Analysis and extension of the quadratic constitutive relation for RANS methods

The quadratic constitutive relation was proposed as an extension of minimal complexity to linear eddy-viscosity models in order to improve mean flow predictions by better estimating turbulent stress distributions. However, the successes of this modification have been relatively modest and are limited to improved calculations of flow along streamwise corners, which are influenced by weak secondary vortices. This paper revisits the quadratic constitutive relation in an attempt to explain its capabilities and deficiencies. The success in streamwise corner flows cannot be entirely explained by significant improvements in turbulent stress estimates in general, but is instead due to better prediction of the particular turbulent stress combinations which appear in the mean streamwise vorticity equation. As a consequence of this investigation, a new formulation of turbulent stress modification is proposed, which appears to better predict the turbulent stress distributions for a variety of flows: channel flow, equilibrium boundary layers, pipe flow, separated boundary layers and square duct flow.

Statistically Targeted Forcing (STF) Method for Synthetic Turbulence Generation of Initial Conditions in Three-Dimensional Turbulent Mixing Layer Flow

Computational fluid dynamics (CFD) results are presented for synthetic turbulence generation of initial conditions for the canonical test case of a temporally-developing turbulent mixing layer (TTML) flow. This numerical study investigates the performance of a newly proposed Statistically Targeted Forcing (STF) method, and its capability to act as a restoring force to match the target mean velocity and turbulent stress in a temporally-developing flow where highly unsteady destabilizing mechanisms and influence are evident. Several previous investigations exist documenting vortex dynamics of the turbulent mixing layer, but limited investigations exist on synthetic turbulence generation forcing methods to prescribe initial conditions. The objective of this study is to evaluate the performance of the newly proposed STF method to capture the vortex dynamics and effectively match target mean velocity and resolved turbulent stress predictions using large-eddy simulation. Results are interrogated and compared to statistical velocity and turbulent stress distributions obtained from DNS simulations available in the literature. Results show that the STF method can successfully reproduce desired statistical distributions in a turbulent mixing layer flow.

Atmospheric Boundary Layer Turbulence in the Presence of Swell: Turbulent Kinetic Energy Budget, Monin–Obukhov Similarity Theory, and Inertial Dissipation Method

Turbulence over the mobile ocean surface has distinct properties compared to turbulence over land. Thus, findings that are based on the turbulent kinetic energy (TKE) budget and Monin–Obukhov similarity theory (MOST) over land may not be applicable to conditions over ocean partly because of the existence of a wave boundary layer (the lower part of atmospheric boundary layer including effects of surface waves; we used the term “WBL” in this article for convenience), where the total stress can be separated into turbulent stress and wave coherent stress. Here the turbulent stress is defined as the stress generated by wind shear and buoyancy, while the wave coherent stress accounts for the momentum transfer between ocean waves and atmosphere. In this study, applicability of the turbulent kinetic energy (TKE) budget and the inertial dissipation method (IDM) in the context of the MOST within the WBL are examined. It was found that turbulent transport terms in the TKE budget should not be neglected when calculating the total stress under swell conditions. This was confirmed by observations made on a fixed platform. The results also suggested that turbulent stress, rather than total stress, should be used when applying the MOST within the WBL. By combining the TKE budget and MOST, our study showed that the stress computed by the traditional IDM corresponds to the turbulent stress rather than the total stress. The swell wave coherent stress should be considered when applying the IDM to calculate the stress in the WBL.

Atmospheric boundary layer turbulence in the presence of swell: turbulent kinetic energy budget, Monin-Obukhov similarity theory and inertial dissipation method

<p><span>Turbulence over the mobile ocean surface has distinct properties compared to turbulence over land. This raises the issue of whether functions such as the turbulent kinetic energy (TKE) budget and Monin-Obukhov similarity theory (MOST) determined over land are directly applicable to ocean surfaces because of the existence of a wave boundary layer (the lower part of atmospheric boundary layer including effects of surface waves. We used the term “WBL” in this article for convenience), where the total stress can be separated into turbulent stress and wave coherent stress. Here the turbulent stress is defined as the stress generated by wind shear and buoyancy, and wave coherent stress accounts for the momentum transfer between ocean waves and atmosphere. In this study, applications of the turbulent kinetic energy (TKE) budget and the inertial dissipation method (IDM) in the context of the Monin-Obukhov similarity theory (MOST) within the WBL are examined. It was found that turbulent transport terms in the TKE budget should not be neglected when calculating the total stress under swell conditions. This was confirmed by observations made on a fixed platform. The results also suggested that turbulent stress, rather than total stress should be used when applying the MOST within the WBL. By combing the TKE budget and MOST, our study showed that the stress computed by the traditional IDM corresponds to turbulent stress rather than total stress. The swell wave coherent stress should be considered when applying the IDM to calculate the stress in the WBL.</span></p>

Sampling Methods for Metocean Data Aiming at Hydrodynamic Modeling of Estuarine and Coastal Areas

Field observations require adequate metocean data gathering to promote the link between environmental diagnostic and prognostic obtained from modeling techniques. In general, model confidence can be improved by using data which present better quality and by improved parametrizations. This paper discusses and suggests timing routines for data gathering which are enough to describe the hydrodynamic behavior of estuarine and coastal areas. From the environmental diagnostics viewpoint, a sampling procedure is defined to the temporal scales providing data with adequate resolution to describe the natural process without signal aliasing. The proposed sampling procedure was based on the analysis of a data set of tides, currents, waves, water temperature, and meteorological variables observed at several stations along the Brazilian coast. The instrument setup was based mainly on the results of the harmonic analysis of tides. It is shown that the setup of instruments for simultaneous measurements of currents and waves requires special attention particularly in sites that present low currents and the action of waves. A subset of data gathered in shallow bays was used to estimate the surface turbulent stress by using a classical and a slightly modified parametrization for the wind drag coefficient. Under near neutral atmospheric stability conditions and high tide excursion, the surface turbulent stress obtained with the classical and the modified parametrization differed but the current profiles are expected to be only partially affected by wind-induced drift currents.

Noll’s Axioms and Formulation of the Closure Relations for the Subgrid Turbulent Tensor in Large Eddy Simulation

In this paper, the relation between the Noll formulation of the principle of material frame indifference and the principle of turbulent frame indifference in large eddy simulation, is revised. The principle of material frame indifference and the principle of turbulent frame indifference proposed by Hutter and Joenk imposes that both constitutive equations and turbulent closure relations must respect both the requirement of form invariance, and the requirement of frame independence. In this paper, a new rule for the formalization of turbulent closure relations, is proposed. The generalized SGS turbulent stress tensor is related exclusively to the generalized SGS turbulent kinetic energy, which is calculated by means of its balance equation, and the modified Leonard tensor.

Improved Junction Body Flow Modeling Through Data-Driven Symbolic Regression

A novel data-driven turbulence modeling framework is presented and applied to the problem of junction body flow. In particular, a symbolic regression approach is used to find nonlinear analytical expressions of the turbulent stress‐strain coupling that are ready for implementation in computational fluid dynamics (CFD) solvers using Reynolds-averaged Navier‐Stokes (RANS) closures. Results from baseline linear RANS closure calculations of a finite square-mounted cylinder with a Reynolds number of <inline-graphic xlink:href="josr09180053inf1.tif"/>, based on diameter and freestream velocity, are shown to considerably overpredict the separated flow region downstream of the square cylinder, mainly because of the failure of the model to accurately represent the complex vortex structure generated by the junction flow. In the present study, a symbolic regression tool built on a gene expression programming technique is used to find a nonlinear constitutive stress‐strain relationship. In short, the algorithm finds the most appropriate linear combination of basis functions and spatially varying coefficients that approximate the turbulent stress tensor from high-fidelity data. Here, the high-fidelity data, or the so-called training data, were obtained from a hybrid RANS/Large Eddy Simulation (LES) calculation also developed with symbolic regression that showed excellent agreement with direct numerical simulation data. The present study, therefore, also demonstrates that training data required for RANS closure development can be obtained using computationally more affordable approaches, such as hybrid RANS/LES. A procedure is presented to evaluate which of the individual basis functions that are available for model development are most likely to produce a successful nonlinear closure. A new model is built using those basis functions only. This new model is then tested, i.e., an actual CFD calculation is performed, on the well-known periodic hills case and produces significantly better results than the linear baseline model, despite this test case being fundamentally different from the training case. Finally, the new model is shown to also improve predictive accuracy for a surface-mounted cube placed in a channel at a cube height Reynolds number of <inline-graphic xlink:href="josr09180053inf2.tif"/> over traditional linear RANS closures.