Self-consistent high-Reynolds-number asymptotics for zero-pressure-gradient turbulent boundary layers

Monkewitz, Peter A.; Chauhan, Kapil; Nagib, Hassan

doi:10.1063/1.2780196

Cited by 178 publications

(162 citation statements)

References 23 publications

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“…where is the von Kármán constant ͑ Ϸ 0.4͒ and u ‫ء‬ is the shear velocity: These values are in accordance with the measured values in high-Reynolds wall-induced turbulence [32][33][34] and results of DNS. 35 Shown in Fig.…”

Section: A Nonuniquenesssupporting

confidence: 76%

Langevin and diffusion equation of turbulent fluid flow

Brouwers

2010

Physics of Fluids

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A derivation of the Langevin and diffusion equations describing the statistics of fluid particle displacement and passive admixture in turbulent flow is presented. Use is made of perturbation expansions. The small parameter is the inverse of the Kolmogorov constant C 0 , which arises from Lagrangian similarity theory. The value of C 0 in high Reynolds number turbulence is 5-6. To achieve sufficient accuracy, formulations are not limited to terms of leading order in C 0 −1 including terms next to leading order in C 0 −1 as well. Results of turbulence theory and statistical mechanics are invoked to arrive at the descriptions of the Langevin and diffusion equations, which are unique up to truncated terms of O͑C 0 −2 ͒ in displacement statistics. Errors due to truncation are indicated to amount to a few percent. The coefficients of the presented Langevin and diffusion equations are specified by fixed-point averages of the Eulerian velocity field. The equations apply to general turbulent flow in which fixed-point Eulerian velocity statistics are non-Gaussian to a degree of O͑C 0 −1 ͒. The equations provide the means to calculate and analyze turbulent dispersion of passive or almost passive admixture such as fumes, smoke, and aerosols in areas ranging from atmospheric fluid motion to flows in engineering devices.

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Section: A Nonuniquenesssupporting

confidence: 76%

Langevin and diffusion equation of turbulent fluid flow

Brouwers

2010

Physics of Fluids

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“…1, we present the correlation functions of particle velocity versus the dimensionless time t in both the case of a classical system (ε 1 = 0 in Eqs. (18)- (21) These values agree with measured values in wall-induced turbulence at a high Reynolds number [24]- [26] and with DNS results [27].…”

Section: Reciprocitysupporting

confidence: 81%

Langevin equation of a fluid particle in wall-induced turbulence

Brouwers

2010

Theor Math Phys

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“…Nickels [13] and Monkewitz et al [14] (hereafter referred to as MCN) are examples of the first kind (see next subsection), while George et al suggested a power law for TBL [8] and a log low for channel [15] (hereafter referred to as WCG). Furthermore, at a finite Re, setting Re-or y-dependent constants in Eq.…”

Section: Scaling Analysismentioning

confidence: 99%

New perspective in statistical modeling of wall-bounded turbulence

She

Chen

et al. 2010

Acta Mech Sin

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Despite dedicated effort for many decades, statistical description of highly technologically important wall turbulence remains a great challenge. Current models are unfortunately incomplete, or empirical, or qualitative. After a review of the existing theories of wall turbulence, we present a new framework, called the structure ensemble dynamics (SED), which aims at integrating the turbulence dynamics into a quantitative description of the mean flow. The SED theory naturally evolves from a statistical physics understanding of non-equilibrium open systems, such as fluid turbulence, for which mean quantities are intimately coupled with the fluctuation dynamics. Starting from the ensemble-averaged Navier-Stokes (EANS) equations, the theory postulates the existence of a finite number of statistical states yielding a multi-layer picture for wall turbulence. Then, it uses order functions (ratios of terms in the mean momentum as well as energy equations) to characterize the states and transitions between states. Application of the SED analysis to an incompressible channel flow and a compressible turbulent boundary layer shows that the order functions successfully reveal the multi-layer structure for wall-bounded turbulence, which arises as a quantitative extension of the traditional view in terms of sub-layer, buffer layer, log layer and wake. Furthermore, an idea of using a set of hyperbolic functions for modeling transitions between layers is proposed for a quantitative model of order functions across the entire flow domain. We conclude that the SED provides a theoretical framework for expressing the yet-unknown effects of fluctuation structures on the mean quantities, and offers new methods to analyze experimental and simulation data. Combined with asymptotic analysis, it also offers a way to evaluate convergence of simulations. The SED approach successfully describes the dynamics at both momentum and energy levels, in contrast with all prevalent approaches describing the mean velocity profile only. Moreover, the SED theoretical framework is general, independent of the flow system to study, while the actual functional form of the order functions may vary from flow to flow. We assert that as the knowledge of order functions is accumulated and as more flows are analyzed, new principles (such as hierarchy, symmetry, group invariance, etc.) governing the role of turbulent structures in the mean flow properties will be clarified and a viable theory of turbulence might emerge.

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Self-consistent high-Reynolds-number asymptotics for zero-pressure-gradient turbulent boundary layers

Cited by 178 publications

References 23 publications

Langevin and diffusion equation of turbulent fluid flow

Langevin and diffusion equation of turbulent fluid flow

Langevin equation of a fluid particle in wall-induced turbulence

New perspective in statistical modeling of wall-bounded turbulence

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