scholarly journals Nonlinear spectral model for rotating sheared turbulence

2019 ◽  
Vol 866 ◽  
pp. 5-32 ◽  
Author(s):  
Ying Zhu ◽  
C. Cambon ◽  
F. S. Godeferd ◽  
A. Salhi
Keyword(s):  
Turbulent Shear ◽  
Finite Difference Schemes ◽  
Turbulent Shear Flow ◽  
Third Order ◽  
Mean Velocity ◽  
Coupled Equations ◽  
Velocity Gradients ◽  
Model Predictions ◽  
Pseudo Scalar ◽  
High Order Finite Difference

We propose a statistical model for homogeneous turbulence undergoing distortions, which improves and extends the MCS model by Mons, Cambon & Sagaut (J. Fluid Mech., vol. 788, 2016, 147–182). The spectral tensor of two-point second-order velocity correlations is predicted in the presence of arbitrary mean-velocity gradients and in a rotating frame. For this, we numerically solve coupled equations for the angle-dependent energy spectrum${\mathcal{E}}(\boldsymbol{k},t)$that includes directional anisotropy, and for the deviatoric pseudo-scalar $Z(\boldsymbol{k},t)$, that underlies polarization anisotropy ($\boldsymbol{k}$ is the wavevector,$t$the time). These equations include two parts: (i) exact linear terms representing the viscous spectral linear theory (SLT) when considered alone; (ii) generalized transfer terms mediated by two-point third-order correlations. In contrast with MCS, our model retains the complete angular dependence of the linear terms, whereas the nonlinear transfer terms are closed by a reduced anisotropic eddy damped quasi-normal Markovian (EDQNM) technique similar to MCS, based on truncated angular harmonics expansions. And in contrast with most spectral approaches based on characteristic methods to represent mean-velocity gradient terms, we use high-order finite-difference schemes (FDSs). The resulting model is applied to homogeneous rotating turbulent shear flow with several Coriolis parameters and constant mean shear rate. First, we assess the validity of the model in the linear limit. We observe satisfactory agreement with existing numerical SLT results and with theoretical results for flows without rotation. Second, fully nonlinear results are obtained, which compare well to existing direct numerical simulation (DNS) results. In both regimes, the new model improves significantly the MCS model predictions. However, in the non-rotating shear case, the expected exponential growth of turbulent kinetic energy is found only with a hybrid model for nonlinear terms combining the anisotropic EDQNM closure and Weinstock’s return-to-isotropy model.

Three-Dimensional Buoyant Wall Jets Released Into a Coflowing Turbulent Boundary Layer

1990 ◽  
Vol 112 (2) ◽  
pp. 356-362 ◽  
Author(s):  
J. R. Sinclair ◽  
P. R. Slawson ◽  
G. A. Davidson
Keyword(s):  
Three Dimensional ◽  
Ground Level ◽  
Turbulent Shear ◽  
Wall Jet ◽  
Turbulent Shear Flow ◽  
Streamwise Vorticity ◽  
Buoyant Jet ◽  
Buoyant Jets ◽  
Jet Trajectory ◽  
Model Predictions

Experiments have been conducted in a water flume to simulate finite-length line sources of heat that issue horizontally at ground level into a coflowing turbulent shear flow. The downstream development of each buoyant jet is documented by detailed mean temperature measurements, which are analyzed to determine the jet trajectory, spread rates, and distance to the point of liftoff from the surface. In addition, a three-dimensional, parabolic, numerical model based on the fundamental conservation equations is developed. Model predictions of several buoyant jets compare reasonably with the experimental data and suggest that the strength of the streamwise vorticity plays an important role in governing liftoff of a buoyant wall jet from the surface.

Further experiments in nearly homogeneous turbulent shear flow

1977 ◽  
Vol 81 (4) ◽  
pp. 657-687 ◽  
Author(s):  
V. G. Harris ◽  
J. A. H. Graham ◽  
S. Corrsin
Keyword(s):  
Wind Tunnel ◽  
Shear Flow ◽  
Energy Exchange ◽  
Turbulent Energy ◽  
Turbulent Shear ◽  
Asymptotic State ◽  
Turbulent Shear Flow ◽  
Tensor Structure ◽  
Mean Velocity ◽  
Exchange Hypothesis

The experiment of Champagne, Harris & Corrsin in generating and studying a nearly homogeneous turbulent shear flow has been extended to larger values of the dimensionless downstream time or strain by the use of a larger mean velocity gradient in the same wind tunnel. The system appears to reach an asymptotic state in which scales and turbulent energy grow monotonically. Two-point covariances and tensor structure of one-point ‘Reynolds stress’ and ‘pressure/strain-rate covariance’ agree with the earlier case. However, the linear intercomponent energy exchange hypothesis due to Rotta, very roughly confirmed by the earlier experiment, is contradicted by the present data.

Anisotropic pressure correlation spectra in turbulent shear flow

2012 ◽  
Vol 694 ◽  
pp. 50-77 ◽  
Author(s):  
Yoshiyuki Tsuji ◽  
Yukio Kaneda
Keyword(s):  
Mixing Layer ◽  
Inertial Subrange ◽  
Turbulent Shear ◽  
Pressure Probe ◽  
Anisotropic Pressure ◽  
Turbulent Shear Flow ◽  
Velocity Correlation ◽  
Mean Velocity ◽  
Correlation Spectrum ◽  
The Mean

AbstractWe measured the correlation spectrum ${\hat {Q} }_{p} (\mathbi{k})$ of pressure fluctuations in a driving mixing layer with a Taylor-scale Reynolds number ${R}_{\lambda } $ up to ${\simeq }700$ by a newly developed pressure probe with spatial and temporal resolutions that are sufficient to analyse inertial-subrange statistics. The influence of the mean velocity gradient tensor ${S}_{ij} $ in the mixing layer, which is almost constant near its centreline, is studied using an idea similar to that underlying the linear response theory developed in statistical mechanics for systems at or near thermal equilibrium. If we write the spectrum ${\hat {Q} }_{p} (\mathbi{k})$ as ${\hat {Q} }_{p} (\mathbi{k})= { \hat {Q} }_{p}^{(0)} (\mathbi{k})+ \mrm{\Delta} {\hat {Q} }_{p} (\mathbi{k})$, where ${ \hat {Q} }_{p}^{(0)} (\mathbi{k})$ is the isotropic Kolmogorov spectrum in the absence of mean shear, then for small ${S}_{ij} $ the deviation $ \mrm{\Delta} {\hat {Q} }_{p} (\mathbi{k})$ due to the shear is approximately linear and is determined by a few non-dimensional universal constants in addition to ${S}_{ij} $, $k$ and the mean energy dissipation rate. We also measured the pressure–velocity and velocity–velocity correlation spectra. Deviations from isotropy due to shear are shown to be approximately proportional to ${S}_{ij} $ at large ${R}_{\lambda } $.

Magneto-fluid-mechanic pipe flow in a transverse magnetic field. Part 1. Isothermal flow

1971 ◽  
Vol 47 (4) ◽  
pp. 737-764 ◽  
Author(s):  
R. A. Gardner ◽  
P. S. Lykoudis
Keyword(s):  
Magnetic Field ◽  
Transverse Magnetic Field ◽  
Reynolds Numbers ◽  
Transverse Magnetic ◽  
Isothermal Flow ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Axial Pressure ◽  
Mean Velocity ◽  
Velocity Fluctuations

An experimental investigation was conducted in a circular pipe to examine the influence of a transverse magnetic field on the structure of turbulent shear flow of a conducting fluid (mercury). In the present paper, part 1, mean velocity profiles, turbulence intensity profiles, velocity fluctuation spectra, axial pressure drop profiles, and skin friction data are presented which quantitatively exhibit the Hartmann effect and damping of the velocity fluctuations over a broad range of Reynolds numbers and magnetic fields. The results of heat transfer experiments will be reported by the authors in the following paper, part 2.

Lagrangian similarity hypothesis applied to diffusion in turbulent shear flow

1963 ◽  
Vol 15 (1) ◽  
pp. 49-64 ◽  
Author(s):  
J. E. Cermak
Keyword(s):  
Boundary Layer ◽  
Surface Layer ◽  
Shear Flow ◽  
Turbulent Shear ◽  
Solid Boundary ◽  
Turbulent Shear Flow ◽  
Mean Velocity ◽  
Similarity Hypothesis ◽  
Neutral Boundary Layer ◽  
Continuous Point

The concept suggested by Batchelor that motion of a marked particle in turbulent shear flow may be similar at stations downstream from the point of release is applied to a variety of diffusion data obtained in the laboratory and in the surface layer of the atmosphere. Two types of shear flow parallel to a plane solid boundary are considered. In the first case mean velocity is a linear function of logz(neutral boundary layer) and in the second case the mean velocity is slightly perturbed from the logarithmic relationship by temperature variation in thez-direction (diabatic boundary layer). Besides the parameters introduced in previous applications of the Lagrangian similarity hypothesis to turbulent diffusion, the ratio of source height to roughness lengthh/z0is shown to be of major importance. Predictions of the variation of maximum ground-level concentration for continuous point and line sources and the variation of plume width for a continuous point source with distance downstream from the source agree with the assorted data remarkably well for a range of length scales extending over three orders-of-magnitude. It is concluded that results from application of the Lagrangian similarity hypothesis are significant for the laboratory modelling of diffusion in the atmospheric surface layer.

Outline of a theory of turbulent shear flow

1956 ◽  
Vol 1 (5) ◽  
pp. 521-539 ◽  
Author(s):  
W. V. R. Malkus
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Boundary Conditions ◽  
Momentum Transport ◽  
Turbulent Shear ◽  
Spectral Structure ◽  
Turbulent Shear Flow ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

In this paper the spatial variations and spectral structure of steady-state turbulent shear flow in channels are investigated without the introduction of empirical parameters. This is made possible by the assumption that the non-linear momentum transport has only stabilizing effects on the mean field of flow. Two constraints on the possible momentum transport are drawn from this assumption: first, that the mean flow will be statistically stable if an Orr-Sommerfeld type equation is satisfied by fluctuations of the mean; second, that the smallest scale of motion that can be present in the spectrum of the momentum transport is the scale of the marginally stable fluctuations of the mean. Within these two constraints, and for a given mass transport, an upper limit is sought for the rate of dissipation of potential energy into heat. Solutions of the stability equation depend upon the shape of the mean velocity profile. In turn, the mean velocity profile depends upon the spatial spectrum of the momentum transport. A variational technique is used to determine that momentum transport spectrum which is both marginally stable and produces a maximum dissipation rate. The resulting spectrum determines the velocity profile and its dependence on the boundary conditions. Past experimental work has disclosed laminar, ‘transitional’, logarithmic and parabolic regions of the velocity profile. Several experimental laws and their accompanying constants relate the extent of these regions to the boundary conditions. The theoretical profile contains each feature and law that is observed. First approximations to the constants are found, and give, in particular, a value for the logarithmic slope (von Kármán's constant) which is within the experimental error. However, the theoretical boundary constant is smaller than the observed value. Turbulent channel flow seems to achieve the extreme state found here, but a more decisive quantitative comparison of theory and experiment requires improvement in the solutions of the classical laminar stability problem.

scholarly journals Mean velocity and suspended sediment concentration profile model of turbulent shear flow with probability density function

2017 ◽  
Vol 21 (3) ◽  
pp. 129-134
Author(s):  
Guanglin Wu ◽  
Liangsheng Zhu ◽  
Fangcheng Li
Keyword(s):  
Probability Density Function ◽  
Shear Flow ◽  
Probability Density ◽  
Density Function ◽  
Suspended Sediment Concentration ◽  
Sediment Concentration ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Mean Velocity ◽  
Profile Model

This work purposes a general mean velocity and a suspended sediment concentration (SSC) model to express distribution at every point of the cross section of turbulent shear flow by using a probability density function method. The probability density function method was used to describe the velocity and concentration profiles interacted on directly by fluid particles in the turbulent shear flow to solve turbulent flow and avoid different dynamical mechanics. The velocity profile model was obtained by solving for the profile integral with the product of the laminar velocity and probability density, through adopting an exponential probability density function to express probability distribution of velocity alteration of a fluid particle in turbulent shear flow. An SSC profile model was also created following a method similar to the above and based on the Schmidt diffusion equation. Different velocity and SSC profiles were created while changing the parameters of the models. The models were verified by comparing the calculated results with traditional models. It was shown that the probability density function model was superior to log-law in predicting stream-wise velocity profiles in coastal currents, and the probability density function SSC profile model was superior to the Rouse equation for predicting average SSC profiles in rivers and estuaries. Outlooks for precision investigation are stated at the end of this article.

Experimental investigation of turbulent shear flow with quadratic mean-velocity profiles

1976 ◽  
Vol 73 (1) ◽  
pp. 165-188 ◽  
Author(s):  
H. K. Richards ◽  
J. B. Morton
Keyword(s):  
Flow Direction ◽  
Correlation Coefficients ◽  
Velocity Profiles ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Quadratic Mean ◽  
The Mean

Three turbulent shear flows with quadratic mean-velocity profiles are generated by using an appropriately designed honeycomb and parallel-rod grids with adjustable rod spacing. The details of two of the flow fields, with quadratic mean-velocity profiles with constant positive mean-shear gradients ($\partial^2\overline{U}_1/\partial X^2_2 >0$), are obtained, and include, in the mean flow direction, the development and distribution of mean velocities, fluctuating velocities, Reynolds stresses, microscales, integral scales, energy spectra, shear correlation coefficients and two-point spatial velocity correlation coefficients. A third flow field is generated with a quadratic mean velocity profile with constant negative mean-shear gradient ($\partial^2\overline{U}_1/\partial X^2_2 < 0$), to investigate in the mean flow direction the effect of the change in sign on the resulting field. An open-return wind tunnel with a 2 × 2 × 20 ft test-section is used.

The effect of contraction on a homogeneous turbulent shear flow

1985 ◽  
Vol 154 ◽  
pp. 187-213 ◽  
Author(s):  
K. R. Sreenivasan
Keyword(s):  
Shear Flow ◽  
Area Ratio ◽  
Turbulent Shear ◽  
Shear Strain Rate ◽  
Turbulent Shear Flow ◽  
Turbulent Stress ◽  
Mean Velocity ◽  
Stage Of Development ◽  
Flow Through ◽  
The Mean

A homogeneous turbulent shear flow in its asymptotic stage of development was subjected to an additional (longitudinal) strain by passing the flow through gradual contraction in the direction perpendicular to that of the mean shear. Two contractions, of area ratio 1.4 and 2.6, were used. Mean velocity and turbulent stress (both normal and shear) distributions were measured at several streamwise locations in the contraction region. The mean velocity distributions agree quite well with calculations based on the (inviscid) Bernoulli equation. Until at least half-way down the contraction with the larger area ratio, the rapid-distortion calculations considering only the streamwise acceleration were found to be reasonably successful in predicting the turbulent intensities. For the smaller-area-ratio contraction, corrections for the ‘natural development’ of the shear flow become important nearly everywhere. Similar calculations considering the shear as the only straining mechanism are generally less successful, although the shear strain rate is at least as rapid as, or even more so than, the longitudinal one. The pressure-rate-of-strain covariance terms estimated from the approximate component energy balance were used to test the adequacy of three models with varying degrees of complexity. Although none of these models appears general enough, their performance is generally adequate for the lower-area-ratio contraction; perhaps not surprisingly, the more complex the model the better its performance.

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