Academic literature on the topic 'Turbulence Closures'

This study investigates the pressure–strain tensor ($\unicode[STIX]{x1D72B}$) in Langmuir turbulence. The pressure–strain tensor is determined from large-eddy simulations (LES), and is partitioned into components associated with the mean current shear (rapid), the Stokes shear and the turbulent–turbulent (slow) interactions. The rapid component can be parameterized using existing closure models, although the coefficients in the closure models are particular to Langmuir turbulence. A closure model for the Stokes component is proposed, and it is shown to agree with results from the LES. The slow component of $\unicode[STIX]{x1D72B}$ does not agree with existing ‘return-to-isotropy’ closure models for five of the six components of the Reynolds stress tensor, and a new closure model is proposed that accounts for these deviations which vary systematically with Langmuir number, $La_{t}$, and depth. The implications of these results for second- and first-order closures of Langmuir turbulence are discussed.

In previous computational fluid dynamics studies of breaking waves, there has been a marked tendency to severely over-estimate turbulence levels, both pre- and post-breaking. This problem is most likely related to the previously described (though not sufficiently well recognized) conditional instability of widely used turbulence models when used to close Reynolds-averaged Navier–Stokes (RANS) equations in regions of nearly potential flow with finite strain, resulting in exponential growth of the turbulent kinetic energy and eddy viscosity. While this problem has been known for nearly 20 years, a suitable and fundamentally sound solution has yet to be developed. In this work it is demonstrated that virtually all commonly used two-equation turbulence closure models are unconditionally, rather than conditionally, unstable in such regions. A new formulation of the $k$–$\unicode[STIX]{x1D714}$ closure is developed which elegantly stabilizes the model in nearly potential flow regions, with modifications remaining passive in sheared flow regions, thus solving this long-standing problem. Computed results involving non-breaking waves demonstrate that the new stabilized closure enables nearly constant form wave propagation over long durations, avoiding the exponential growth of the eddy viscosity and inevitable wave decay exhibited by standard closures. Additional applications on breaking waves demonstrate that the new stabilized model avoids the unphysical generation of pre-breaking turbulence which widely plagues existing closures. The new model is demonstrated to be capable of predicting accurate pre- and post-breaking surface elevations, as well as turbulence and undertow velocity profiles, especially during transition from pre-breaking to the outer surf zone. Results in the inner surf zone are similar to standard closures. Similar methods for formally stabilizing other widely used closure models ($k$–$\unicode[STIX]{x1D714}$ and $k$–$\unicode[STIX]{x1D700}$ variants) are likewise developed, and it is recommended that these be utilized in future RANS simulations of surface waves. (In the above $k$ is the turbulent kinetic energy density, $\unicode[STIX]{x1D714}$ is the specific dissipation rate, and $\unicode[STIX]{x1D700}$ is the dissipation.)

Within the framework of the theory of unsteady turbulent flows in a stratified fluid, a new parameterization of the turbulent Prandtl number is proposed. The parameterization is included in the k-ε-closure and used within the three-dimensional model of thermohydrodynamics of an enclosed water body where density distribution includes pycnocline. This allows us to describe turbulence in a stratified shear flow without the restrictions associated with the gradient Richardson number and justify the choice of closure constants. Numerical experiments, where the downward penetration of turbulence was considered, confirm the advantage of the developed approach in describing the effects neglected in the classical closures.

Abstract This paper presents a turbulence closure for neutral and stratified atmospheric conditions. The closure is based on the concept of the total turbulent energy. The total turbulent energy is the sum of the turbulent kinetic energy and turbulent potential energy, which is proportional to the potential temperature variance. The closure uses recent observational findings to take into account the mean flow stability. These observations indicate that turbulent transfer of heat and momentum behaves differently under very stable stratification. Whereas the turbulent heat flux tends toward zero beyond a certain stability limit, the turbulent stress stays finite. The suggested scheme avoids the problem of self-correlation. The latter is an improvement over the widely used Monin–Obukhov-based closures. Numerous large-eddy simulations, including a wide range of neutral and stably stratified cases, are used to estimate likely values of two free constants. In a benchmark case the new turbulence closure performs indistinguishably from independent large-eddy simulations.

AbstractA prior second-moment closure (SMC) model of Langmuir turbulence in the upper ocean is modified by introduction of inhomogeneous pressure–strain rate and pressure–scalar gradient closures that are similar to the high Reynolds number, near-wall treatments for solid wall boundaries. This repairs several near-surface defects in the algebraic Reynolds stress model (ARSM) of the prior SMC by redirecting Craik–Leibovich (CL) vortex force production of turbulent kinetic energy out of the surface-normal vertical component and into a horizontal one, with an associated reduction in near-surface CL production of vertical momentum flux. A surface-proximity function introduces a new closure parameter that is tuned to previous results from large-eddy simulations (LES), and a numerical SMC model based on stability functions from the new ARSM produces improved comparisons with mean profiles of momentum and TKE components from steady-state LES results forced by aligned wind and waves. An examination of higher-order quasi-homogeneous closures and a numerical simulation of Langmuir turbulence away from the boundaries both show the near-surface inhomogeneous closure to be both necessary for consistency and preferable for simplicity.

We consider a relaxation equation for turbulence wavenumber for use in semi-empirical turbulence closures. It is shown that the well-known phenomenological equation for the dissipation rate of turbulent kinetic energy can be related to this relaxation equation as a close approximation of the latter for stably stratified quasi-stationary flows. The proposed approach allows for more physically found definition of the empirical constants and improvement of atmospheric and oceanic boundary layer turbulence closures by using direct numerical and large eddy simulation data to define equilibrium states and relaxation mechanisms.

This international scientific workshop was organized in Lyon, France, from 10 to 12 May 2000. Its focus was ‘Two-point closures and their applications’, with the understanding that the analysis and design of such models requires expert knowledge coming from a wide range of areas in turbulence research, e.g. experiments, numerical simulations, asymptotic models, etc.In the global challenge of turbulence modelling, two-point closures prove useful in many ways. Two-point correlations and spectra are useful measures of the distortion of the eddy structure of turbulence by stratification, large-scale strains, rotation, etc. In some cases, e.g. near boundaries, spectra can be drastically changed. In addition to the accurate characterization of turbulence, the explicit computation of two-point correlations or spectra shows how the internal dynamics of the various scales of motion are affected by such distortion, especially the cascade process on which the production/dissipation relationship depends. Distortion can be the cause of large departures from isotropic homogeneous turbulence, pulling turbulent flows far away from the local equilibrium that is often assumed. A rather weak departure can allow the use of linearized theories such as rapid distortion theory, for the applicability of which rational bounds may be estimated by comparisons with weakly nonlinear calculations. A different approach is necessary when dealing with larger departures, for instance due to growth of instabilities. In that case new physical or similarity arguments have to be employed to obtain a satisfactory description of the modification to the cascade process, which can even undergo reversal in the limit when three-dimensional turbulence becomes two-dimensional. Of course, significant changes in spectra have direct implications for one-point measures of turbulence – which can be explicitly derived by integration of two-point correlations – used in most industrial closure schemes. Such one-point models consequently need to be adapted when turbulence is strongly affected by distortion.

The flow and turbulence in an IC engine cylinder were studied using the SSG variant of the Reynolds stress turbulence closure model. In-cylinder turbulence is characterized by strong turbulence anisotropy and flow rotation, which aid in air-fuel mixing. It is argued that solving the differential transport equations for each turbulent stress tensor component, as implied by second-moment closures, can better reproduce stress anisotropy and effects of rotation, than with eddy-viscosity models. Therefore, a Reynolds stress model that can meet the demands of in-cylinder flows was incorporated into an engine flow solver. The solver and SSG turbulence model were first successfully tested with two different validation cases. Finally, simulations were applied to IC-engine like geometries. The results showed that the Reynolds stress model predicted additional flow structures and yielded less diffusive profiles than those predicted by an eddy-viscosity model. [S0742-4795(00)00101-0]

This paper presents an assessment of machine-learned turbulence closures, trained for improving wake-mixing prediction, in the context of LPT flows. To this end, a three-dimensional cascade of industrial relevance, representative of modern LPT bladings, was analyzed, using a state-of-the-art RANS approach, over a wide range of Reynolds numbers. To ensure that the wake originates from correctly reproduced blade boundary-layers, preliminary analyses were carried out to check for the impact of transition closures, and the best-performing numerical setup was identified. Two different machine-learned closures were considered. They were applied in a prescribed region downstream of the blade trailing edge, excluding the endwall boundary layers. A sensitivity analysis to the distance from the trailing edge at which they are activated is presented in order to assess their applicability to the whole wake affected portion of the computational domain and outside the training region. It is shown how the best-performing closure can provide results in very good agreement with the experimental data in terms of wake loss profiles, with substantial improvements relative to traditional turbulence models. The discussed analysis also provides guidelines for defining an automated zonal application of turbulence closures trained for wake-mixing predictions.

Abridged statistical dynamical closures, for the interaction of two-dimensional inhomogeneous turbulent flows with topography and Rossby waves on a beta–plane, are formulated from the Quasi-diagonal Direct Interaction Approximation (QDIA) theory, at various levels of simplification. An abridged QDIA is obtained by replacing the mean field trajectory, from initial-time to current-time, in the time history integrals of the non-Markovian closure by the current-time mean field. Three variants of Markovian Inhomogeneous Closures (MICs) are formulated from the abridged QDIA by using the current-time, prior-time, and correlation fluctuation dissipation theorems. The abridged MICs have auxiliary prognostic equations for relaxation functions that approximate the information in the time history integrals of the QDIA. The abridged MICs are more efficient than the QDIA for long integrations with just two relaxation functions required. The efficacy of the closures is studied in 10-day simulations with an easterly large-scale flow impinging on a conical mountain to generate rapidly growing Rossby waves in a turbulent environment. The abridged closures closely agree with the statistics of large ensembles of direct numerical simulations for the mean and transients. An Eddy Damped Markovian Inhomogeneous Closure (EDMIC), with analytical relaxation functions, which generalizes the Eddy Dampened Quasi Normal Markovian (EDQNM) to inhomogeneous flows, is formulated and shown to be realizable under the same circumstances as the homogeneous EDQNM.