Theoretical Formulation

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Mohsen Zayernouri - One of the best experts on this subject based on the ideXlab platform.

  • a fractional subgrid scale model for turbulent flows Theoretical Formulation and a priori study
    Physics of Fluids, 2020
    Co-Authors: Mehdi Samiee, Ali Akhavansafaei, Mohsen Zayernouri
    Abstract:

    Coherent structures/motions in turbulence inherently give rise to intermittent signals with sharp peaks, heavy-skirt, and skewed distributions of velocity increments, highlighting the non-Gaussian nature of turbulence. This suggests that the spatial nonlocal interactions cannot be ruled out of the turbulence physics. Furthermore, filtering the Navier–Stokes equations in the large eddy simulation of turbulent flows would further enhance the existing nonlocality, emerging in the corresponding subgrid scale fluid motions. This urges the development of new nonlocal closure models, which respect the corresponding non-Gaussian statistics of the subgrid stochastic motions. To this end and starting from the filtered Boltzmann equation, we model the corresponding equilibrium distribution function with a Levy-stable distribution, leading to the proposed fractional-order modeling of subgrid-scale stresses. We approximate the filtered equilibrium distribution function with a power-law term and derive the corresponding filtered Navier–Stokes equations. Subsequently in our functional modeling, the divergence of subgrid-scale stresses emerges as a single-parameter fractional Laplacian, (−Δ)α(·), α ∈ (0, 1], of the filtered velocity field. The only model parameter, i.e., the fractional exponent, appears to be strictly dependent on the filter-width and the flow Reynolds number. We furthermore explore the main physical and mathematical properties of the proposed model under a set of mild conditions. Finally, the introduced model undergoes a priori evaluations based on the direct numerical simulation database of forced and decaying homogeneous isotropic turbulent flows at relatively high and moderate Reynolds numbers, respectively. Such analysis provides a comparative study of predictability and performance of the proposed fractional model.

  • a fractional subgrid scale model for turbulent flows Theoretical Formulation and a priori study
    arXiv: Computational Engineering Finance and Science, 2019
    Co-Authors: Mehdi Samiee, Ali Akhavansafaei, Mohsen Zayernouri
    Abstract:

    Coherent structures/motions in turbulence inherently give rise to intermittent signals with sharp peaks, heavy-skirt, and skewed distributions of velocity increments, highlighting the non-Gaussian nature of turbulence. That suggests that the spatial nonlocal interactions cannot be ruled out of the turbulence physics. Furthermore, filtering the Navier-Stokes equations in the large eddy simulation of turbulent flows would further enhance the existing nonlocality, emerging in the corresponding subgrid scale fluid motions. That urges the development of new nonlocal closure models, which respect the corresponding non-Gaussian statistics of the subgrid stochastic motions. To this end and starting from the filtered Boltzmann equation, we model the corresponding equilibrium distribution function with a \textit{Levy}-stable distribution, leading to the proposed fractional-order modeling of subgrid-scale stresses. We approximate the filtered equilibrium distribution function with a power-law term, and derive the corresponding filtered Navier-Stokes equations. Subsequently in our functional modeling, the divergence of subgrid-scale stresses emerges as a single-parameter fractional Laplacian, $(-\Delta)^{\alpha}(\cdot)$, $\alpha \in (0,1]$, of the filtered velocity field. The only model parameter, i.e., the fractional exponent, appears to be strictly depending on the filter-width and the flow Reynolds number. We furthermore explore the main physical and mathematical properties of the proposed model under a set of mild conditions. Finally, the introduced model undergoes \textit{a priori} evaluations based on the direct numerical simulation database of forced and decaying homogeneous isotropic turbulent flows at relatively high and moderate Reynolds numbers, respectively. Such analysis provides a comparative study of predictability and performance of the proposed fractional model.

R Samadi - One of the best experts on this subject based on the ideXlab platform.

  • excitation of stellar p modes by turbulent convection i Theoretical Formulation
    Astronomy and Astrophysics, 2001
    Co-Authors: R Samadi, M J Goupil
    Abstract:

    Stochatic excitation of stellar oscillations by turbulent convection is investigated and an expression for the power injected into the oscillations by the turbulent convection of the outer layers is derived which takes into account excitation through turbulent Reynolds stresses and turbulent entropy fluctuations. This formula- tion generalizes results from previous works and is built so as to enable investigations of various possible spatial and temporal spectra of stellar turbulent convection. For the Reynolds stress contribution and assuming the Kolmogorov spectrum we obtain a similar Formulation to those derived by previous authors. The entropy contri- bution to excitation is found to originate from the advection of the Eulerian entropy fluctuations by the turbulent velocity eld. Numerical computations in the solar case in a companion paper indicate that the entropy source term is dominant over the Reynold stress contribution to mode excitation, except at high frequencies.

  • excitation of stellar p modes by turbulent convection 1 Theoretical Formulation
    arXiv: Astrophysics, 2001
    Co-Authors: R Samadi, Mariejo Goupil
    Abstract:

    Stochatic excitation of stellar oscillations by turbulent convection is investigated and an expression for the power injected into the oscillations by the turbulent convection of the outer layers is derived which takes into account excitation through turbulent Reynolds stresses and turbulent entropy fluctuations. This Formulation generalizes results from previous works and is built so as to enable investigations of various possible spatial and temporal spectra of stellar turbulent convection. For the Reynolds stress contribution and assuming the Kolmogorov spectrum we obtain a similar Formulation than those derived by previous authors. The entropy contribution to excitation is found to originate from the advection of the Eulerian entropy fluctuations by the turbulent velocity field. Numerical computations in the solar case in a companion paper indicate that the entropy source term is dominant over Reynold stress contribution to mode excitation, except at high frequencies.

Mehdi Samiee - One of the best experts on this subject based on the ideXlab platform.

  • a fractional subgrid scale model for turbulent flows Theoretical Formulation and a priori study
    Physics of Fluids, 2020
    Co-Authors: Mehdi Samiee, Ali Akhavansafaei, Mohsen Zayernouri
    Abstract:

    Coherent structures/motions in turbulence inherently give rise to intermittent signals with sharp peaks, heavy-skirt, and skewed distributions of velocity increments, highlighting the non-Gaussian nature of turbulence. This suggests that the spatial nonlocal interactions cannot be ruled out of the turbulence physics. Furthermore, filtering the Navier–Stokes equations in the large eddy simulation of turbulent flows would further enhance the existing nonlocality, emerging in the corresponding subgrid scale fluid motions. This urges the development of new nonlocal closure models, which respect the corresponding non-Gaussian statistics of the subgrid stochastic motions. To this end and starting from the filtered Boltzmann equation, we model the corresponding equilibrium distribution function with a Levy-stable distribution, leading to the proposed fractional-order modeling of subgrid-scale stresses. We approximate the filtered equilibrium distribution function with a power-law term and derive the corresponding filtered Navier–Stokes equations. Subsequently in our functional modeling, the divergence of subgrid-scale stresses emerges as a single-parameter fractional Laplacian, (−Δ)α(·), α ∈ (0, 1], of the filtered velocity field. The only model parameter, i.e., the fractional exponent, appears to be strictly dependent on the filter-width and the flow Reynolds number. We furthermore explore the main physical and mathematical properties of the proposed model under a set of mild conditions. Finally, the introduced model undergoes a priori evaluations based on the direct numerical simulation database of forced and decaying homogeneous isotropic turbulent flows at relatively high and moderate Reynolds numbers, respectively. Such analysis provides a comparative study of predictability and performance of the proposed fractional model.

  • a fractional subgrid scale model for turbulent flows Theoretical Formulation and a priori study
    arXiv: Computational Engineering Finance and Science, 2019
    Co-Authors: Mehdi Samiee, Ali Akhavansafaei, Mohsen Zayernouri
    Abstract:

    Coherent structures/motions in turbulence inherently give rise to intermittent signals with sharp peaks, heavy-skirt, and skewed distributions of velocity increments, highlighting the non-Gaussian nature of turbulence. That suggests that the spatial nonlocal interactions cannot be ruled out of the turbulence physics. Furthermore, filtering the Navier-Stokes equations in the large eddy simulation of turbulent flows would further enhance the existing nonlocality, emerging in the corresponding subgrid scale fluid motions. That urges the development of new nonlocal closure models, which respect the corresponding non-Gaussian statistics of the subgrid stochastic motions. To this end and starting from the filtered Boltzmann equation, we model the corresponding equilibrium distribution function with a \textit{Levy}-stable distribution, leading to the proposed fractional-order modeling of subgrid-scale stresses. We approximate the filtered equilibrium distribution function with a power-law term, and derive the corresponding filtered Navier-Stokes equations. Subsequently in our functional modeling, the divergence of subgrid-scale stresses emerges as a single-parameter fractional Laplacian, $(-\Delta)^{\alpha}(\cdot)$, $\alpha \in (0,1]$, of the filtered velocity field. The only model parameter, i.e., the fractional exponent, appears to be strictly depending on the filter-width and the flow Reynolds number. We furthermore explore the main physical and mathematical properties of the proposed model under a set of mild conditions. Finally, the introduced model undergoes \textit{a priori} evaluations based on the direct numerical simulation database of forced and decaying homogeneous isotropic turbulent flows at relatively high and moderate Reynolds numbers, respectively. Such analysis provides a comparative study of predictability and performance of the proposed fractional model.

M J Goupil - One of the best experts on this subject based on the ideXlab platform.

  • excitation of stellar p modes by turbulent convection i Theoretical Formulation
    Astronomy and Astrophysics, 2001
    Co-Authors: R Samadi, M J Goupil
    Abstract:

    Stochatic excitation of stellar oscillations by turbulent convection is investigated and an expression for the power injected into the oscillations by the turbulent convection of the outer layers is derived which takes into account excitation through turbulent Reynolds stresses and turbulent entropy fluctuations. This formula- tion generalizes results from previous works and is built so as to enable investigations of various possible spatial and temporal spectra of stellar turbulent convection. For the Reynolds stress contribution and assuming the Kolmogorov spectrum we obtain a similar Formulation to those derived by previous authors. The entropy contri- bution to excitation is found to originate from the advection of the Eulerian entropy fluctuations by the turbulent velocity eld. Numerical computations in the solar case in a companion paper indicate that the entropy source term is dominant over the Reynold stress contribution to mode excitation, except at high frequencies.

Ali Akhavansafaei - One of the best experts on this subject based on the ideXlab platform.

  • a fractional subgrid scale model for turbulent flows Theoretical Formulation and a priori study
    Physics of Fluids, 2020
    Co-Authors: Mehdi Samiee, Ali Akhavansafaei, Mohsen Zayernouri
    Abstract:

    Coherent structures/motions in turbulence inherently give rise to intermittent signals with sharp peaks, heavy-skirt, and skewed distributions of velocity increments, highlighting the non-Gaussian nature of turbulence. This suggests that the spatial nonlocal interactions cannot be ruled out of the turbulence physics. Furthermore, filtering the Navier–Stokes equations in the large eddy simulation of turbulent flows would further enhance the existing nonlocality, emerging in the corresponding subgrid scale fluid motions. This urges the development of new nonlocal closure models, which respect the corresponding non-Gaussian statistics of the subgrid stochastic motions. To this end and starting from the filtered Boltzmann equation, we model the corresponding equilibrium distribution function with a Levy-stable distribution, leading to the proposed fractional-order modeling of subgrid-scale stresses. We approximate the filtered equilibrium distribution function with a power-law term and derive the corresponding filtered Navier–Stokes equations. Subsequently in our functional modeling, the divergence of subgrid-scale stresses emerges as a single-parameter fractional Laplacian, (−Δ)α(·), α ∈ (0, 1], of the filtered velocity field. The only model parameter, i.e., the fractional exponent, appears to be strictly dependent on the filter-width and the flow Reynolds number. We furthermore explore the main physical and mathematical properties of the proposed model under a set of mild conditions. Finally, the introduced model undergoes a priori evaluations based on the direct numerical simulation database of forced and decaying homogeneous isotropic turbulent flows at relatively high and moderate Reynolds numbers, respectively. Such analysis provides a comparative study of predictability and performance of the proposed fractional model.

  • a fractional subgrid scale model for turbulent flows Theoretical Formulation and a priori study
    arXiv: Computational Engineering Finance and Science, 2019
    Co-Authors: Mehdi Samiee, Ali Akhavansafaei, Mohsen Zayernouri
    Abstract:

    Coherent structures/motions in turbulence inherently give rise to intermittent signals with sharp peaks, heavy-skirt, and skewed distributions of velocity increments, highlighting the non-Gaussian nature of turbulence. That suggests that the spatial nonlocal interactions cannot be ruled out of the turbulence physics. Furthermore, filtering the Navier-Stokes equations in the large eddy simulation of turbulent flows would further enhance the existing nonlocality, emerging in the corresponding subgrid scale fluid motions. That urges the development of new nonlocal closure models, which respect the corresponding non-Gaussian statistics of the subgrid stochastic motions. To this end and starting from the filtered Boltzmann equation, we model the corresponding equilibrium distribution function with a \textit{Levy}-stable distribution, leading to the proposed fractional-order modeling of subgrid-scale stresses. We approximate the filtered equilibrium distribution function with a power-law term, and derive the corresponding filtered Navier-Stokes equations. Subsequently in our functional modeling, the divergence of subgrid-scale stresses emerges as a single-parameter fractional Laplacian, $(-\Delta)^{\alpha}(\cdot)$, $\alpha \in (0,1]$, of the filtered velocity field. The only model parameter, i.e., the fractional exponent, appears to be strictly depending on the filter-width and the flow Reynolds number. We furthermore explore the main physical and mathematical properties of the proposed model under a set of mild conditions. Finally, the introduced model undergoes \textit{a priori} evaluations based on the direct numerical simulation database of forced and decaying homogeneous isotropic turbulent flows at relatively high and moderate Reynolds numbers, respectively. Such analysis provides a comparative study of predictability and performance of the proposed fractional model.