Stratified Shear Layer Research Articles

Turbulence and mixing from neighbouring stratified shear layers

Studies of Kelvin–Helmholtz (KH) instability have typically modelled the initial mean flow as an isolated stratified shear layer. However, geophysical flows frequently exhibit multiple layers. As a step towards understanding these flows, we examine the case of two adjacent stratified shear layers using both linear stability analysis and direct numerical simulations. With sufficiently large layer separation, the characteristics of instability and mixing converge towards the familiar KH turbulence, and similarly when the separation is near zero and the layers add to make a single layer, albeit with a reduced Richardson number. Here, our focus is on intermediate separations, which produce new and complex phenomena. As the separation distance $D$ increases from zero to a critical value $D_c$ , approximately half the thickness of the shear layer, the growth rate and wavenumber both decrease monotonically. The minimum Richardson number is relatively low, potentially inducing pairing, and shear-aligned convective instability (SCI) is the primary mechanism for transition. Consequently, mixing is relatively strong and efficient. When $D\sim D_c$ , billow length is increased but growth is slowed. Despite the modest growth rate, mixing is strong and efficient, engendered primarily by secondary shear instability manifested on the braids, and by SCI occurring on the eyelids. Shear-aligned vortices are driven in part by buoyancy production; however, shear production and vortex stretching are equally important mechanisms. When $D>D_c$ , neighbouring billow interactions suppress the growth of both KH instability and SCI. Strength and efficiency of mixing decrease abruptly as $D_c$ is exceeded. As turbulence decays, layers of marginal instability may arise.

Evidence for layered anisotropic stratified turbulence in a freely evolving horizontal shear flow

We present evidence for layered anisotropic stratified turbulence (LAST) and mixing produced in a freely evolving uniformly stratified shear layer where the direction of shear is orthogonal to gravity. As originally reported by Basak & Sarkar (J. Fluid. Mech., vol. 568, 2006, pp. 19–54), such a flow develops a rich three-dimensional structure in the form of interlocking columnar vortices formed by horizontal shear instability that remain coherent at large scales due to the stabilising vertical stratification. Here, we modify the initial velocity field by introducing additional small-amplitude vertical perturbations designed to be representative of pre-existing horizontal layers often observed in strongly stratified ocean environments. This reveals a novel finite amplitude, non-normal mode growth mechanism through which the vertical shear between layers may be rapidly amplified by its interaction with the horizontal shear layer prior to the growth of shear instability, leading to a rapid turbulent transition instigated by the subsequent interaction of the layers with the emerging columnar vortices. Through a consideration of relevant flow statistics and associated dimensionless parameters, we demonstrate that turbulence can enter the LAST regime, thereby indicating a generic mechanism leading to the transient development of regions of strongly stratified turbulence in the ocean. We discuss the properties of mixing and the parameterisation of mixing efficiency in terms of the relationship between turbulent length scales in the flow, in particular highlighting links to models based on the classical vertical shear instability paradigm typically associated with more weakly stratified flows that produce isolated turbulent ‘patches’.

Geometry of stratified turbulent mixing: local alignment of the density gradient with rotation, shear and viscous dissipation

We introduce a geometric analysis of turbulent mixing in density-stratified flows based on the alignment of the density gradient in two orthogonal bases that are locally constructed from the velocity gradient tensor. The first basis connects diapycnal mixing to rotation and shearing motions, building on the recent ‘rortex–shear decomposition’ in stratified shear layers (Jiang et al., J. Fluid Mech., vol. 947, 2022, A30), while the second basis connects mixing to the principal axes of the viscous dissipation tensor. Applying this framework to datasets taken in the stratified inclined duct laboratory experiment reveals that density gradients in locations of high shear tend to align preferentially (i) along the direction of minimum dissipation and (ii) normal to the plane spanned by the rortex and shear vectors. The analysis of the local alignment across increasingly turbulent flows offers new insights into the intricate relationship between the density gradient and dissipation, and thus diapycnal mixing.

Wind Dependencies of Deep Cycle Turbulence in the Equatorial Cold Tongues

Abstract Several years of moored turbulence measurements from χpods at three sites in the equatorial cold tongues of Atlantic and Pacific Oceans yield new insights into proxy estimates of turbulence that specifically target the cold tongues. They also reveal previously unknown wind dependencies of diurnally varying turbulence in the near-critical stratified shear layers beneath the mixed layer and above the core of the Equatorial Undercurrent that we have come to understand as deep cycle (DC) turbulence. Isolated by the mixed layer above, the DC layer is only indirectly linked to surface forcing. Yet, it varies diurnally in concert with daily changes in heating/cooling. Diurnal composites computed from 10-min averaged data at fixed χpod depths show that transitions from daytime to nighttime mixing regimes are increasingly delayed with weakening wind stress τ. These transitions are also delayed with respect to depth such that they follow a descent rate of roughly 6 m h−1, independent of τ. We hypothesize that this wind-dependent delay is a direct result of wind-dependent diurnal warm layer deepening, which acts as the trigger to DC layer instability by bringing shear from the surface downward but at rates much slower than 6 m h−1. This delay in initiation of DC layer instability contributes to a reduction in daily averaged values of turbulence dissipation. Both the absence of descending turbulence in the sheared DC layer prior to arrival of the diurnal warm layer shear and the magnitude of the subsequent descent rate after arrival are roughly predicted by laboratory experiments on entrainment in stratified shear flows. Significance Statement Only recently have long time series measurements of ocean turbulence been available anywhere. Important sites for these measurements are the equatorial cold tongues where the nature of upper-ocean turbulence differs from that in most of the world’s oceans and where heat uptake from the atmosphere is concentrated. Critical to heat transported downward from the mixed layer is the diurnally varying deep cycle of turbulence below the mixed layer and above the core of the Equatorial Undercurrent. Even though this layer does not directly contact the surface, here we show the influence of the surface winds on both the magnitude of the deep cycle turbulence and the timing of its descent into the depths below.

Gravity Waves Emitted From Kelvin‐Helmholtz Instabilities

AbstractFritts, Wang, Lund, and Thorpe (2022, https://doi.org/10.1017/jfm.2021.1085) and Fritts, Wang, Thorpe, and Lund (2022, https://doi.org/10.1017/jfm.2021.1086) described a 3‐dimensional direct numerical simulation of interacting Kelvin‐Helmholtz instability (KHI) billows and resulting tube and knot (T&K) dynamics that arise at a stratified shear layer defined by an idealized, large‐amplitude inertia‐gravity wave. Using similar initial conditions, we performed a high‐resolution compressible simulation to explore the emission of GWs by these dynamics. The simulation confirms that such shear can induce strong KHI with large horizontal scales and billow depths that readily emit GWs having high frequencies, small horizontal wavelengths, and large vertical group velocities. The density‐weighted amplitudes of GWs reveal “fishbone” structures in vertical cross sections above and below the KHI source. Our results reveal that KHI, and their associated T&K dynamics, may be an important additional source of high‐frequency, small‐scale GWs at higher altitudes.

The butterfly effect and the transition to turbulence in a stratified shear layer

In a stably stratified shear layer, multiple competing instabilities produce sensitivity to small changes in initial conditions, popularly called the butterfly effect (as a flapping wing may alter the weather). Three ensembles of 15 simulated mixing events, identical but for small perturbations to the initial state, are used to explore differences in the route to turbulence, the maximum turbulence level and the total amount and efficiency of mixing accomplished by each event. Comparisons show that a small change in the initial state alters the strength and timing of the primary Kelvin–Helmholtz instability, the subharmonic pairing instability and the various three-dimensional secondary instabilities that lead to turbulence. The effect is greatest in, but not limited to, the parameter regime where pairing and the three-dimensional secondary instabilities are in strong competition. Pairing may be accelerated or prevented; maximum turbulence kinetic energy may vary by up to a factor of 4.6, flux Richardson number by 12 %–15 % and net mixing by a factor of 2.

Potential and Limitations of a Commercial Broadband Echo Sounder for Remote Observations of Turbulent Mixing

Abstract Stratified oceanic turbulence is strongly intermittent in time and space, and therefore generally underresolved by currently available in situ observational approaches. A promising tool to at least partly overcome this constraint are broadband acoustic observations of turbulent microstructure that have the potential to provide mixing parameters at orders of magnitude higher resolution compared to conventional approaches. Here, we discuss the applicability, limitations, and measurement uncertainties of this approach for some prototypical turbulent flows (stratified shear layers, turbulent flow across a sill), based on a comparison of broadband acoustic observations and data from a free-falling turbulence microstructure profiler. We find that broadband acoustics are able to provide a quantitative description of turbulence energy dissipation in stratified shear layers (correlation coefficient r = 0.84) if the stratification parameters required by the method are carefully preprocessed. Essential components of our suggested preprocessing algorithm are 1) a vertical low-pass filtering of temperature and salinity profiles at a scale slightly larger than the Ozmidov length scale of turbulence and 2) an automated elimination of weakly stratified layers according to a gradient threshold criterion. We also show that in weakly stratified conditions, the acoustic approach may yield acceptable results if representative averaged vertical temperature and salinity gradients rather than local gradients are used. Our findings provide a step toward routine turbulence measurements in the upper ocean from moving vessels by combining broadband acoustics with in situ CTD profiles.

Dynamics of mixing flow with double-layer density stratification: Enstrophy and vortical structures

Previous studies on stratified shear layers involving two streams with different densities have been conducted under the Boussinesq approximation, while the combined effect of stratified instability and mean shear in relation to multi-layer density stratification induced by scalar fields remains an unresolved fundamental question. In this paper, the shear-driven mixing flow involving initial double-layer density interfaces due to the compositional differences are numerically investigated, in which the mean shear interacts with Rayleigh–Taylor instability (RTI). Since its critical role in dynamics of shear layers and scalar transport, we focus on the evolution of entrophy and vortical structures. We find that the dynamics of mixing layers are determined by the mean shear and the distance between the initial density stratification. The mean shear and the Kelvin–Helmholtz instability dominate the evolution of shear layers at the initial stage. The increase in mean shear, therefore, is favorable for turbulent mixing, irrespective of effect of RTI. However, once the transition of turbulence occurs, the mean shear becomes weaker and RTI becomes prominent. This promotes the destruction of hairpin vortex and generation of vortex tube. In addition, the interaction of mean shear with RTI becomes weaker with increasing distance between initial density stratification. Furthermore, the viscous dissipation of enstrophy is larger than enstrophy production in the turbulent region due to the effect of RTI. The baroclinic term has the larger contribution in the turbulent region than near the turbulent/non-turbulent interface, which is different from the results of stably stratified flow under the Boussinesq approximation.

A Gradient Tensor–Based Subgrid-Scale Parameterization for Large-Eddy Simulations of Stratified Shear Layers Using the Weather Research and Forecasting Model

Abstract The transition process from laminar stratified shear layer to fully developed turbulence is usually captured using direct numerical simulations, in which the computational cost is extremely high and the numerical domain size is limited. In this work, we introduce a scale-aware subgrid-scale (SGS) parameterization, based on the gradient tensor of resolved variables, which is implemented in the Weather Research and Forecasting (WRF) Model. With this new SGS model, we can skillfully resolve the characteristics of transition process, including formation of vortex cores, merging vorticity billows, breaking waves into smaller scales, and developing secondary instability in the stratified shear layer even at coarse-resolution simulations. Our new model is developed such that the time scales of the eddy viscosity and diffusivity terms are represented using the tensor of the gradient and not that of the rate-of-strain, which is commonly used in the parameterization of turbulent-viscosity models. We show that time scales of unresolved transition processes in our new model are correlated with those of vorticity fields. At early times, the power-law slopes in the kinetic and available potential energy spectra are consistent with the process of formation and merging waves with an upscale energy transfer. At later times, the power-law slopes are in line with the process of breaking waves into small-scale motions with a downscale transfer. More importantly, the efficiency of turbulent mixing is mainly high at the edge of vortex filaments and not at the vortices’ eyes. These findings can improve our understanding of turbulent mixing process in large-scale wind-induced events, such as tropical cyclones, using the WRF Model. Significance Statement The evolution of instabilities in stratified shear layers has significant impacts on the structure of large-scale geophysical flows and also on the energy pathway to smaller-scale motions in internal waves and turbulence. Resolving transition processes in stratified shear layers requires very high-resolution simulations in climate models. We propose a new subgrid-scale parameterization that is implemented in the Weather Research and Forecasting Model to capture the dynamics of transition process from laminar to three-dimensional turbulence in stratified shear layers at coarse-resolution simulations. Our new scale-aware parameterization can reduce biases in climate models by skillfully representing unresolved fluxes, leading to higher accuracy in weather predictions of temperature, precipitation, and surface fluxes with an affordable computational cost.

Thermally stratified free shear layers: Combined Kelvin–Helmholtz Rayleigh–Taylor instability

A numerical investigation of Rayleigh–Taylor instability (RTI) with different unstable thermal stratifications, and coupled Kelvin–Helmholtz (KH) and RTI (referred to as KHRTI) is performed by solving the compressible Navier–Stokes equation. Two air masses having temperature differences of ΔT*=21.75 and 46.5 K [corresponding to Gay–Lussac numbers (Ga) of 0.073 and 0.156] are considered in an isolated box, initially separated by a non-conducting interface for studying RTI. For KHRTI, dimensionless tangential shear of ΔU=0.92 and 1.89 is additionally imposed on the two air masses with ΔT*=21.75 K. Onset propagation and fully developed stages of the instabilities are explored via time-resolved and instantaneous temperature and vorticity. For RTI, lower ΔT* case shows retarded growth of the mixing layer and a set of interpenetrating bubbles. The higher ΔT* case shows an accelerated growth of the mixing layer with alternating rows of spikes and bubbles. For KHRTI, flow is governed by KH dynamics at early times and RT dynamics at later times. To further understand the interaction between RT and KH mechanisms, a compressible enstrophy transport equation in Suman et al. [“A novel compressible enstrophy transport equation based analysis of instability of Magnus–Robins effects for very high rotation rates,” Phys. Fluids 34, 044114 (2022)] is used. Depending on Ga, either vortex stretching or compressibility contribution terms of the enstrophy transport are dominant for RTI. Depending on the shear imposed, either baroclinic torque or viscous terms are dominant for KHRTI.

The evolution of coherent vortical structures in increasingly turbulent stratified shear layers

We study the morphology of Eulerian vortical structures and their interaction with density interfaces in increasingly turbulent stably stratified shear layers. We analyse the three-dimensional, simultaneous velocity and density fields obtained in the stratified inclined duct laboratory experiment (SID). We track, across 15 datasets, the evolution of coherent structures from pre-turbulent Holmboe waves, through intermittent turbulence, to full turbulence and mixing. We use the rortex–shear decomposition of the local vorticity vectors into a rortex vector capturing rigid-body rotation and a shear vector. We describe the morphology of ubiquitous hairpin-like vortical structures (revealed by the rortex), similar to those commonly observed in boundary-layer turbulence. These are born as relatively weak vortices around the strong three-dimensional shearing structures of confined Holmboe waves, and gradually strengthen and deform under increasing turbulence, transforming into pairs of upward- and downward-pointing hairpins propagating in opposite directions on the top and bottom edge of the shear layer. The pair of legs for each hairpin are counter-rotating and entrain fluid laterally and vertically, whereas their arched-up ‘heads’, which are transverse vortices, entrain fluid vertically. We then elucidate how this large-scale vortex morphology stirs and mixes the density field. Essentially, vortices located at the sharp density interface on either edge of the mixing layer (mostly hairpin heads) engulf blobs of unmixed fluid into the mixing layer, whereas vortices inside the mixing layer (mostly hairpin legs) further stir it, generating strong, small-scale shear, enhancing mixing. These findings provide new insights into the role of turbulent coherent structures in shear-driven stratified mixing.

A comparative study of turbulent stratified shear layers: effect of density gradient distribution

Direct numerical simulations are performed to compare the evolution of turbulent stratified shear layers with different density gradient profiles at a high Reynolds number. The density profiles include uniform stratification, two-layer hyperbolic tangent profile and a composite of these two profiles. All profiles have the same initial bulk Richardson number (Ri_{b,0}); however, the minimum gradient Richardson number and the distribution of density gradient across the shear layer are varied among the cases. The objective of the study is to provide a comparative analysis of the evolution of the shear layers in term of shear layer growth, turbulent kinetic energy as well as the mixing efficiency and its parameterization. The evolution of the shear layers in all cases shows the development of Kelvin–Helmholtz billows, the transition to turbulence by secondary instabilities followed by the decay of turbulence. Comparison among the cases reveals that the amount of turbulent mixing varies with the density gradient distribution inside the shear layer. The minimum gradient Richardson number and the initial bulk Richardson number do not correlate well with the integrated TKE production, dissipation and buoyancy flux. The bulk mixing efficiency for fixed Ri_{b,0} is found to be highest in the case with two-layer density profile and lowest in the case with uniform stratification. However, the parameterizations of the flux coefficient based on buoyancy Reynolds number and the ratio of Ozmidov and Ellison scales show similar scaling in all cases.

Vertical confinement effects on a fully developed turbulent shear layer

The effects of vertical confinement on a turbulent shear layer are investigated with large-eddy simulations of a freely developing shear layer (FSL) and a wall-confined shear layer (WSL) that develops between two horizontal walls. In the case of the WSL, the growth of the shear layer is inhibited by the walls. Once the walls prevent the development of the shear layer, highly anisotropic velocity fluctuations become prominent in the flow. These anisotropic velocity fluctuations are recognized as elongated large-scale structures (ELSS), whose streamwise length is much larger than the length scales in the other directions. Spectral analysis confirms that the turbulent kinetic energy is dominated by the ELSS, whose streamwise length grows continuously. A proper orthogonal decomposition can effectively extract a velocity component associated with the ELSS. The isotropy of the Reynolds stress tensor is changed by the presence of the ELSS. These changes in flow characteristics due to the ELSS are not observed in the FSL, where the shear layer thickness increases continuously. These behaviors of the WSL are consistent with those of stably stratified shear layers (SSSLs), where flow structures similar to ELSS also develop when the vertical flow development is confined by the stable stratification. The vertical confinement by the walls or stable stratification strengthens mean shear effects. The flow behavior at large scales in the WSL and SSSL is consistent with rapid distortion theory for turbulence subject to mean shear, suggesting that the development of ELSS is caused by the mean shear.

Multi-scale dynamics of Kelvin–Helmholtz instabilities. Part 1. Secondary instabilities and the dynamics of tubes and knots

We perform a direct numerical simulation (DNS) of interacting Kelvin–Helmholtz instabilities (KHI) that arise at a stratified shear layer where KH billow cores are misaligned or exhibit varying phases along their axes. Significant evidence of these dynamics in early laboratory shear-flow studies by Thorpe (Geophys. Astrophys. Fluid Dyn., vol. 34, 1985, pp. 175–199) and Thorpe (J. Geophys. Res., vol. 92, 1987, pp. 5231–5248), in observations of KH billow misalignments in tropospheric clouds (Thorpe, Q. J. R. Meteorol. Soc., vol. 128, 2002, pp. 1529–1542) and in recent direct observations of such events in airglow and polar mesospheric cloud imaging in the upper mesosphere reveals that these dynamics are common. More importantly, the laboratory and mesospheric observations suggest that these dynamics lead to more rapid and more intense instabilities and turbulence than secondary convective instabilities in billow cores and secondary KHI in stratified braids between and around adjacent billows. To date, however, no simulations exploring the dynamics and energetics of interacting KH billows (apart from pairing) have been performed. Our DNS performed for Richardson number $Ri=0.10$ and Reynolds number $Re=5000$ demonstrates that KHI tubes and knots (i) comprise strong and complex vortex interactions accompanying misaligned KH billows, (ii) accelerate the transition to turbulence relative to secondary instabilities of individual KH billows, (iii) yield significantly stronger turbulence than secondary KHI in billow braids and secondary convective instabilities in KHI billow cores and (iv) expand the suite of secondary instabilities previously recognized to contribute to KHI dynamics and breakdown to turbulence in realistic geophysical environments.

Experimental properties of continuously forced, shear-driven, stratified turbulence. Part 1. Mean flows, self-organisation, turbulent fractions

We study the experimental properties of exchange flows in a stratified inclined duct, which are simultaneously turbulent, strongly stratified by a mean vertical density gradient, driven by a mean vertical shear, and continuously forced by gravity. We focus on the ‘core’ shear layer away from the duct walls, where these flows are excellent experimentally realisable approximations of canonical hyperbolic-tangent stratified shear layers, whose forcing allows mean and turbulent properties to reach quasi-steady states. We analyse state-of-the-art data sets of the time-resolved density and velocity in three-dimensional subvolumes of the duct in 16 experiments covering a range of flow regimes (Holmboe waves, intermittent turbulence, full turbulence). In this Part 1 we first reveal the permissible regions in the multidimensional parameter space (Reynolds number, bulk Richardson number, velocity-to-density layer thickness ratio), and their link to experimentally controllable parameters. Reynolds-averaged balances then reveal the subtle momentum forcing and dissipation mechanisms in each layer, the broadening or sharpening of the density interface, and the importance of the streamwise non-periodicity of these flows. Mean flows suggest a tendency towards self-similarity of the velocity and density profiles with increasing turbulence, and gradient Richardson number statistics support prior ‘internal mixing’ theories of ‘equilibrium Richardson number’, ‘marginal stability’ and ‘self-organised criticality’. Turbulent volume fractions based on enstrophy and overturn thresholds quantify the nature of turbulence between different regimes in different regions of parameter space, while highlighting the challenges of obtaining representative statistics in spatiotemporally intermittent flows. These insights may stimulate and assist the development of numerical simulations with a higher degree of experimental realism.

Second Moment Closure Modeling and Direct Numerical Simulation of Stratified Shear Layers

AbstractBuoyant shear layers encountered in many engineering and environmental applications have been studied by researchers for decades. Often, these flows have high Reynolds and Richardson numbers, which leads to significant/intractable space–time resolution requirements for direct numerical simulation (DNS) or large eddy simulation (LES). On the other hand, many of the important physical mechanisms, such as stress anisotropy, wake stabilization, and regime transition, inherently render eddy viscosity-based Reynolds-averaged Navier–Stokes (RANS) modeling inappropriate. Accordingly, we pursue second-moment closure (SMC), i.e., full Reynolds stress/flux/variance modeling, for moderate Reynolds number nonstratified, and stratified shear layers for which DNS is possible. A range of submodel complexity is pursued for the diffusion of stresses, density fluxes and variance, pressure strain and scrambling, and dissipation. These submodels are evaluated in terms of how well they are represented by DNS in comparison to the exact Reynolds-averaged terms, and how well they impact the accuracy of full RANS closure. For the nonstratified case, SMC model predicts the shear layer growth rate and Reynolds shear stress profiles accurately. Stress anisotropy and budgets are captured only qualitatively. Comparing DNS of exact and modeled terms, inconsistencies in model performance and assumptions are observed, including inaccurate prediction of individual statistics, non-negligible pressure diffusion, and dissipation anisotropy. For the stratified case, shear layer and gradient Richardson number growth rates, and stress, flux and variance decay rates, are captured with less accuracy than corresponding flow parameters in the nonstratified case. These studies lead to several recommendations for model improvement.

Large-scale characteristics of a stably stratified turbulent shear layer

Implicit large eddy simulation is performed to investigate large-scale characteristics of a temporally evolving, stably stratified turbulent shear layer arising from the Kelvin–Helmholtz instability. The shear layer at late time has two energy-containing length scales: the scale of the shear layer thickness, which characterizes large-scale motions (LSM) of the shear layer; and the larger streamwise scale of elongated large-scale structures (ELSS), which increases with time. The ELSS forms in the middle of the shear layer when the Richardson number is sufficiently large. The contribution of the ELSS to velocity and density variances becomes relatively important with time although the LSM dominate the momentum and density transport. The ELSS have a highly anisotropic Reynolds stress, to a degree similar to the near-wall region of turbulent boundary layers, while the Reynolds stress of the LSM is as anisotropic as in the outer region. Peaks in the spectral energy density associated with the ELSS emerge because of the slow decay of turbulence at very large scales. A forward interscale energy transfer from large to small scales occurs even at a small buoyancy Reynolds number. However, an inverse transfer also occurs for the energy of spanwise velocity. Negative production of streamwise velocity and density spectra, i.e. counter-gradient transport of momentum and density, is found at small scales. These behaviours are consistent with channel flows, indicating similar flow dynamics in the stratified shear layer and wall-bounded shear flows. The structure function exhibits a logarithmic law at large scales, implying a $k^{-1}$ scaling of energy spectra.

Determining a priori a RANS model’s applicable range via global epistemic uncertainty quantification

Calibrating a Reynolds-averaged Navier–Stokes (RANS) model against data leads to an improvement. Determining a priori if such an improvement generalizes to flows outside the calibration data is an outstanding challenge. This work attempts to address this challenge via global epistemic Uncertainty Quantification (UQ). Unlike the available epistemic UQ methods that are local and tell us a model’s uncertainty at one specific flow condition, the global epistemic UQ method presented in this work tells us also whether a perturbation of the original model would generalize. Specifically, the global epistemic UQ method evaluates a potential improvement in terms of its “effectiveness” and “inconsistency”. Any improvement can be put in one of the following four quadrants: first, high effectiveness, low inconsistency; second, high effectiveness, high inconsistency; third, low effectiveness, low inconsistency; and fourth, low effectiveness, high inconsistency. An improvement would generalize if and only if it is in the high effectiveness, low inconsistency quadrant. To demonstrate the concept, we apply the global epistemic UQ to full Reynolds stress modeling of a stratified shear layer. The global epistemic UQ results point to a model coefficient in the pressure-strain correlation closure (among others) as effective and consistent for predicting the quantity of interest of shear layer’s growth. We calibrate the model coefficients such that our RANS matches direct numerical simulation data at one flow condition. We show that the calibrated model generalizes to several other test flow conditions. On the other hand, when calibrating a high inconsistency term, the model does not generalize beyond the calibration condition.

Turbulent shear layers in a uniformly stratified background: DNS at high Reynolds number

Abstract

Simulation of Deep Cycle Turbulence by a Global Ocean General Circulation Model

AbstractDeep cycle turbulence (DCT) is a diurnally oscillating turbulence that penetrates into a stratified shear layer below the surface mixed layer, which is often observed in the eastern Pacific and Atlantic above the Equatorial Undercurrent (EUC). Here we present the simulation of DCT by a global ocean general circulation model (OGCM) for the first time. As the k‐ε vertical mixing scheme is used in the OGCM, the simulation of observed DCT structure based on in situ microstructure measurements can be explicitly demonstrated. The simulated DCT is found in all equatorial ocean basins, and its characteristics agree very well with observations. Zonal and meridional variations of DCT in the entire equatorial Pacific and Atlantic are described through constructing the composite diurnal cycle. In the central Pacific where the maximum shear associated with EUC is deep, the separation of DCT from the surface mixed layer is much more prominent than other areas.