skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Tempered fractional LES modeling
The presence of non-local interactions and intermittent signals in the homogeneous isotropic turbulence grant multi-point statistical functions a key role in formulating a new generation of large-eddy simulation (LES) models of higher fidelity. We establish a tempered fractional-order modelling framework for developing non-local LES subgrid-scale models, starting from the kinetic transport. We employ a tempered Lévy-stable distribution to represent the source of turbulent effects at the kinetic level, and we rigorously show that the corresponding turbulence closure term emerges as the tempered fractional Laplacian, $$(\varDelta +\lambda )^{\alpha } (\cdot )$$ , for $$\alpha \in (0,1)$$ , $$\alpha \neq \frac {1}{2}$$ and $$\lambda >0$$ in the filtered Navier–Stokes equations. Moreover, we prove the frame invariant properties of the proposed model, complying with the subgrid-scale stresses. To characterize the optimum values of model parameters and infer the enhanced efficiency of the tempered fractional subgrid-scale model, we develop a robust algorithm, involving two-point structure functions and conventional correlation coefficients. In an a priori statistical study, we evaluate the capabilities of the developed model in fulfilling the closed essential requirements, obtained for a weaker sense of the ideal LES model (Meneveau, Phys. Fluids , vol. 6, issue 2, 1994, pp. 815–833). Finally, the model undergoes the a posteriori analysis to ensure the numerical stability and pragmatic efficiency of the model.  more » « less
Award ID(s):
1923201
PAR ID:
10359632
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Journal of Fluid Mechanics
Volume:
932
ISSN:
0022-1120
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; (, Physics of Fluids)
    Extensive experimental evidence highlights that scalar turbulence exhibits anomalous diffusion and stronger intermittency levels at small scales compared to that in fluid turbulence. This renders the corresponding subgrid-scale dynamics modeling for scalar turbulence a greater challenge to date. We develop a new large eddy simulation (LES) paradigm for efficiently and dynamically nonlocal LES modeling of the scalar turbulence. To this end, we formulate the underlying nonlocal model starting from the filtered Boltzmann kinetic transport equation, where the divergence of subgrid-scale scalar fluxes emerges as a fractional-order Laplacian term in the filtered advection–diffusion model, coding the corresponding superdiffusive nature of scalar turbulence. Subsequently, we develop a robust data-driven algorithm for estimation of the fractional (noninteger) Laplacian exponent, where we, on the fly, calculate the corresponding model coefficient employing a new dynamic procedure. Our a priori tests show that our new dynamically nonlocal LES paradigm provides better agreement with the ground-truth filtered direct numerical simulation data in comparison to the conventional static and dynamic Prandtl–Smagorinsky models. Moreover, in order to analyze the numerical stability and assessing the model's performance, we carry out comprehensive a posteriori tests. They unanimously illustrate that our new model considerably outperforms other existing functional models, correctly predicting the backscattering phenomena and, at the same time, providing higher correlations at small-to-large filter sizes. We conclude that our proposed nonlocal subgrid-scale model for scalar turbulence is amenable for coarse LES and very large eddy simulation frameworks even with strong anisotropies, applicable to environmental applications. 
    more » « less
  2. ; (, Journal of Fluid Mechanics)
    In this study, we revisit the spectral transfer model for the turbulent intensity in passive scalar transport (under large-scale anisotropic forcing), and a subsequent modification to the scaling of scalar variance cascade is presented. From the modified spectral transfer model, we obtain a revised scalar transport model using a fractional-order Laplacian operator that facilitates the robust inclusion of the non-local effects originating from large-scale anisotropy transferred across the multitude of scales in the turbulent cascade. We provide ana prioriestimate for the non-local model based on the scaling analysis of the scalar spectrum, and later examine our developed model through direct numerical simulation. We present a detailed analysis on the evolution of the scalar variance, high-order statistics of the scalar gradient and important two-point statistical metrics of the turbulent transport to make a comprehensive comparison between the non-local model and its standard version. Finally, we present an analysis that seamlessly reconciles the similarities between the developed model with the fractional-order subgrid-scale scalar flux model for large-eddy simulation (Akhavan-Safaeiet al.,J. Comput. Phys., vol. 446, 2021, 110571) when the filter scale approaches the dissipative scales of turbulent transport. In order to perform this task, we employ a Gaussian process regression model to predict the model coefficient for the fractional-order subgrid model. 
    more » « less
  3. ; ; ; ; (, Journal of Advances in Modeling Earth Systems)
    Abstract Because of their limited spatial resolution, numerical weather prediction and climate models have to rely on parameterizations to represent atmospheric turbulence and convection. Historically, largely independent approaches have been used to represent boundary layer turbulence and convection, neglecting important interactions at the subgrid scale. Here we build on an eddy‐diffusivity mass‐flux (EDMF) scheme that represents all subgrid‐scale mixing in a unified manner, partitioning subgrid‐scale fluctuations into contributions from local diffusive mixing and coherent advective structures and allowing them to interact within a single framework. The EDMF scheme requires closures for the interaction between the turbulent environment and the plumes and for local mixing. A second‐order equation for turbulence kinetic energy (TKE) provides one ingredient for the diffusive local mixing closure, leaving a mixing length to be parameterized. Here, we propose a new mixing length formulation, based on constraints derived from the TKE balance. It expresses local mixing in terms of the same physical processes in all regimes of boundary layer flow. The formulation is tested at a range of resolutions and across a wide range of boundary layer regimes, including a stably stratified boundary layer, a stratocumulus‐topped marine boundary layer, and dry convection. Comparison with large eddy simulations (LES) shows that the EDMF scheme with this diffusive mixing parameterization accurately captures the structure of the boundary layer and clouds in all cases considered. 
    more » « less
  4. ; (, Physics of Fluids)
    We developed a novel autonomously dynamic nonlocal turbulence model for the large and very large eddy simulation (LES, VLES) of homogeneous isotropic turbulent flows. The model is based on a generalized (integer-to-noninteger)-order Laplacian of the filtered velocity field, and a novel dynamic model has been formulated to avoid the need for tuning the model constant. Three data-driven approaches were introduced for the determination of the fractional-order to have a model that is totally free of any tuning parameter. Our analysis includes both the a priori and the a posteriori tests. In the former test, using a high-fidelity and well-resolved dataset from direct numerical simulations (DNSs), we computed the correlation coefficients for the stress components of the subgrid-scale (SGS) stress tensor and the one we get directly from the DNS results. Moreover, we compared the probability density function of the ensemble-averaged SGS forces for different filter sizes. In the latter, we employed our new model along with other conventional models including the static and dynamic Smagorinsky models into our pseudo-spectral solver and tested the final predicted quantities. The results of the newly developed model exhibit an expressive agreement with the ground-truth DNS results in all components of the SGS stress and forces. Also, the model exhibits promising results in the VLES region as well as the LES region, which could be remarkably important for cost-efficient nonlocal turbulence modeling, e.g., in meteorological and environmental applications. 
    more » « less
  5. ; ; (, Computers fluids)
    Langmuir turbulence consists of Langmuir circulation (LC) generated at the surface of rivers, lakes, bays, and oceans by the interaction between the wind-driven shear and surface gravity waves. In homogeneous shallow water, LC can extend to the bottom of the water column and interact with the bottom boundary layer. Large-eddy simulation (LES) of LC in shallow water was performed with the finite volume method and various forms of subgrid-scale (SGS) model characterized by different near-wall treatments of the SGS eddy viscosity. The wave forcing relative to wind forcing in the LES was set following the field measurements of full-depth LC during the presence of LC engulfing a water column 15 m in depth in the coastal ocean, reported in the literature. It is found that the SGS model can greatly impact the structure of LC in the lower half of the water column. Results are evaluated in terms of (1) the Langmuir turbulence velocity statistics and (2) the lateral (crosswind) length scale and overall cell structure of LC. LES with an eddy viscosity with velocity scale in terms of S and Ω (where S is the norm of the strain rate tensor and Ω is the norm of the vorticity tensor) and a Van Driest wall damping function (referred to as the S-Omega model) is found to provide best agreement with pseudo-spectral LES in terms of the lateral length scale and overall cell structure of LC. Two other SGS models, namely the dynamic Smagorinsky model and the wall-adapting local-eddy viscosity model are found to provide less agreement with pseudo- spectral LES, for example, as they lead to less coherent bottom convergence of the cells and weaker associ ated upward transport of slow downwind moving fluid. Finally, LES with the S-Omega SGS model is also found to lead to good agreement with physical measurements of LC in the coastal ocean in terms of Langmuir turbulence decay during periods of surface heating 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email