Spectral derivation of the classic laws of wall-bounded turbulent flows

Gioia, Gustavo; Chakraborty, Pinaki

doi:10.1098/rspa.2017.0354

Cited by 10 publications

(4 citation statements)

References 19 publications

(25 reference statements)

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“…The different curves correspond to different values of the dimensionless parameter β e . Note that the spectral model can reproduce all of the salient § Analysis of such generic aspects of the spectrum can be used to shed light on the scaling relations for the MVPs 2017). trends in the experimental and computational data (also shown in Figs.…”

Section: Equations Of the Mvpsmentioning

confidence: 99%

Spectral link and macroscopic non-universality in turbulent plane Couette flow

Zhang¹

2019

Fluid Dyn. Res.

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In fully developed turbulent plane Couette flow the classical experimental data of frictional factor f vs. Reynolds number Re display well-known disparities which have long remained unexplained. These disparities are accompanied by previously unnoticed disparities in the wakes, and only in the wakes, of the attendant meanvelocity profiles (MVPs). To help explain these experimental data, we apply the model of the "spectral link" for MVPs to turbulent plane Couette flows. The model links the dissipative range, the inertial range, and the energetic range of the standard phenomenological model of the spectrum of turbulent kinetic energy to, respectively, the buffer layer, the log layer, and the wake of the MVPs. By assessing the empirical data using the spectral model, we argue for the existence, in plane Couette flow, of multiple states of turbulence which differ from one another only at the largest lengthscales in the flow, corresponding to the energetic range, where the spectrum is subject to finite-domain effects. Thus, the multiplicity of turbulent states is entirely consistent with small-scale universality, and the experimental data on plane Couette flow pose no challenge to the phenomenological theory of turbulence. Our findings might apply more broadly to a general class of flows engendered by moving boundaries.

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Section: Equations Of the Mvpsmentioning

confidence: 99%

Spectral link and macroscopic non-universality in turbulent plane Couette flow

Zhang¹

2019

Fluid Dyn. Res.

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“…Formulating RSL effects as an adjustment to C instead of U is desirable as dU=dz is Galilean invariant, whereas U is not. 29 On the practical side, extensions to stratified flow cases become convenient as / RSL can be framed as a generalized similarity function derived from the product of the standard form of the Monin-Obukhov 30 stability correction function and a function representing the RSL effects on C. Thus, / RSL ðÁÞ is a dimensionless roughness sublayer modification function yet to be determined and frames the scope of the work here for near-neutral stratification. Near-neutral stratification forms a logical starting point for any extension toward stratified cases in the future.…”

Section: Introductionmentioning

confidence: 99%

Adjustments to the law of the wall above an Amazon forest explained by a spectral link

et al. 2023

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Modification to the law-of-the wall represented by a dimensionless correction function $\phi_{RSL}(z/h)$ is derived using near-neutral atmospheric turbulence measurements collected at two sites in the Amazon in near-neutral stratification, where $z$ is the distance from the forest floor and $h$ is the mean canopy height. The sites are the Amazon Tall Tower Observatory (ATTO) for $z/h\in [1,2.3]$ and the Green Ocean Amazon (GoAmazon) site for $z/h\in[1,1.4]$. A link between the vertical velocity spectrum $E_{ww}(k)$ ($k$ is the longitudinal wavenumber) and $\phi_{RSL}$ is then established using a co-spectral budget (CSB) model interpreted by the moving-equilibrium hypothesis (MEH). The key finding is that $\phi_{RSL}$ is determined by the ratio of two turbulent viscosities and is given as $\nu_{t,BL}/\nu_{t,RSL}$, where $\nu_{t,RSL}=(1/A)\int_{0}^{\infty}\tau(k) E_{ww}(k)dk$, $\nu_{t,BL}=\kappa (z-d) u_*$, $\tau(k)$ is a scale-dependent decorrelation time scale between velocity components, $A=C_R/(1-C_I)=4.5$ is predicted from the Rotta constant $C_R=1.8$ and the isotropization of production constant $C_I=3/5$ given by Rapid Distortion Theory, $\kappa$ is the von K\'arm\'an constant, $u_*$ is the friction velocity at the canopy top, and $d$ is the zero-plane displacement. Because the transfer of energy across scales is conserved in $E_{ww}(k)$ and is determined by the turbulent kinetic energy dissipation rate ($\epsilon$), the CSB model also predicts that $\phi_{RSL}$ scales with $L_{BL}/L_d$, where $L_{BL}$ is the length scale of attached eddies to $z=d$, $L_d=u_*^3/\epsilon$ is a macro-scale dissipation length.

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“…First experiments on turbulence in non-Newtonian fluids were already performed in 1959 [4]. Since then, most theoretical studies have focused on drag reduction [5,6], and the mathematical modeling of wall stresses and boundary layers [7][8][9]. For isotropic turbulence in dilute polymer solutions, De Angelis et al[10] found through DNS that relaxation connecting different scales significantly alters the energy cascade.Intuitively, in the inertial subrange, molecular stresses should have a negligible influence on the motion and size of the eddies, regardless of the rheological nature of the fluid [11].…”

mentioning

confidence: 99%

“…First experiments on turbulence in non-Newtonian fluids were already performed in 1959 [4]. Since then, most theoretical studies have focused on drag reduction [5,6], and the mathematical modeling of wall stresses and boundary layers [7][8][9]. For isotropic turbulence in dilute polymer solutions, De Angelis et al [10] found through DNS that relaxation connecting different scales significantly alters the energy cascade.…”

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confidence: 99%

Self-organization in purely viscous non-Newtonian turbulence

et al. 2019

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We investigate through Direct Numerical Simulations (DNS) the statistical properties of turbulent flows in the inertial subrange for non-Newtonian power-law fluids. The structural invariance found for the vortex size distribution is achieved through a self-organized mechanism at the microscopic scale of the turbulent motion that adjusts, according to the rheological properties of the fluid, the ratio between the viscous dissipations inside and outside the vortices. Moreover, the deviations from the K41 theory of the structure functions' exponents reveal that the anomalous scaling exhibits a systematic nonuniversal behavior with respect to the rheological properties of the fluids. PACS numbers:In many situations ranging from blood flow [1, 2] to atomization of slurries in industrial processing [3], one encounters non-Newtonian fluids in turbulent conditions. First experiments on turbulence in non-Newtonian fluids were already performed in 1959 [4]. Since then, most theoretical studies have focused on drag reduction [5,6], and the mathematical modeling of wall stresses and boundary layers [7][8][9]. For isotropic turbulence in dilute polymer solutions, De Angelis et al.[10] found through DNS that relaxation connecting different scales significantly alters the energy cascade.Intuitively, in the inertial subrange, molecular stresses should have a negligible influence on the motion and size of the eddies, regardless of the rheological nature of the fluid [11]. More precisely, even if a more complex constitutive law than a linear one is necessary to describe the stress-strain relation of a moving fluid, one should expect the statistical results obtained for the structure of Newtonian turbulence at the inertial subrange to remain valid. A relevant question that naturally arises is how the local rheological properties of the fluid must rearrange in space and time to comply with this alleged structural invariance. Here we provide an answer for this question by investigating through DNS the statistical properties of coherent structures of Newtonian and non-Newtonian turbulent flows in terms of distributions of eddy sizes and structure functions [12].For our numerical analysis, we consider a cubic box containing a non-Newtonian fluid and subjected to periodic boundary conditions in all three directions. The mathematical formulation of the fluid mechanics is based on the assumptions that we have an incompressible fluid flowing under isothermal conditions, for which the momentum and mass conservation equations reduce to,andwhere u and p are the velocity and pressure fields, respectively, Γ is a forcing term and T is the deviatoric stress tensor given by,Here E = ∇u + ∇u T /2 is the strain rate tensor anḋ γ = √ 2E : E its second principal invariant. The function µ (γ) defines the constitutive relation, which for a crosspower-law fluid is given byThe constants µ 1 and µ 2 are the lower and upper cutoffs, K is called the consistency index and n is the rheological exponent. Fluids with n > 1 are shear-thickening, while shear-thin...

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Spectral derivation of the classic laws of wall-bounded turbulent flows

Cited by 10 publications

References 19 publications

Spectral link and macroscopic non-universality in turbulent plane Couette flow

Spectral link and macroscopic non-universality in turbulent plane Couette flow

Adjustments to the law of the wall above an Amazon forest explained by a spectral link

Self-organization in purely viscous non-Newtonian turbulence

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