Measurements of turbulent fluctuations and Reynolds stresses in a tidal current

1956 ◽  
Vol 237 (1210) ◽  
pp. 422-438 ◽  
Keyword(s):  
Tidal Current ◽  
Electromagnetic Flowmeter ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Flat Bottom ◽  
Auto Correlation ◽  
Vertical Scale ◽  
Sea Bed ◽  
The Mean ◽  
The Magnetic Field

Observations have been made of u and w , the horizontal and vertical components of turbulent velocity, in a tidal current, at heights of 50 to 175 cm above the bottom. The measuring instrument was an electromagnetic flowmeter, in which the magnetic field was produced by a. c. at 50 c/s and the p. d. induced in the flowing water was measured by two pairs of electrodes. The measuring head of the instrument was 10 cm in diameter, and two such heads were mounted on a tripod which was laid on the sea bed. The observations were made off Red Wharf Bay, Anglesey, in depths of 12 to 22 m, on a fairly flat bottom consisting mainly of firm sand. For mean currents, U , in the range 25 to 50 cm/s, the r. m. s. values of u were of the order of 10% of U , while those of w were about 6% of U . On a number of records, u and w were recorded simultaneously, and from these the Reynolds stress — ρ [ uw ] was evaluated. At 75 cm above the bottom the values of stress were from 2 to 4 dyn/cm 2 , the corresponding coefficient of correlation between u and w averaging —0·4. Auto-correlation curves and spectrum functions computed from these records showed that u contained considerably more energy in the fluctuations of longer period than w did. Other records were of traces of u or of w at two different heights and showed the smaller vertical scale of w compared with that of u . In the case of u the vertical scale appears to be only about one-third of the scale in the direction of the mean flow.

Further observations of the turbulent fluctuations in a tidal current

1952 ◽  
Vol 244 (883) ◽  
pp. 335-356 ◽  
Keyword(s):  
Tidal Current ◽  
Mean Flow ◽  
Integral Scale ◽  
Distance Correlation ◽  
Turbulent Fluctuations ◽  
Auto Correlation ◽  
Order Of Magnitude ◽  
The Mean ◽  
The Individual ◽  
Mersey Estuary

The component of turbulent velocity in the direction of the mean flow has been studied for the tidal current in the Mersey estuary. Two Doodson current meters were used, recording simultaneously on the same photographic paper. The more interesting results were obtained within about 2 m of the bottom, the two meters being supported in a stand, with various vertical and horizontal separations. The periods of the turbulent fluctuations recorded varied from a few seconds up to several minutes. Various methods of analysis have failed to show any predominant periods or bands of periods (when the effects of surface waves have been excluded), and it appears that, as in other types of turbulence, a continuous spectrum of fluctuations is present. Distancecorrelation coefficients in the vertical and lateral directions have been computed from the simultaneous recordings, as well as auto-correlation curves from the recordings of the individual meters. Inferring the distance-correlation in the direction of flow from the auto-correlations, the integral scale of the turbulence in this direction is estimated to be of the order of 7 m, compared with 14 m, the mean depth of water. From the simultaneous correlations, it is suggested, tentatively, that the scales in the vertical and lateral directions are of the same order of magnitude and of the order of one-third of the scale in the direction of the mean flow.

Simple explicit model of liquid mean flow in region above axial impeller

1985 ◽  
Vol 50 (11) ◽  
pp. 2396-2410
Author(s):  
Miloslav Hošťálek ◽  
Ivan Fořt
Keyword(s):  
Vortex Flow ◽  
Flow Model ◽  
Quantitative Agreement ◽  
Mean Flow ◽  
Flat Bottom ◽  
Proposed Model ◽  
Minimum Number ◽  
The Mean ◽  
Model Equations ◽  
Radial Circulation

The study describes a method of modelling axial-radial circulation in a tank with an axial impeller and radial baffles. The proposed model is based on the analytical solution of the equation for vortex transport in the mean flow of turbulent liquid. The obtained vortex flow model is tested by the results of experiments carried out in a tank of diameter 1 m and with the bottom in the shape of truncated cone as well as by the data published for the vessel of diameter 0.29 m with flat bottom. Though the model equations are expressed in a simple form, good qualitative and even quantitative agreement of the model with reality is stated. Apart from its simplicity, the model has other advantages: minimum number of experimental data necessary for the completion of boundary conditions and integral nature of these data.

Fluctuating boundary layer on a magnetized plate

1967 ◽  
Vol 63 (2) ◽  
pp. 513-525 ◽  
Author(s):  
Sahib Singh Chawla
Keyword(s):  
Boundary Layer ◽  
Low Frequency ◽  
Surface Current ◽  
Frequency Range ◽  
Mean Flow ◽  
Wave Type ◽  
High Frequencies ◽  
Phase Lead ◽  
The Mean ◽  
The Magnetic Field

The laminar boundary layer on a magnetized plate, when the magnetic field oscillates in magnitude about a constant non-zero mean, is analysed. For low-frequency fluctuations the solution is obtained by a series expansion in terms of a frequency parameter, while for high frequencies the flow pattern is of the ‘skin-wave’ type unaffected by the mean flow. In the low-frequency range, the phase lead and the amplitude of the skin-friction oscillations increase at first and then decrease to their respective ‘skin-wave’ values. On the other hand the phase angle of the surface current decreases from 90° to 45° and its amplitude increases with frequency.

scholarly journals Self-consistent triple decomposition of the turbulent flow over a backward-facing step under finite amplitude harmonic forcing

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190018
Author(s):  
E. Yim ◽  
P. Meliga ◽  
F. Gallaire
Keyword(s):  
Turbulent Flow ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Backward Facing Step ◽  
Eddy Viscosity Model ◽  
Coherent Interaction ◽  
Self Consistent ◽  
The Mean

We investigate the saturation of harmonically forced disturbances in the turbulent flow over a backward-facing step subjected to a finite amplitude forcing. The analysis relies on a triple decomposition of the unsteady flow into mean, coherent and incoherent components. The coherent–incoherent interaction is lumped into a Reynolds averaged Navier–Stokes (RANS) eddy viscosity model, and the mean–coherent interaction is analysed via a semi-linear resolvent analysis building on the laminar approach by Mantič-Lugo & Gallaire (2016 J. Fluid Mech. 793 , 777–797. ( doi:10.1017/jfm.2016.109 )). This provides a self-consistent modelling of the interaction between all three components, in the sense that the coherent perturbation structures selected by the resolvent analysis are those whose Reynolds stresses force the mean flow in such a way that the mean flow generates exactly the aforementioned perturbations, while also accounting for the effect of the incoherent scale. The model does not require any input from numerical or experimental data, and accurately predicts the saturation of the forced coherent disturbances, as established from comparison to time-averages of unsteady RANS simulation data.

scholarly journals Effect of fluctuations on mean-field dynamos

2018 ◽  
Vol 84 (4) ◽  
Author(s):  
A. Alexakis ◽  
S. Fauve ◽  
C. Gissinger ◽  
F. Pétrélis
Keyword(s):  
Turbulent Flows ◽  
Mean Field ◽  
Liquid Sodium ◽  
Mean Flow ◽  
Dynamo Action ◽  
Scale Separation ◽  
Turbulent Fluctuations ◽  
The Mean ◽  
The One ◽  
The Magnetic Field

We discuss the effect of different types of fluctuations on dynamos generated in the limit of scale separation. We first recall that the magnetic field observed in the VKS (von Karman flow of liquid sodium) experiment is not the one that would be generated by the mean flow alone and that smaller scale turbulent fluctuations therefore play an important role. We then consider how velocity fluctuations affect the dynamo threshold in the framework of mean-field magnetohydrodynamics. We show that the detrimental effect of turbulent fluctuations observed with many flows disappears in the case of helical flows with scale separation. We also find that fluctuations of the electrical conductivity of the fluid, for instance related to temperature fluctuations in convective flows, provide an efficient mechanism for dynamo action. Finally, we conclude by describing an experimental configuration that could be used to test the validity of mean-field magnetohydrodynamics in strongly turbulent flows.

scholarly journals Effects of Rear Angle on the Turbulent Wake Flow between Two in-Line Ahmed Bodies

Atmosphere ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 328
Author(s):  
Ebenezer Essel ◽  
Subhadip Das ◽  
Ram Balachandar
Keyword(s):  
Wake Flow ◽  
Recirculation Region ◽  
Wake Region ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Slant Angle ◽  
The Road ◽  
Rear Angle ◽  
Turbulent Statistics ◽  
The Mean

Understanding the wake characteristics between two in-line vehicles is essential for improving and developing new strategies for reducing in-cabin air pollution. In this study, Ahmed bodies are used to investigate the effects of the rear slant angle of a leading vehicle on the mean flow and turbulent statistics between two vehicles. The experiments were conducted with a particle image velocimetry at a fixed Reynolds number, R e H = 1.7 × 10 4 , and inter-vehicle spacing distance of 0.75 L , where H and L are the height and length of the model. The rear slant angles investigated were a reference square back, high-drag angle ( α = 25 ° ) and low-drag angle ( α = 35 ° ). The mean velocities, Reynolds stresses, production of turbulent kinetic energy and instantaneous swirling strength are used to provide physical insight into the wake dynamics between the two bodies. The results indicate that the recirculation region behind the square back Ahmed body increases while those behind the slant rear-end bodies decreases in the presence of a follower. For the square back models, the dominant motion in the wake region is a strong upwash of jet-like flow away from the road but increasing the rear slant angle induces a stronger downwash flow that suppresses the upwash and dominates the wake region.

scholarly journals Influence of Bottom Topography on Integral Constraints in Zonal Flows with Parameterized Potential Vorticity Fluxes

2013 ◽  
Vol 43 (2) ◽  
pp. 311-323 ◽  
Author(s):  
V. O. Ivchenko ◽  
B. Sinha ◽  
V. B. Zalesny ◽  
R. Marsh ◽  
A. T. Blaker
Keyword(s):  
Potential Vorticity ◽  
Bottom Topography ◽  
Momentum Conservation ◽  
Integral Constraint ◽  
Mean Flow ◽  
Transfer Coefficients ◽  
Flat Bottom ◽  
Zonal Flows ◽  
Eddy Fluxes ◽  
The Mean

Abstract An integral constraint for eddy fluxes of potential vorticity (PV), corresponding to global momentum conservation, is applied to two-layer zonal quasigeostrophic channel flow. This constraint must be satisfied for any type of parameterization of eddy PV fluxes. Bottom topography strongly influences the integral constraint compared to a flat bottom channel. An analytical solution for the mean flow solution has been found by using asymptotic expansion in a small parameter, which is the ratio of the Rossby radius to the meridional extent of the channel. Applying the integral constraint to this solution, one can find restrictions for eddy PV transfer coefficients that relate the eddy fluxes of PV to the mean flow. These restrictions strongly deviate from restrictions for the channel with flat bottom topography.

scholarly journals A Framework for Parameterizing Eddy Potential Vorticity Fluxes

2012 ◽  
Vol 42 (4) ◽  
pp. 539-557 ◽  
Author(s):  
David P. Marshall ◽  
James R. Maddison ◽  
Pavel S. Berloff
Keyword(s):  
Stress Tensor ◽  
Potential Vorticity ◽  
Large Scale ◽  
Eddy Diffusivity ◽  
Linear Instability ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Conservation Of Energy ◽  
The Mean ◽  
Energy And Momentum

Abstract A framework for parameterizing eddy potential vorticity fluxes is developed that is consistent with conservation of energy and momentum while retaining the symmetries of the original eddy flux. The framework involves rewriting the residual-mean eddy force, or equivalently the eddy potential vorticity flux, as the divergence of an eddy stress tensor. A norm of this tensor is bounded by the eddy energy, allowing the components of the stress tensor to be rewritten in terms of the eddy energy and nondimensional parameters describing the mean shape and orientation of the eddies. If a prognostic equation is solved for the eddy energy, the remaining unknowns are nondimensional and bounded in magnitude by unity. Moreover, these nondimensional geometric parameters have strong connections with classical stability theory. When applied to the Eady problem, it is shown that the new framework preserves the functional form of the Eady growth rate for linear instability. Moreover, in the limit in which Reynolds stresses are neglected, the framework reduces to a Gent and McWilliams type of eddy closure where the eddy diffusivity can be interpreted as the form proposed by Visbeck et al. Simulations of three-layer wind-driven gyres are used to diagnose the eddy shape and orientations in fully developed geostrophic turbulence. These fields are found to have large-scale structure that appears related to the structure of the mean flow. The eddy energy sets the magnitude of the eddy stress tensor and hence the eddy potential vorticity fluxes. Possible extensions of the framework to ensure potential vorticity is mixed on average are discussed.

scholarly journals A Geometric Interpretation of Eddy Reynolds Stresses in Barotropic Ocean Jets

2016 ◽  
Vol 46 (8) ◽  
pp. 2285-2307 ◽  
Author(s):  
Talia Tamarin ◽  
James R. Maddison ◽  
Eyal Heifetz ◽  
David P. Marshall
Keyword(s):  
Stress Tensor ◽  
Ray Tracing ◽  
Analytic Solutions ◽  
Geometric Interpretation ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Nonlinear Simulation ◽  
Fully Nonlinear ◽  
Geometric Decomposition ◽  
The Mean

AbstractBarotropic eddy fluxes are analyzed through a geometric decomposition of the eddy stress tensor. Specifically, the geometry of the eddy variance ellipse, a two-dimensional visualization of the stress tensor describing the mean eddy shape and tilt, is used to elucidate eddy propagation and eddy feedback on the mean flow. Linear shear and jet profiles are analyzed and theoretical results are compared against fully nonlinear simulations. For flows with zero planetary vorticity gradient, analytic solutions for the eddy ellipse tilt and anisotropy are obtained that provide a direct relationship between the eddy tilt and the phase difference of a normal-mode solution. This allows a straightforward interpretation of the eddy–mean flow interaction in terms of classical stability theory: the initially unstable jet gives rise to eddies that are tilted “against the shear” and extract energy from the mean flow; once the jet stabilizes, eddies become tilted “with the shear” and return their energy to the mean flow. For a nonzero planetary vorticity gradient, ray-tracing theory is used to predict ellipse geometry and its impact on eddy propagation within a jet. An analytic solution for the eddy tilt is found for a Rossby wave on a constant background shear. The ray-tracing results broadly agree with the eddy tilt diagnosed from a fully nonlinear simulation.

3D Reynolds Stress Modelling of Turbulent Flow in Linear Turbine Cascade

1997 ◽  
Author(s):  
M. Kanniche ◽  
R. Boudjemadi ◽  
F. Déjean ◽  
F. Archambeau
Keyword(s):  
Reynolds Stress ◽  
Eddy Viscosity ◽  
Strain Tensor ◽  
Secondary Flows ◽  
Turbulence Closure ◽  
Turbine Cascade ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Principal Axes ◽  
The Mean

The flow in a linear turbine cascade (Gregory-Smith et al. (1990)) is numerically investigated using a Reynolds Stress Turbulence closure. A particular attention is given to secondary flows where the normal Reynolds stresses are expected to play an important role. The most classical turbulence closure, the k-epsilon model uses the Boussinesq Eddy Viscosity concept which assumes an isotropic turbulent viscosity. The Reynolds stresses are then related to local velocity gradients by this isotropic eddy viscosity. Corollary, the principal axes of the Reynolds stress tensor are colinear with those of the mean strain tensor. The advantage of Reynolds Stress Turbulence closure is the calculation of Reynolds stresses by their own individual transport equations. This leads to a more realistic description of the turbulence and of its dependance on the mean flow. The most classical Second Order turbulence model (Launder et al. (1975)) is applied to a linear turbine cascade, and the results are compared to secondary velocity and turbulence measurements at cross-passage planes.

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