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.

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.

Observations on the turbulent fluctuations of a tidal current

1949 ◽  
Vol 199 (1058) ◽  
pp. 311-327 ◽  
Keyword(s):  
Time Scale ◽  
Tidal Current ◽  
Velocity Fluctuations ◽  
Turbulent Fluctuations ◽  
Long Period ◽  
Auto Correlation ◽  
Short Period ◽  
Wide Range ◽  
First Time ◽  
A Current

Records have been obtained of fluctuations in the speed of the tidal current in the Mersey estuary, using a current meter in a stand on the bottom, and compared with other records taken with the meter suspended freely at various depths. The fluctuations covered a wide range of periods but could be separated into two main types: ‘short period’, having periods of the order of a few seconds, and ‘long period’, with periods from 30 sec. to several minutes. The amplitudes, periods and auto-correlation of the short-period fluctuations have been examined in some detail, and it is concluded that the fluctuations observed near the bottom are evidence of the turbulence associated with bottom friction. It is believed to be the first time that the presence of turbulent velocity fluctuations of this time-scale in the sea has been established experimentally. The long-period fluctuations resemble those found in previous investigations and show features consistent with their being turbulent in origin also, although turbulence of the time-scale involved in their case would probably be mainly horizontal.

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 Statistical energy conservation principle for inhomogeneous turbulent dynamical systems

2015 ◽  
Vol 112 (29) ◽  
pp. 8937-8941 ◽  
Author(s):  
Andrew J. Majda
Keyword(s):  
Dynamical Systems ◽  
Energy Conservation ◽  
Upper And Lower Bounds ◽  
Grand Challenge ◽  
Mean Flow ◽  
Turbulent Fluctuations ◽  
Conservation Principle ◽  
Wide Range ◽  
The Mean ◽  
Energy Conservation Principle

Understanding the complexity of anisotropic turbulent processes over a wide range of spatiotemporal scales in engineering shear turbulence as well as climate atmosphere ocean science is a grand challenge of contemporary science with important societal impact. In such inhomogeneous turbulent dynamical systems there is a large dimensional phase space with a large dimension of unstable directions where a large-scale ensemble mean and the turbulent fluctuations exchange energy and strongly influence each other. These complex features strongly impact practical prediction and uncertainty quantification. A systematic energy conservation principle is developed here in a Theorem that precisely accounts for the statistical energy exchange between the mean flow and the related turbulent fluctuations. This statistical energy is a sum of the energy in the mean and the trace of the covariance of the fluctuating turbulence. This result applies to general inhomogeneous turbulent dynamical systems including the above applications. The Theorem involves an assessment of statistical symmetries for the nonlinear interactions and a self-contained treatment is presented below. Corollary 1 and Corollary 2 illustrate the power of the method with general closed differential equalities for the statistical energy in time either exactly or with upper and lower bounds, provided that the negative symmetric dissipation matrix is diagonal in a suitable basis. Implications of the energy principle for low-order closure modeling and automatic estimates for the single point variance are discussed below.

scholarly journals THE FLICKER RESPONSE FUNCTION FOR THE TURTLE PSEUDEMYS

1939 ◽  
Vol 22 (3) ◽  
pp. 311-340 ◽  
Author(s):  
W. J. Crozier ◽  
Ernst Wolf ◽  
Gertrud Zerrahn-Wolf
Keyword(s):  
Flash Intensity ◽  
Rods And Cones ◽  
Sensory Effects ◽  
Retinal Rods ◽  
Fixed Proportion ◽  
Order Of Magnitude ◽  
The Mean ◽  
Probability Integral ◽  
The Individual ◽  
Critical Intensity

1. At constant temperature, with a fixed proportion of light time in a flash cycle (namely, tL/tD = 1), the mean critical intensity for motor response to visual flicker by the turtle Pseudemys scripta follows a probability integral (log I) as a function of flash frequency F. The fit is close and satisfactory; certain quite minor but consistent deviations are adequately explained by features of the experiments. 2. The variation (σI) of critical I is directly proportional to the mean critical intensity (Im), over the entire explorable range. 3. These facts are consistent with the fact that the retina of this turtle is devoid of rods. It contains only cones, histologically, which, with their central representations, provide a single population of sensory effects. The properties of this population are compared with those of homologous populations deduced from corresponding measurements with other forms (various fishes; amphibian; man) which exhibit two such groups of sensory effects associated with the possession of retinal rods and cones. 4. Certain other formulations which have previously been applied to homologous data obtained with other organisms do not properly describe the Pseudemys measurements. 5. The use of a probability integral to describe the data of response to visual flicker for the dissection of the compound curves provided by animals possessing both rods and cones, is accordingly Justified. 6. Persisting differences among individuals of Pseudemys as regards the values of the critical flash intensity under various conditions of experimentation are of the same order of magnitude as are the transitory differences found in lots of other kinds of animals. 7. Determinations of mean critical flash frequency (Fm) at fixed levels of I lie slightly above determinations of Im at fixed values of I, as with other forms. The variation of critical flash frequency goes through a maximum as log I is increased; its height is lower than with certain other forms, in correlation with the low general slope of the F - log I curve (more properly, band). 8. These facts are consistent with the view that the dispersions of the individual critical intensities (and flash frequencies) are determined by organic variation rather than by "experimental error." 9. When the temperature is altered the F - log Im curve is shifted, with no change of Fmax. or of shape; the curve moves to lower intensities as the temperature is raised. 10. The reciprocal of the mean critical intensity, at fixed flash frequency, is a measure of excitability. With increase of temperature (12.5° to 36°) 1/Im for given F follows the Arrhenius equation, exhibiting a "break" at 29.5° (µ = 26,700, 12.5° to 29.5°; 12,400, 29.5° to 36°). This is explained by the necessary theory that, the number of elements of sensory effect required for the index response at fixed F being constant, the ease of their excitation is governed by temperature through its control of the velocity of an interrelated system of catalyzed processes common to all of the sensory elements concerned.

scholarly journals Turbulence and Scale Measurements in a Square Channel with Transverse Square Ribs

1996 ◽  
Vol 2 (3) ◽  
pp. 209-218 ◽  
Author(s):  
Richard B. Rivir ◽  
Mingking K. Chyu ◽  
Paul K. Maciejewski
Keyword(s):  
Turbulence Intensity ◽  
Turbulent Shear ◽  
Mean Flow ◽  
Integral Scale ◽  
Square Channel ◽  
Turbulent Shear Layer ◽  
The Third ◽  
Mainstream Flow ◽  
The Mean ◽  
Flow Turbulence

Hot-wire measurements of the mean flow, turbulence characteristics, and integral scale in a square channel roughened with transverse ribs mounted on two opposing sidewalls are presented for three rib configurations: single rib, in-line multiple ribs, and staggered multiple ribs. Test conditions for multiple ribs use p/H = 10, H/D 0.17, andRe⁡D23,000. Measured results highlight the spatial distribution and evolution of turbulence intensity and integral scale from the flow entrance of the first period to the developed regime near the exit of the third period. The highly turbulent, shear layer initiated near the trailing upper-edge of a rib elevates the turbulence level in the mainstream of the channel. The magnitude of turbulence intensity in the channel core rises from 0.7% in the approaching flow to about 20–25% near the exit of the third period. The integral scale dominating the mainstream flow increases from approximately one-half the rib-height, 0.5H, in the approaching flow to 1.5-2.5H behind the first rib and further downstream.

scholarly journals Large-scale mean patterns in turbulent convection

2015 ◽  
Vol 776 ◽  
pp. 96-108 ◽  
Author(s):  
Mohammad S. Emran ◽  
Jörg Schumacher
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Mean Flow ◽  
Turbulent Fluctuations ◽  
The Mean ◽  
Prandtl Numbers ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard

Large-scale patterns, which are well-known from the spiral defect chaos (SDC) regime of thermal convection at Rayleigh numbers $\mathit{Ra}<10^{4}$, continue to exist in three-dimensional numerical simulations of turbulent Rayleigh–Bénard convection in extended cylindrical cells with an aspect ratio ${\it\Gamma}=50$ and $\mathit{Ra}>10^{5}$. They are revealed when the turbulent fields are averaged in time and turbulent fluctuations are thus removed. We apply the Boussinesq closure to estimate turbulent viscosities and diffusivities, respectively. The resulting turbulent Rayleigh number $\mathit{Ra}_{\ast }$, that describes the convection of the mean patterns, is indeed in the SDC range. The turbulent Prandtl numbers are smaller than one, with $0.2\leqslant \mathit{Pr}_{\ast }\leqslant 0.4$ for Prandtl numbers $0.7\leqslant \mathit{Pr}\leqslant 10$. Finally, we demonstrate that these mean flow patterns are robust to an additional finite-amplitude sidewall forcing when the level of turbulent fluctuations in the flow is sufficiently high.

scholarly journals Bluff bodies in deep turbulent boundary layers: Reynolds-number issues

2007 ◽  
Vol 571 ◽  
pp. 97-118 ◽  
Author(s):  
HEE CHANG LIM ◽  
IAN P. CASTRO ◽  
ROGER P. HOXEY
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Delta Wing ◽  
Body Height ◽  
Turbulent Boundary Layers ◽  
The Body ◽  
Bluff Bodies ◽  
Mean Flow ◽  
Order Of Magnitude ◽  
The Mean

It is generally assumed that flows around wall-mounted sharp-edged bluff bodies submerged in thick turbulent boundary layers are essentially independent of the Reynolds number Re, provided that this exceeds some (2–3) × 104. (Re is based on the body height and upstream velocity at that height.) This is a particularization of the general principle of Reynolds-number similarity and it has important implications, most notably that it allows model scale testing in wind tunnels of, for example, atmospheric flows around buildings. A significant part of the literature on wind engineering thus describes work which implicitly rests on the validity of this assumption. This paper presents new wind-tunnel data obtained in the ‘classical’ case of thick fully turbulent boundary-layer flow over a surface-mounted cube, covering an Re range of well over an order of magnitude (that is, a factor of 22). The results are also compared with new field data, providing a further order of magnitude increase in Re. It is demonstrated that if on the one hand the flow around the obstacle does not contain strong concentrated-vortex motions (like the delta-wing-type motions present for a cube oriented at 45° to the oncoming flow), Re effects only appear on fluctuating quantities such as the r.m.s. fluctuating surface pressures. If, on the other hand, the flow is characterized by the presence of such vortex motions, Re effects are significant even on mean-flow quantities such as the mean surface pressures or the mean velocities near the surfaces. It is thus concluded that although, in certain circumstances and for some quantities, the Reynolds-number-independency assumption is valid, there are other important quantities and circumstances for which it is not.

scholarly journals The Life Cycle of Spontaneously Generated Internal Waves

2018 ◽  
Vol 48 (2) ◽  
pp. 343-359 ◽  
Author(s):  
Callum J. Shakespeare ◽  
Andrew McC. Hogg
Keyword(s):  
Internal Waves ◽  
Vertical Shear ◽  
Spontaneous Generation ◽  
Net Energy ◽  
Mean Flow ◽  
Ocean Energy ◽  
Energy Transfers ◽  
The Mean ◽  
Internal Wave Generation ◽  
The Individual

AbstractRecent numerical modeling studies have suggested significant spontaneous internal wave generation near the ocean surface and energy transfers to and from these waves in the ocean interior. Spontaneous generation is the emission of waves by unbalanced, large Rossby number flows in the absence of direct forcing. Here, the authors’ previous work is extended to investigate where and how these waves exchange energy with the nonwave (mean) flow. A novel double-filtering technique is adopted to separate first the wave and nonwave fields, then the individual upward- and downward-propagating wave fields, and thereby identify the pathways of energy transfer. These energy transfers are dominated by the interaction of the waves with the vertical shear in the mean flow. Spontaneously generated waves are found to be oriented such that the downward-propagating wave is amplified by the mean shear. The internal waves propagate through the entire model depth while dissipating energy and reflect back upward. The now-upward-propagating waves have the opposite sign interaction with the mean shear and decay, losing most of their energy to the nonwave flow in the upper 500 m. Overall, in the simulations described here, approximately 30% of the wave energy is dissipated, and 70% is returned to the mean flow. The apparent preferential orientation of spontaneous generation suggests a potentially unique role for these waves in the ocean energy budget in uniformly drawing net energy from mean flow in the upper-ocean interior and transporting it to depth.

Peristaltic Transport

1968 ◽  
Vol 35 (4) ◽  
pp. 669-675 ◽  
Author(s):  
Y. C. Fung ◽  
C. S. Yih
Keyword(s):  
Velocity Profile ◽  
Pressure Gradient ◽  
Amplitude Ratio ◽  
Critical Value ◽  
Positive Pressure ◽  
Peristaltic Motion ◽  
Mean Flow ◽  
Peristaltic Pumping ◽  
Order Of Magnitude ◽  
The Mean

Peristaltic pumping (viscous fluid flow induced by a sinusoidal traveling wave motion of the walls of a tube) at moderate amplitudes of motion is analyzed in the two-dimensional case. The nonlinear convective acceleration is considered and the nonslip condition is applied on the wavy wall (rather than on the mean position) in order to account for the mean flow induced by the wall motion. In the case in which there is no other cause of flow, the mean flow induced by the peristaltic motion of the wall is proportional to the square of the amplitude ratio (wave amplitude/half width of channel). The velocity profile depends on the mean pressure gradient. In this paper only those cases in which the pressure gradient will produce a flow of the same order of magnitude as that induced by the peristaltic motion are considered. If the pressure gradient is positive and equal to a certain critical value, then the velocity is zero on the center line. Pumping against a positive pressure gradient greater than the critical value would induce a backward flow (reflux) in the core region of the stream. There will be no reflux if the pressure gradient is smaller than the critical value. The velocity profile and the value of the critical pressure gradient are presented in this paper.

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