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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Double Resonances and Spectral Scaling in the Weak Turbulence Theory of Rotating and Stratified Turbulence

In rotating turbulence, stably stratified turbulence, and in rotating stratified turbulence, heuristic arguments concerning the turbulent time scale suggest that the inertial range energy spectrum scales as k(exp -2). From the viewpoint of weak turbulence theory, there are three possibilities which might invalidate these arguments: four-wave interactions could dominate three-wave interactions leading to a modified inertial range energy balance, double resonances could alter the time scale, and the energy flux integral might not converge. It is shown that although double resonances exist in all of these problems, they do not influence overall energy transfer. However, the resonance conditions cause the flux integral for rotating turbulence to diverge logarithmically when evaluated for a k(exp -2) energy spectrum; therefore, this spectrum requires logarithmic corrections. Finally, the role of four-wave interactions is briefly discussed.

Rubinstein, Robert↗
DOE OSTI2024

Prandtl number effects on extreme mixing events in forced stratified turbulence

Relatively strongly stratified turbulent flows tend to self-organise into a ‘layered anisotropic stratified turbulence’ (LAST) regime, characterised by relatively deep and well-mixed density ‘layers’ separated by relatively thin ‘interfaces’ of enhanced density gradient. Understanding the associated mixing dynamics is a central problem in geophysical fluid dynamics. It is challenging to study LAST mixing, as it is associated with Reynolds numbers $Re := UL/\nu \gg 1$ and Froude numbers $Fr :=(2{\rm \pi} U)/(L N) \ll 1$ ( $U$ and $L$ being characteristic velocity and length scales, $\nu$ the kinematic viscosity and $N$ the buoyancy frequency). Since a sufficiently large dynamic range (largely) unaffected by stratification and viscosity is required, it is also necessary for the buoyancy Reynolds number $Re_{b} := \epsilon /(\nu N^{2}) \gg 1$ , where $\epsilon$ is the (appropriately volume-averaged) turbulent kinetic energy dissipation rate. This requirement is exacerbated for oceanically relevant flows, as the Prandtl number $Pr := \nu /\kappa = {O}(10)$ in thermally stratified water (where $\kappa$ is the thermal diffusivity), thus leading (potentially) to even finer density field structures. We report here on four forced fully resolved direct numerical simulations of stratified turbulence at various Froude ( $Fr=0.5, 2$ ) and Prandtl ( $Pr=1, 7$ ) numbers forced so that $Re_{b}=50$ , with resolutions up to $30\,240 \times 30\,240 \times 3780$ . We find that, as $Pr$ increases, emergent ‘interfaces’ become finer and their contribution to bulk mixing characteristics decreases at the expense of the small-scale density structures populating the well-mixed ‘layers’. However, extreme mixing events (as quantified by significantly elevated local destruction rates of buoyancy variance $\chi _0$ ) are always preferentially found in the (statically stable) interfaces, irrespective of the value of $Pr$ .

Mechanics↗
DOE OSTI2023

A data-driven method for modelling dissipation rates in stratified turbulence

We present a deep probabilistic convolutional neural network (PCNN) model for predicting local values of small-scale mixing properties in stratified turbulent flows, namely the dissipation rates of turbulent kinetic energy and density variance, $\varepsilon$ and $\chi$ . Inputs to the PCNN are vertical columns of velocity and density gradients, motivated by data typically available from microstructure profilers in the ocean. The architecture is designed to enable the model to capture several characteristic features of stratified turbulence, in particular the dependence of small-scale isotropy on the buoyancy Reynolds number $Re_b:=\varepsilon /(\nu N^2)$ , where $\nu$ is the kinematic viscosity and $N$ is the background buoyancy frequency, the correlation between suitably locally averaged density gradients and turbulence intensity and the importance of capturing the tails of the probability distribution functions of values of dissipation. Empirically modified versions of commonly used isotropic models for $\varepsilon$ and $\chi$ that depend only on vertical derivatives of density and velocity are proposed based on the asymptotic regimes $Re_b\ll 1$ and $Re_b\gg 1$ , and serve as an instructive benchmark for comparison with the data-driven approach. When trained and tested on a simulation of stratified decaying turbulence which accesses a range of turbulent regimes (associated with differing values of $Re_b$ ), the PCNN outperforms assumptions of isotropy significantly as $Re_b$ decreases, and additionally demonstrates improvements over the fitted empirical models. A differential sensitivity analysis of the PCNN facilitates a comparison with the theoretical models and provides a physical interpretation of the features enabling it to make improved predictions.

42 ENGINEERING↗
DOE OSTI2024

Numerical validation of scaling laws for stratified turbulence

Recent theoretical progress using multiscale asymptotic analysis has revealed various possible regimes of stratified turbulence. Notably, buoyancy transport can either be dominated by advection or diffusion, depending on the effective Péclet number of the flow. Two types of asymptotic models have been proposed, which yield measurably different predictions for the characteristic vertical velocity and length scale of the turbulent eddies in both diffusive and non-diffusive regimes. The first, termed a ‘single-scale model’, is designed to describe flow structures having large horizontal and small vertical scales, while the second, termed a ‘multiscale model’, additionally incorporates flow features with small horizontal scales, and reduces to the single-scale model in their absence. By comparing predicted vertical velocity scaling laws with direct numerical simulation data, we show that the multiscale model correctly captures the properties of strongly stratified turbulence within regions dominated by small-scale isotropic motions, whose volume fraction decreases as the stratification increases. Meanwhile its single-scale reduction accurately describes the more orderly, layer-like, quiescent flow outside those regions.

Mechanics↗
DOE OSTI2024

Machine-learned closure of URANS for stably stratified turbulence: connecting physical timescales & data hyperparameters of deep time-series models

Stably stratified turbulence (SST), a model that is representative of the turbulence found in the oceans and atmosphere, is strongly affected by fine balances between forces and becomes more anisotropic in time for decaying scenarios. Moreover, there is a limited understanding of the physical phenomena described by some of the terms in the Unsteady Reynolds-Averaged Navier–Stokes (URANS) equations—used to numerically simulate approximate solutions for such turbulent flows. Rather than attempting to model each term in URANS separately, it is attractive to explore the capability of machine learning (ML) to model groups of terms, i.e. to directly model the force balances. We develop deep time-series ML for closure modeling of the URANS equations applied to SST. We consider decaying SST which are homogeneous and stably stratified by a uniform density gradient, enabling dimensionality reduction. We consider two time-series ML models: long short-term memory and neural ordinary differential equation. Both models perform accurately and are numerically stable in a posteriori (online) tests. Furthermore, we explore the data requirements of the time-series ML models by extracting physically relevant timescales of the complex system. We find that the ratio of the timescales of the minimum information required by the ML models to accurately capture the dynamics of the SST corresponds to the Reynolds number of the flow. The current framework provides the backbone to explore the capability of such models to capture the dynamics of high-dimensional complex dynamical system like SST flows.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

SST-TG-P1F4R3200: Decaying Stably-Stratified Turbulence (SST), Initialized Using Taylor-Green Vortices (TG) at Prandtl Number Pr=1, Froude Number Fr=4, Reynolds Number Re=3200

This dataset comprises direct numerical simulations (DNS) of decaying stably-stratified turbulence influenced by a linear background density gradient, initialized using an array of Taylor-Green vortices, as described in [Riley & de Bruyn Kops (2003)](https://doi.org/10.1063/1.1578077). The initial Prandtl, Froude, and Reynolds numbers are (Pr, Fr, Re) = (1, 4, 3200). A total of 15,000 snapshots are recorded at uniform time intervals, each with a spatial resolution of 512x512x256 grid points. Four flow variables are associated with each snapshot: the three velocity components (u,v,w) and the perturbed density field (rho) away from the background gradient. All fields are stored in binary format (32-bit little-endian), each with a size of 255 MB, yielding a total dataset size of 15.3 TB. Further details are referenced in the attached README file, and a current list of publications and associated analysis tools are provided at https://stratified-turbulence.github.io/web/.

42 ENGINEERING↗
DOE OSTI2025

SST-TG-P50F4R3200: Decaying Stably-Stratified Turbulence (SST), Initialized Using Taylor-Green Vortices (TG) at Prandtl Number Pr=50, Froude Number Fr=4, Reynolds Number Re=3200

This dataset comprises direct numerical simulations (DNS) of decaying stably-stratified turbulence influenced by a linear background density gradient, initialized using an array of Taylor-Green vortices, extending the Pr=1 simulations performed in [Riley and de Bruyn Kops (2003)](https://doi.org/10.1063/1.1578077). The initial Prandtl, Froude, and Reynolds numbers are (Pr, Fr, Re) = (50, 4, 3200). A total of 1,680 snapshots are recorded at uniform time intervals, each with a spatial resolution of 3584x3584x1792 grid points. Four flow variables are associated with each snapshot: the three velocity components (u,v,w) and the perturbed density field (rho) away from the background gradient. All fields are stored in binary format (32-bit little-endian), each with a size of 85.8 GB, yielding a total dataset size of 577 TB. Further details are referenced in the attached README file, and a current list of publications and associated analysis tools are provided at https://stratified-turbulence.github.io/web/.

42 ENGINEERING↗
DOE OSTI2025

SST-TG-P7F4R3200: Decaying Stably-Stratified Turbulence (SST), Initialized Using Taylor-Green Vortices (TG) at Prandtl Number Pr=7, Froude Number Fr=4, Reynolds Number Re=3200

This dataset comprises direct numerical simulations (DNS) of decaying stably-stratified turbulence influenced by a linear background density gradient, initialized using an array of Taylor-Green vortices, extending the Pr=1 simulations performed in [Riley and de Bruyn Kops (2003)](https://doi.org/10.1063/1.1578077). The initial Prandtl, Froude, and Reynolds numbers are (Pr, Fr, Re) = (7, 4, 3200). A total of 15,250 snapshots are recorded at uniform time intervals, each with a spatial resolution of 1280x1280x640 grid points. Four flow variables are associated with each snapshot: the three velocity components (u,v,w) and the perturbed density field (rho) away from the background gradient. All fields are stored in binary format (32-bit little-endian), each with a size of 4 GB, yielding a total dataset size of 244 TB. Further details are referenced in the attached README file, and a current list of publications and associated analysis tools are provided at https://stratified-turbulence.github.io/web/.

42 ENGINEERING↗
NASA NTRS1993

Similarity states of homogeneous stably-stratified turbulence at infinite Froude number

We present evidence of similarity states which may develop inhomogeneous stably-stratified flows if a dimensionless group in addition to the Reynolds number, the so-called Froude number, is sufficiently large. Here, we define the Froude number as the ratio of the internal wave time-scale to the turbulence time-scale. We examine three different similarity states which may develop depending on the initial conditions of the velocity and density fields. Theoretical arguments and results of large-eddy simulations will be presented. We will conclude this report with some speculative thoughts on similarity states which may develop in stably-stratified turbulence at arbitrary Froude number as well as our future research plans in this area.

Chasnov, Jeffrey R.↗
NASA NTRS1992

Direct simulation of the stably stratified turbulent Ekman layer

The Navier-Stokes equations and the Boussinesq approximation were used to compute a 3D time-dependent turbulent flow in the stably stratified Ekman layer over a smooth surface. The simulation data are found to be in very good agreement with atmospheric measurements when nondimensionalized according to Nieuwstadt's local scaling scheme. Results suggest that, when Reynolds number effects are taken into account, the 'constant Froud number' stable layer model (Brost and Wyngaard, 1978) and the 'shearing length' stable layer model (Hunt, 1985) for the dissipitation rate of turbulent kinetic energy are both valid. It is concluded that there is good agreement between the direct numerical simulation results and large-eddy simulation results obtained by Mason and Derbyshire (1990).

Coleman, G. N.↗
NASA NTRS2014

Direct Numerical Simulation of a Weakly Stratified Turbulent Wake

Direct numerical simulation (DNS) is used to investigate a time-dependent turbulent wake evolving in a stably stratified background. A large initial Froude number is chosen to allow the wake to become fully turbulent and axisymmetric before stratification affects the spreading rate of the mean defect. The uncertainty introduced by the finite sample size associated with gathering statistics from a simulation of a time-dependent flow is reduced, compared to earlier simulations of this flow. The DNS reveals the buoyancy-induced changes to the turbulence structure, as well as to the mean-defect history and the terms in the mean-momentum and turbulence-kinetic-energy budgets, that characterize the various states of this flow - namely the three-dimensional (essentially unstratified), non-equilibrium (or 'wake-collapse') and quasi-two-dimensional (or 'two-component') regimes observed elsewhere for wakes embedded in both weakly and strongly stratified backgrounds. The wake-collapse regime is not accompanied by transfer (or 'reconversion') of the potential energy of the turbulence to the kinetic energy of the turbulence, implying that this is not an essential feature of stratified-wake dynamics. The dependence upon Reynolds number of the duration of the wake-collapse period is demonstrated, and the effect of the details of the initial/near-field conditions of the wake on its subsequent development is examined.

Redford, J. A.↗
NASA NTRS1993

Stratified turbulence in the atmosphere and oceans - A new subgrid model

Turbulence in stably and unstably stratified media is studied, and the results are used to construct a subgrid simulation (SGS) model for use in large eddy simulation (LES). It was found that, although the assumption of inertiality of the subgrid scales is reasonable for the case of unstable stratification, it ceases to be so in the case of stable stratification, where gravity removes kinetic energy from the eddies: the generation of gravity waves becomes the dominant physical process, with dissipation relegated to higher wavenumbers. Preliminary results show that the total kinetic energy dissipation length scale increases with stability, in accordance with LES results but in disagreement with Deardorff's model that suggests a decrease of all dissipation scales in presence of stratification.

Canuto, V. M.↗
NASA NTRS2002

Waves in Turbulent Stably Stratified Shear Flow

Two approaches for the identification of internal gravity waves in sheared and unsheared homogeneous stratified turbulence are investigated. First, the phase angle between the vertical velocity and density fluctuations is considered. It was found, however, that a continuous distribution of the phase angle is present in weakly and strongly stratified flow. Second, a projection onto the solution of the linearized inviscid equations of motion of unsheared stratified flow is investigated. It was found that a solution of the fully nonlinear viscous Navier-Stokes equations can be represented by the linearized inviscid solution. The projection yields a decomposition into vertical wave modes and horizontal vortical modes.

Jacobitz, F. G.↗
NASA NTRS2002

Waves in Turbulent Stably-Stratified Shear Flow

Two approaches for the identification of internal gravity waves in sheared and unsheared homogeneous stratified turbulence are investigated. First, the phase angle between the vertical velocity and density fluctuations is considered. It is found, however, that a continuous distribution of the phase angle is present in weakly and strongly stratified flow. Second, a projection onto the solution of the linearized inviscid equations of motion of unsheared stratified flow is investigated. It is found that a solution of the fully nonlinear viscous Navier-Stokes equations can be represented by the linearized inviscid solution. The projection yields a decomposition into vertical wave modes and horizontal vortical modes.

Jacobitz, F. G.↗
NASA NTRS2002

Entrainment-Zone Restratification and Flow Structures in Stratified Shear Turbulence

Late-time dynamics and morphology of a stratified turbulent shear layer are examined using 1) Reynolds-stress and heat-flux budgets, 2) the single-point structure tensors introduced by Kassinos et al. (2001), and 3) flow visualization via 3D volume rendering. Flux reversal is observed during restratification in the edges of the turbulent layer. We present a first attempt to quantify the turbulence-mean-flow interaction and to characterize the predominant flow structures. Future work will extend this analysis to earlier times and different values of the Reynolds and Richardson numbers.

Reif, B. Anders Pettersson↗
NASA NTRS1990

Direct numerical simulations of stably-stratified sheared turbulence: Implications for oceanic mixing

Direct numerical simulations of the time evolution of homogeneous stably stratified turbulent shear flows have been performed for several Richardson numbers Ri and Reynolds numbers R(sub lambda) in earlier works. The results show excellent agreement with length scale models developed from laboratory experiments to characterize oceanic turbulence. When the Richardson number Ri is less than the stationary value Ri(sub s), the turbulence intensity grows at all scales, and the growth rate appears to be a function of Ri. The size of the vertical density inversions also increases. On the other hand, when Ri is greater than or equal to Ri(sub s) the largest turbulent eddies become vertically constrained by buoyancy when the Ellison (turbulence) scale L(sub E) and the Ozmidov (buoyancy) scale L(sub O) are equal. At this point, the mixing efficiency is maximal and corresponds to a flux Richardson number R(sub f) = 0.20. The vertical mass flux becomes counter-gradient when epsilon = 19(nu)N(exp 2) and vertical density overturns are suppressed in less than half a Brunt-Vaisala period. The results of the simulations were also recast in terms of the Hydrodynamic Phase Diagram introduced in fossil turbulence models. The so-called point of fossilization occurs when epsilon = 4DCN(exp 2); Gibson proposed 13DCN(exp 2). This value is in agreement with indirect laboratory observations and field observations. Finally, the validity of the steady-state models to estimate vertical eddy diffusivities in the oceanic thermocline is discussed.

Itsweire, E. C.↗
NASA NTRS1994

Stably stratified shear turbulence: A new model for the energy dissipation length scale

A model is presented to compute the turbulent kinetic energy dissipation length scale l(sub epsilon) in a stably stratified shear flow. The expression for l(sub epsilon) is derived from solving the spectral balance equation for the turbulent kinetic energy. The buoyancy spectrum entering such equation is constructed using a Lagrangian timescale with modifications due to stratification. The final result for l(sub epsilon) is given in algebraic form as a function of the Froude number Fr and the flux Richardson number R(sub f), l(sub epsilon) = l(sub epsilon)(Fr, R(sub f). The model predicts that for R(sub f) less than R(sub fc), l(sub epsilon) decreases with stratification. An attractive feature of the present model is that it encompasses, as special cases, some seemingly different models for l(sub epsilon) that have been proposed in the past by Deardorff, Hunt et al., Weinstock, and Canuto and Minotti. An alternative form for the dissipation rate epsilon is also discussed that may be useful when one uses a prognostic equation for the heat flux. The present model is applicable to subgrid-scale models, which are needed in large eddy simulations (LES), as well as to ensemble average models. The model is applied to predict the variation of l(sub epsilon) with height z in the planetary boundary layer. The resulting l(sub epsilon) versus z profile reproduces very closely the nonmonotonic profile of l(sub epsilon) exhibited by many LES calculations, beginning with the one by Deardorff in 1974.

Cheng, Y.↗