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Abstract The marine atmospheric boundary layer (ABL) and oceanic boundary layer (OBL) are a two-way coupled system. At the ocean surface, the ABL and OBL share surface fluxes of momentum and buoyancy that incorporate variations in sea surface temperature (SST) and currents. To investigate the interactions, a coupled ABL–OBL large-eddy simulation (LES) code is developed and exercised over a range of atmospheric stability. At each time step, the coupling algorithm passes oceanic currents and SST to the atmospheric LES, which in turn computes surface momentum, temperature, and humidity fluxes driving the oceanic LES. Equations for each medium are time advanced using the same time step but utilize different grid resolutions: the horizontal grid resolution in the ocean is approximately four times finer, e.g., (Δx_o, Δx_a) = (1.22, 4.88) m. Interpolation and anterpolation (its adjoint) routines connect the atmosphere and ocean surface layers. In the simplest setup of a statistically horizontally homogeneous flow, the largest scale ABL turbulent shear-convective rolls leave an imprint on the OBL currents in the upper layers. This result is shown by comparing simulations that use coupling rules that are applied either instantaneously at everyx–ygrid point or averaged across anx–yplane. The spanwise scale of the ABL turbulence is ∼1000 m, while the depth of the OBL is ∼20 m. In these homogeneous, fully coupled cases, the large-scale spatially intermittent turbulent structures in the ABL modulate SST, currents, and the connecting momentum and buoyancy fluxes, but the mean profiles in each medium are only slightly different. 

Two common definitions of the spatially local rate of kinetic energy cascade at some scale$$\ell$$in turbulent flows are (i) the cubic velocity difference term appearing in the ‘scale-integrated local Kolmogorov–Hill’ equation (structure-function approach), and (ii) the subfilter-scale energy flux term in the transport equation for subgrid-scale kinetic energy (filtering approach). We perform a comparative study of both quantities based on direct numerical simulation data of isotropic turbulence at Taylor-scale Reynolds number 1250. While in the past observations of negative subfilter-scale energy flux (backscatter) have led to debates regarding interpretation and relevance of such observations, we argue that the interpretation of the local structure-function-based 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 large-scale rotation rate is strong and the large-scale strain rate is weak. Even stronger net inverse cascading is observed in the ‘vortex compression’$$R>0$$,$$Q>0$$quadrant, where$$R$$and$$Q$$are velocity gradient invariants. Qualitatively similar but quantitatively much weaker trends are observed for the conditionally averaged subfilter-scale energy flux. Flow visualizations show consistent trends, namely that spatially, the inverse cascade events appear to be located within large-scale vortices, specifically in subregions when$$R$$is large. 

Drag for wall-bounded flows is directly related to the spatial flux of spanwise vorticity outward from the wall. In turbulent flows a key contribution to this wall-normal 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$$Re_\tau =1000$$. The net transfer from the wall of spanwise vorticity created by downstream pressure drop is due to two large opposing fluxes, one which is ‘down-gradient’ or outward from the wall, where most vorticity concentrates, and the other which is ‘up-gradient’ or toward the wall and acting against strong viscous diffusion in the near-wall region. We present evidence that the up-gradient/down-gradient 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 anti-symmetric vorticity flux tensor. As evidence for the mechanism, we study (i) statistical correlations of the wall-normal velocity and of wall-normal 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 ‘D-type’ vortices contributing to down-gradient transport in the log layer are found to be attached, hairpin-type vortices. However, the ‘U-type’ vortices contributing to up-gradient transport are detached, wall-parallel, pancake-shaped 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. 

Based on a generalized local Kolmogorov–Hill equation expressing the evolution of kinetic energy integrated over spheres of size$$\ell$$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 non-equilibrium 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$$\ell$$. 

Recent high-resolution large-eddy 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 low-order turbulence moments, i.e., fluxes and variances, with increasing N. The largest discrepancy is in the stably stratified region above the low-level jet. Subfilter-scale (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 energy-containing 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 Reynolds-averaged Navier–Stokes (RANS), the gray zone (a.k.a. “Terra Incognita”), and fine-resolution 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 co-spectra 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 power-law scaling is more evident in the co-spectra 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. 

Direct numerical simulation (DNS) of a transitional boundary layer over a plate with an elliptical leading edge. Navier-Stokes was discretized on a curvilinear grid and solved using a finite volume DNS code. A fractional-step algorithm was adopted, and the spatial discretization was a staggered volume-flux formulation. The viscous terms were integrated in time implicitly using the Crank-Nicolson and the advections terms were treated explicitly using the Adams-Bashforth. Pressure was treated using implicit Euler in the δp-form. The pressure equation was Fourier transformed in the span, and the resulting Helmholtz equation was solved for every spanwise wavenumber using two-dimensional multi-grid. 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 4th-order Lagrange polynomial inter- and extrapolation. The y-locations of the grid points in the vertical direction can be downloaded from this text file.