Turbulent Fluid Motion Research Articles

Anthony Edward Perry 1937 - 2001

Tony Perry was one of Australia's most outstanding researchers in fluid mechanics, particularly in the study of turbulent fluid motion. He was a gifted experimentalist who advanced the techniques of hot-wire anemometry and quantitative flow visualization to make measurements of unparalleled accuracy to answer fundamental scaling questions. He also made seminal theoretical contributions to the physical modelling of wall-bounded turbulence, and pioneered flow topology approaches for the classification and description of fluid motions. He was a gifted lecturer, devoted supervisor to twenty PhD students, and a passionate and enthusiastic influence on numerous colleagues around the world.

New constraints on turbulent transport in accretion discs

Microphysical viscosity is too small to produce observed proto-planetary accretion disc lifetimes. Turbulent transport, in which turbulent motion takes the place of thermal motion, can provide the correct order-of-magnitude accretion rates for reasonable surface densities, though the source of such turbulence remains a matter of discussion. Here, we consider, independent of the source of turbulence, the minimal properties that turbulent motion must possess in order to adequately transport both angular momentum and mass in accretion discs. We find that the resulting angular momentum transport coefficient depends on the turbulent time scale and angular distribution, not only on the product of the turbulent length and velocity scales. More importantly, we also find that the required energy conversion efficiency is prohibitive if angular momentum transport results purely from fluid turbulence supplied by accretion energy and therefore that turbulent fluid motion mediated accretion must be powered by an outside source. Even in the case that the accretion mechanism is not a turbulent viscosity, as can be the case for a Magneto-Rotational Instability (MRI) disc, numerical simulations suggest that energy conservation is a significant constraint even on accretion driving processes such as the MRI.

A deterministic model for the propagation of turbulent oscillations

The deterministic point of view on turbulent fluid motion is to consider the Cauchy problem for equations of Navier–Stokes type associated with large Reynolds numbers and with singular initial data. Although the corresponding mathematical study has a lot progressed, it remains limited by fundamental difficulties related to the presence of instabilities. Precisely, the purpose of this article is to show on a realistic two-dimensional model that, up to some extent, such instabilities can be managed. This is achieved in the framework of a supercritical nonlinear geometric optics. The aim is to provide a theory allowing to take into account the interaction of a large amplitude monophase oscillating wave with waves oscillating at smaller frequencies in the other direction. The effect is that very complicated phenomena can occur in the inertial range, including for instance the production of new scales.

An Introduction to Ocean Turbulence

In an address to the British Association for the Advancement of Science in 1932, Sir Horace Lamb commented, “I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic.” Over the past century, understanding turbulent mixing in the ocean has been one of the most interesting and challenging problems of physical oceanography.

Measurements of coupled fluid and sediment motion over mobile sand dunes in a laboratory flume

The relationship between turbulent fluid motions and sediment particle motions over mobile sand dunes was investigated by using a laser Doppler velocimeter and an acoustic backscatter system in laboratory experiments performed at the USDA-ARS-National Sedimentation Laboratory. Profiles of acoustic backscatter from particles and at-a-point turbulence data were collected while translating both measurement devices downstream at the speed of mobile dune bedforms. The resulting data set was used to examine the frequency (recurrence frequency) at which the fluctuating backscatter and fluid velocity signals exceeded magnitude thresholds based on the standard deviation (σ) of the local velocity and the magnitude the acoustic signal resulting from backscatter from suspended particles. The slope of the downstream and vertical velocity recurrence frequencies generally indicated a gradually increasing recurrence time with increasing elevation. The recurrence frequency for acoustic backscatter data was not strongly variable with elevation. The closest correspondence between the recurrence frequencies of sediment backscatter and vertical velocities at the 1σ magnitude threshold was in a region defined by X/ L<0.4 and y<6 cm. The downstream velocity was most closely related to backscatter in a small region at 0.4< X/ L<0.8 and less than 3–4 cm from the bed.

Nonlinear dynamics of the false bottom during seawater freezing

Melt water concentrated in puddles at the ice surface penetrates through cracks beneath the lower ice boundary and forms underwater thaw lakes. In this process, the salinity of seawater near the ice decreases practically to zero values [1]. The consequent overcooling and convection lead to the nucleation and intergrowth of ice crystals that form an ice crust (false bottom) under the ice cover surface between the layers of saline and fresh waters [2, 3]. The mechanisms of generation and subsequent growth of the false bottom are confirmed by laboratory experiments [4], which revealed the following stages of the process: initial convection, nucleation and lateral growth of ice crystals, formation of the ice crust, and its further upward growth toward the thaw (fresh) water. In the natural conditions, the false bottom can form in a few hours [5] and spread laterally up to a few meters. Its thickness can be as high as a few decimeters, and the growth rate can reach a few centimeters per day [6]. Nansen noted that significant ice growth in the summer months is related to water freezing under the ice cover [7]. The existence of the false bottom strongly decreases the melting rate of thin ice [8] and decreases its reflectance [5]. We can also note that drainage of fresh water through the ice and its accumulation under ice play an important role in the transport of pollutants and biological organisms therein with their possible further freezing owing to the growth of the false bottom [9]. Experimental data indicate that the phase transition during false bottom freezing occurs in an elongated region filled with solid and liquid phases [4, 10]. Mathematical models taking into account the existence of such a region—a two-phase zone and turbulent fluid motion in the ocean—have virtually not been considered thus far, probably because it is extremely difficult to determine all the parameters, nonstationary equations, and boundaries of the phase transition. In our research, we present such a nonlinear model and its exact analytical solutions. Let us consider the process of directed crystallization of a newly formed false bottom along spatial axis z directed vertically upward. We shall consider that melt water and the two-phase zone are located in regions a ( t ) < z < 0 and b ( t ) < z < a ( t ) , respectively, while saline water is located in region z < b ( t ) . Here a ( t ) and b ( t ) denote the locations of boundaries of the melt water‐ two-phase zone and two-phase zone‐ocean phase transitions. We shall assume that the temperature profile in the two-phase zone is a linear function of the spatial coordinate:

Visualization of Vorticity and Vortices in Wall-Bounded Turbulent Flows

This study was initiated by the scientifically interesting prospect of applying advanced visualization techniques to gain further insight into various spatio-temporal characteristics of turbulent flows. The ability to study complex kinematical and dynamical features of turbulence provides means of extracting the underlying physics of turbulent fluid motion. The objective is to analyze the use of a vorticity field line approach to study numerically generated incompressible turbulent flows. In order to study the vorticity field, we present a field line animation technique which uses a specialized particle advection and seeding strategy. Efficient analysis is achieved by decoupling the rendering stage from the preceding stages of the visualization method. This allows interactive exploration of multiple fields simultaneously, which sets the stage for a more complete analysis of the flow field. Multifield visualizations are obtained using a flexible volume rendering framework which is presented in this paper. Vorticity field lines have been employed as indicators to provide a means to identify "ejection" and "sweep" regions; two particularly important spatio-temporal events in wall-bounded turbulent flows. Their relation to the rate of turbulent kinetic energy production and viscous dissipation, respectively, have been identified.

A theoretical model of convective heat exchange in a turbulent flow

New theoretical fundamentals for calculating heat exchange in turbulent fluid flows are considered with the use of spectral representations of hydrodynamic and thermophysical flow parameters. To classify and regulate random and chaotic time variations in the flow parameters the integral Fourier transformations are used to reduce the equations of continuity, momentum and energy to the spectral form. A closed system of equations of turbulent fluid motion was obtained to determine the averaged flow parameters and their statistic characteristics.

Agglomeration Control of l-Ornithine Aspartate Crystals by Operating Variables in Drowning-out Crystallization

The agglomeration of l-ornithine aspartate crystallized by the drowning-out method was investigated in a turbulent agitated semi-batch reactor. To modify the agglomeration conditions, the crystallization operating factors, including the agitation, feed flow rate, feed concentration, and drowning ratio (volume ratio of antisolvent to feed solution), were all varied. The mean particle size of the l-ornithine aspartate in the product suspension increased with increasing feed concentration, drowning ratio, and feeding time, as crystal agglomeration was promoted via an increased crystal population and holding time in the agitated reactor. Conversely, it was sensitively reduced with increasing agitation speed because of the enhanced external force of the turbulent impact. Furthermore, the agglomeration behavior of the crystals was monitored during and after the crystallization to determine the role of supersaturation and turbulent fluid motion.

Effects of strain rate and curvature on the propagation of a spherical flame kernel in the thin-reaction-zones regime

Strain rate and curvature effects on the propagation of turbulent premixed flame kernels have been investigated in the thin-reaction-zones regime using three-dimensional compressible direct numerical simulations (DNS) with single-step Arrhenius chemistry. An initially spherical laminar flame kernel is allowed to interact with the surrounding turbulent fluid motion to provide a propagating turbulent flame with a strong mean spherical curvature. The statistical behavior of the local displacement speed in response to strain and curvature is investigated in detail. The results demonstrate clearly that the mean curvature inherent to the flame kernel configuration has a significant influence on the propagation of the flame. It has been found that the mean density-weighted displacement speed ρ S d in the case of flame kernels varies significantly over the flame brush and remains different from ρ 0 S L (where ρ 0 is the reactant density and S L is laminar flame speed), unlike statistically planar flames. It is also shown that the magnitude of reaction progress variable gradient | ∇ c | is negatively correlated with curvature in the case of flame kernels, in contrast to the weak correlation between | ∇ c | and curvature in the case of planar flames. This correlation induces a net positive correlation between the combined reaction and normal diffusion components of displacement speed ( S r + S n ) and curvature in flame kernels, whereas the previous studies based on statistically planar flames did not observe any appreciable correlation between ( S r + S n ) and curvature.

Comparative study of turbulent mixing in jet in cross-flow configurations using LES

Mixing processes in turbulent fluid motion are of fundamental interest in many situations in engineering practice. Due to its practical importance in a vast number of applications, the generic configuration of the jet in cross-flow has been studied extensively in the past. Recently, the question has received a lot of attention, whether the unsteady behavior of the jet in cross-flow can be influenced by either active or passive means in order to control and enhance the mixing process. In the present paper, we use the large eddy simulation (LES) methodology to investigate how turbulent mixing can be enhanced by varying the angle between the jet and the oncoming cross-flow. After validating the computations against measurements by Andreopoulos and Rodi, we analyze qualitatively and quantitatively the mixing process for three configurations with different angles. It is shown that the inclination influences the characteristics of vortical structures and secondary motion which in turn have an effect on the mixing process. Besides a PDF of the passive scalar and a scalar energy spectrum, a mixedness parameter is used to provide information with respect to the quality and rate of mixing.

Eulerian and Lagrangian studies in surface flow turbulence

Experimental and numerical studies of turbulent fluid motion in a free surface are presented. The flow is realized experimentally on the surface of a tank filled with water stirred well below the surface. Numerically, it is modelled by free-slip boundary conditions. The surface flow is unconventional: it is not incompressible and neither kinetic energy nor enstrophy is conserved in the limit of zero fluid viscosity and in the absence of external driving as is the case for incompressible two-dimensional turbulent flows. The dynamics of passive Lagrangian tracers that are advected in such flows are dominated by rapidly changing patches of the surface flow divergence. Owing to compressibility, particles form clusters within multifractal mass distributions. Also studied is the motion of pairs and triplets of particles. The mean square separation shows an extended range with a reduced scaling exponent in comparison with the classical Richardson value. Clustering is also manifest in strongly deformed triangles spanned within triplets of tracers.

Upper bounds on the resistivity of a turbulent current layer

The basie equations for a layer of an electrically conducting fluid are considered in the magnetohydrodynamic approximation. An electric field is applied parallel to the layer. Because of various instabilities, turbulent fluid motions will be generated in general. The goal of the analysis presented in this paper is the derivation of upper bounds for the average turbulent resistivity of the layer. In order to demonstrate the concept of the upper bound theory, only the simplest case will be treated and the boundary conditions will be assumed in such a way that the analogy with the problem of bounds on the momentum transport in a turbulent Couette layer can be utilized.

A novel laboratory apparatus for simulating isotropic oceanic turbulence at low Reynolds number

A new experimental apparatus to simulate oceanic turbulence at low Reynolds number in the laboratory is described. Actuators located at each corner of a cubic Plexiglas box generated synthetic jets that interacted to create turbulent flow at the center of the saltwater apparatus. Four turbulent intensity levels were established, and velocity measurements were performed using digital particle image velocimetry. The flow characteristics in the center of the apparatus were confirmed to be nearly isotropic and homogeneous. The range of the dissipation rate (10−3 to 1 cm2s−3) and the Kolmogorov microscale (0.03 to 0.2 cm) agreed well with natural oceanic environments in the coastal zone, and the length scales and magnitude of the velocity and strain rate fluctuations were appropriate for zooplankton studies. The flow characteristics compared favorably with previous approaches for generating turbulence in the laboratory, in particular, oscillating‐grid apparatus. The current design also possessed increased simplicity, controllability, and transportability. Future objectives include studying the behavioral response of zooplankton to turbulent fluid motions.

A Note on Stochastic Burgers’ System of Equations

We consider a stochastic version of a system of two equations formulated by Burgers [Burgers, J.M. Mathematical examples illustrating relations occurring in the theory of turbulent fluid motion. Verh. Kon. Nerderl. Akad. Weten-Schappen Amsterdam, Afdeel Natuurkunde, 1939, 17 (2), 1–53] with the aim to describe the laminar and turbulent motions of a fluid in a channel. The existence and uniqueness theorem for a global solution is established. The paper generalizes the result from the paper by Da Prato and Ga¸tarek [Da Prato, G.; Ga¸tarek, D. Stochastic Burgers equation with correlated noise. Stochastics Stochastics Rep. 1995, 52, 29–41] dealing with the equation describing only the turbulent motion.

Spectral estimates of bed shear stress using suspended‐sediment concentrations in a wave‐current boundary layer

High‐resolution time series of suspended‐sediment profiles have been obtained using an acoustic backscatter system at an inner shelf site (North Carolina) where flows are dominated by wind‐driven currents and waves. We analyzed the spatial and temporal structure of near‐bed turbulence in particle‐transporting flows and scalar‐like fluctuations of suspended‐sediment concentrations. An important element of our analysis is a new inertial dissipation method for passive tracers to estimate the shear stress acting on the seabed, using the spectral properties of suspended sediment concentrations observed by acoustic backscatter sensors. In flows that provide adequate separation of the scales of turbulence production and dissipation, a sufficiently thick constant stress wall layer, and significant sediment suspension, frequency (or associated wave number) spectra of near‐bed sediment concentration exhibit a −5/3 slope in the inertial subrange that spans frequencies of order 1 Hz. This observation suggests that the suspended sediment is effectively a passive tracer of turbulent fluid motions. Inversion of the relevant, Kolmogorov scaling equations yields estimates of the shear velocity that agree reasonably well with other, independent and widely used measures. High‐ and low‐frequency limits on application of the inertial dissipation method to sediment concentration are related to the inertial response time of sediment particles and the sediment settling timescale. We propose that, in future applications, the inertial dissipation method for passive tracers can be used to estimate either the shear velocity, effective settling velocity of suspended sediment (or equivalent particle size) or dynamic bed roughness if two of these three quantities are independently known.

Spatial test filters for dynamic model large‐eddy simulation with finite elements

AbstractIn this article we will develop spatial filters required in the dynamic model of small‐scale turbulent fluid motions in large‐eddy simulation with finite elements. The characterization of these finite element filters is crucial because it is seen to have an impact on incompressible Navier–Stokes simulation results. Copyright © 2003 John Wiley &amp; Sons, Ltd.

Small-scale nutrient patches in tidally mixed coastal waters

MEPS Marine Ecology Progress Series Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsTheme Sections MEPS 232:29-44 (2002) - doi:10.3354/meps232029 Small-scale nutrient patches in tidally mixed coastal waters Laurent Seuront1,*, Valérie Gentilhomme2, Yvan Lagadeuc3 1Department of Ocean Sciences, Tokyo University of Fisheries, 4-5-7 Konan, Minato-ku, Tokyo 108-8477, Japan 2Ecosystem Complexity Research Group, Station Marine de Wimereux, UMR 8013 ELICO, Université des Sciences et Technologies de Lille, BP 80, 62930 Wimereux, France 3Université de Caen, Laboratoire de Biologie et Biotechnologies Marines, IUT Génie Biologique, Bd du Maréchal Juin, 14032 Caen cedex, France *Present address: Ecosystem Complexity Research Group, Station Marine de Wimereux, UMR 8013 ELICO, Université des Sciences et Technologies de Lille, BP 80, 62930 Wimereux, France. E-mail: laurent.seuront@univ-lille1.fr ABSTRACT: In the eastern English Channel, characterized by its megatidal regime and the resulting very high turbulence, phytoplankton biomass and purely passive scalars such as temperature and salinity are basically regarded as homogenised by turbulent fluid motions. However, recent studies have demonstrated‹on the basis of innovative statistical analyses in marine ecology‹that these parameters were heterogeneously distributed at a small scale. We extend these concepts to high-resolution time series of dissolved nitrogen (NO2-). We first demonstrate the validity of our sampling procedure of continuously measuring nitrite concentration (3 s temporal resolution). Second, we describe how these time series recorded at different times of 4 tidal cycles can be characterized as heterogeneously distributed using fractal and multifractal parameters, and then can be described in terms of small-scale patches. In addition, we show how multifractal parameters can be regarded as being both qualitatively and quantitatively more informative than a single fractal dimension. These parameters showed very specific temporal patterns revealing the absence of density-dependence of nitrite distribution. In contrast, nitrite distributions clearly appeared to be less heterogeneously distributed under higher turbulence, suggesting a physical control of small-scale nutrient patchiness. Nevertheless, taking into account the different structures of nitrite distributions under high and low turbulence, we suggest that the observed small-scale nutrient patches could be the result of complex interactions between hydrodynamic conditions, biological processes related to phytoplankton populations, and the productive efficiency of bacterial populations. This hypothesis is supported by observations that the structure of temperature and salinity‹regarded as passive scalars under purely physical control of turbulent motions‹recorded simultaneously to the nitrite data remained similar under all hydrodynamic conditions. KEY WORDS: Turbulence · Patchiness · Nitrite · Time series · Tidal forcing · Fractal and multifractal analysis Full text in pdf format PreviousNextExport citation RSS - Facebook - Tweet - linkedIn Cited by Published in MEPS Vol. 232. Online publication date: May 03, 2002 Print ISSN: 0171-8630; Online ISSN: 1616-1599 Copyright © 2002 Inter-Research.

Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis on Rotation and Motion Groups

<i>Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis on Rotation and Motion Groups</i>

Predictability of Drifter Trajectories in the Tropical Pacific Ocean

Abstract Predictability of particle motion in the ocean over a timescale of one week is studied using three clusters of buoys consisting of 5–10 drifters deployed in the tropical Pacific Ocean. The analysis is conducted by using three techniques with increasing complexity: the center of mass of the cluster, advection by climatological currents, and a new technique that relies on the assimilation of both velocity and position data from the surrounding drifters into a Markov model for particle motion. A detailed mathematical description of the theory leading to this model is given. The predictability of drifter motion in these clusters is characterized using the data density Nd, defined as the number of drifters over an area scaled by the mean diameter of the cluster. The data density Nd decreases along the drifter trajectories due to the tendency of particles to disperse by turbulent fluid motion. In the first regime, which corresponds to the period after the release of drifters in a tight cluster when Nd ...