namely that spatially, the inverse cascade events appear to be located within largescale vortices, specifically in subregions when$Q$ is large.$R$ Free, publiclyaccessible full text available February 10, 2025 
Drag for wallbounded flows is directly related to the spatial flux of spanwise vorticity outward from the wall. In turbulent flows a key contribution to this wallnormal flux arises from nonlinear advection and stretching of vorticity, interpretable as a cascade. We study this process using numerical simulation data of turbulent channel flow at friction Reynolds number
. The net transfer from the wall of spanwise vorticity created by downstream pressure drop is due to two large opposing fluxes, one which is ‘downgradient’ or outward from the wall, where most vorticity concentrates, and the other which is ‘upgradient’ or toward the wall and acting against strong viscous diffusion in the nearwall region. We present evidence that the upgradient/downgradient transport occurs by a mechanism of correlated inflow/outflow and spanwise vortex stretching/contraction that was proposed by Lighthill. This mechanism is essentially Lagrangian, but we explicate its relation to the Eulerian antisymmetric vorticity flux tensor. As evidence for the mechanism, we study (i) statistical correlations of the wallnormal velocity and of wallnormal flux of spanwise vorticity, (ii) vorticity flux cospectra identifying eddies involved in nonlinear vorticity transport in the two opposing directions and (iii) visualizations of coherent vortex structures which contribute to the transport. The ‘Dtype’ vortices contributing to downgradient transport in the log layer are found to be attached, hairpintype vortices. However, the ‘Utype’ vortices contributing to upgradient transport are detached, wallparallel, pancakeshaped vortices with strong spanwise vorticity, as expected by Lighthill's mechanism. We discuss modifications to the attached eddy model and implications for turbulent drag reduction.$Re_\tau =1000$ Free, publiclyaccessible full text available November 10, 2024 
Based on a generalized local Kolmogorov–Hill equation expressing the evolution of kinetic energy integrated over spheres of size
in the inertial range of fluid turbulence, we examine a possible definition of entropy and entropy generation for turbulence. Its measurement from direct numerical simulations in isotropic turbulence leads to confirmation of the validity of the fluctuation relation (FR) from nonequilibrium thermodynamics in the inertial range of turbulent flows. Specifically, the ratio of probability densities of forward and inverse cascade at scale$\ell$ is shown to follow exponential behaviour with the entropy generation rate if the latter is defined by including an appropriately defined notion of ‘temperature of turbulence’ proportional to the kinetic energy at scale$\ell$ .$\ell$ Free, publiclyaccessible full text available October 25, 2024 
Recent highresolution largeeddy simulations (LES) of a stable atmospheric boundary layer (SBL) with mesh sizes N=(5123,10243,20483) or mesh spacings ▵=(0.78,0.39,0.2) m are analyzed. The LES solutions are judged to be converged based on the good collapse of vertical profiles of mean winds, temperature, and loworder turbulence moments, i.e., fluxes and variances, with increasing N. The largest discrepancy is in the stably stratified region above the lowlevel jet. Subfilterscale (SFS) motions are extracted from the LES with N=20483 and are compared to sonic anemometer fields from the horizontal array turbulence study (HATS) and its sequel over the ocean (OHATS). The results from the simulation and observations are compared using the dimensionless resolution ratio Λw/▵f where ▵f is the filter width and Λw is a characteristic scale of the energycontaining eddies in vertical velocity. The SFS motions from the observations and LES span the ranges 0.1<Λw/▵f<20 and are in good agreement. The small, medium, and large range of Λw/▵f correspond to Reynoldsaveraged Navier–Stokes (RANS), the gray zone (a.k.a. “Terra Incognita”), and fineresolution LES. The gray zone cuts across the peak in the energy spectrum and then flux parameterizations need to be adaptive and account for partially resolved flux but also “stochastic” flux fluctuations that represent the turbulent correlation between the fluctuating rate of strain and SFS flux tensors. LES data with mesh 20483 will be made available to the research community through the web and tools provided by the Johns Hopkins University Turbulence Database.

A model for the structure function tensor is proposed, incorporating the e↵ect of anisotropy as a linear perturbation to the standard isotropic form. The analysis extends the spectral approach of Ishihara et al. (2002) to physical space based on Kolmogorov’s theory and is valid in the inertial range of turbulence. Previous results for velocity cospectra are used to obtain estimates of the model coe"cients. Structure functions measured from direct numerical simulations of channel ﬂow and from experimental measurements in turbulent boundary layers are compared with predicted behaviour and reasonable agreement is found. We note that powerlaw scaling is more evident in the cospectra than for the mixed structure functions. New observations are made about countergradient correlation between Fourier modes of wall normal and streamwise velocity components for wavenumbers approaching the Kolmogorov scale.more » « less

A direct numerical simulation of incompressible channel flow at a friction Reynolds number (Reτ) of 5186 has been performed, and the flow exhibits a number of the characteristics of highReynoldsnumber wallbounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Kármán constant k = 0.384 ± 0.004. There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outerlayer structures and small innerlayer structures. At intermediate distances from the wall, the onedimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits k1 dependence over a short range in wavenumber (k) . Further, consistent with previous experimental observations, when these spectra are multiplied by k (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the k1 range.more » « less

Direct numerical simulation (DNS) of a transitional boundary layer over a plate with an elliptical leading edge. NavierStokes was discretized on a curvilinear grid and solved using a finite volume DNS code. A fractionalstep algorithm was adopted, and the spatial discretization was a staggered volumeflux formulation. The viscous terms were integrated in time implicitly using the CrankNicolson and the advections terms were treated explicitly using the AdamsBashforth. Pressure was treated using implicit Euler in the δpform. The pressure equation was Fourier transformed in the span, and the resulting Helmholtz equation was solved for every spanwise wavenumber using twodimensional multigrid. After the simulation has reached a statistical stationary state, 4701 frames of data, which includes the 3 components of the velocity vector and the pressure, are generated and written in files that can be accessed directly by the database (FileDB system). Since the grid is staggered, data at the wall are not stored in the database. However, JHTDB provides values in the region between the wall and the first grid point, y∈[0, 0.0036], using 4thorder Lagrange polynomial inter and extrapolation. The ylocations of the grid points in the vertical direction can be downloaded from this text file.more » « less

The data is from a direct numerical simulation of rotating stratified turbulence on a 4096cubed periodic grid using a pseudospectral parallel code, GHOST. The simulations are documented in Ref. 1. The relative strength of stratification vs. rotation is characterized by the ratio of the BruntVäisälä to inertial wave frequency, N/f = 4.95. The code solves the Boussinesq equations with a solid body rotation force acting as the only external forcing mechanism. Time integration uses fourthorder RungeKutta. The simulation is initialized with largescale isotropic conditions on a coarser grid. As the simulation progresses resolution is increased, peaking with 4096cubed at maximum dissipation. After the simulation has reached a statistical stationary state, 5 frames of data, which includes the 3 components of the velocity vector and the temperature fluctuations, are generated and written in files that can be accessed directly by the database (FileDB system).more » « less