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Mean flow
About: Mean flow is a research topic. Over the lifetime, 6591 publications have been published within this topic receiving 192571 citations.
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TL;DR: In this paper, the authors present a review of the applicability and applicability of numerical predictions of turbulent flow, and advocate that computational economy, range of applicability, and physical realism are best served by turbulence models in which the magnitudes of two turbulence quantities, the turbulence kinetic energy k and its dissipation rate ϵ, are calculated from transport equations solved simultaneously with those governing the mean flow behaviour.
11,866 citations
TL;DR: In this paper, a complete set of perturbations, ordered by energy growth, is found using variational methods. But the optimal perturbation is not of modal form, and those which grow the most resemble streamwise vortices, which divert the mean flow energy into streaks of streamwise velocity and enable the energy of the perturbance to grow by as much as three orders of magnitude.
Abstract: Transition to turbulence in plane channel flow occurs even for conditions under which modes of the linearized dynamical system associated with the flow are stable. In this paper an attempt is made to understand this phenomena by finding the linear three‐dimensional perturbations that gain the most energy in a given time period. A complete set of perturbations, ordered by energy growth, is found using variational methods. The optimal perturbations are not of modal form, and those which grow the most resemble streamwise vortices, which divert the mean flow energy into streaks of streamwise velocity and enable the energy of the perturbation to grow by as much as three orders of magnitude. It is suggested that excitation of these perturbations facilitates transition from laminar to turbulent flow. The variational method used to find the optimal perturbations in a shear flow also allows construction of tight bounds on growth rate and determination of regions of absolute stability in which no perturbation growth is possible.
1,083 citations
TL;DR: In this article, the average settling velocity in homogeneous turbulence of a small rigid spherical particle subject to a Stokes drag force was shown to depend on the particle inertia and the free-fall terminal velocity in still fluid.
Abstract: The average settling velocity in homogeneous turbulence of a small rigid spherical particle, subject to a Stokes drag force, is shown to depend on the particle inertia and the free-fall terminal velocity in still fluid. With no inertia the particle settles on average at the same rate as in still fluid, assuming there is no mean flow. Particle inertia produces a bias in each trajectory towards regions of high strain rate or low vorticity, which affects the mean settling velocity. Results from a Gaussian random velocity field show that this produces an increased settling velocity.
1,023 citations
TL;DR: The analysis used by Taylor (1954) and based on the Reynolds analogy has been extended to describe the diffusion of marked fluid in the turbulent flow in an open channel as mentioned in this paper.
Abstract: The analysis used by Taylor (1954) and based on the Reynolds analogy has been extended to describe the diffusion of marked fluid in the turbulent flow in an open channel The coefficient of longitudinal diffusion arising from the combined action of turbulent lateral diffusion and convection by the mean flow is computed to be 5·9uτh, where h is the depth of fluid and uτ the friction velocity This is in agreement with experiments described herein The laterla diffusion coefficient is found by experiment to be 0·23uτh, which is three times larger than the value obtained by the assumption of isotropy The same analysis can be used to describe the longitudinal dispersion of discrete particles, both of zero buoyancy and of finite buoyancy, and comparison is made with observations by Batchelor, Binnie & Phillips (1955) and Binnie & Phillips (1958)
924 citations
TL;DR: In this paper, a nonlinear Reynolds stress model is employed to relate the Reynolds stresses and the strain rates of the mean flow for a single wave propagating over a long distance in a constant depth.
Abstract: This paper describes the development of a numerical model for studying the evolution of a wave train, shoaling and breaking in the surf zone. The model solves the Reynolds equations for the mean (ensemble average) flow field and the k–e equations for the turbulent kinetic energy, k, and the turbulence dissipation rate, e. A nonlinear Reynolds stress model (Shih, Zhu & Lumley 1996) is employed to relate the Reynolds stresses and the strain rates of the mean flow. To track free-surface movements, the volume of fluid (VOF) method is employed. To ensure the accuracy of each component of the numerical model, several steps have been taken to verify numerical solutions with either analytical solutions or experimental data. For non-breaking waves, very accurate results are obtained for a solitary wave propagating over a long distance in a constant depth. Good agreement between numerical results and experimental data has also been observed for shoaling and breaking cnoidal waves on a sloping beach in terms of free-surface profiles, mean velocities, and turbulent kinetic energy. Based on the numerical results, turbulence transport mechanisms under breaking waves are discussed.
801 citations