Turbulent Velocity Scale Research Articles

Anisotropy in turbulence profiles of stratified wakes

At sufficiently high values of the Reynolds number (Re⩾4.5×103) and internal Froude number (F⩾4), initially turbulent bluff body wakes evolve in the presence of a stable background density gradient with wake-averaged mean and turbulence length and velocity scales that are independent of Re and F for at least two orders of magnitude extension in both parameters. The way in which the initially three-dimensional motions transition to the characteristic (and Re- and F-independent) late wakes (where vertical velocities, w≪u,v) is both of great practical interest, and complex, hence somewhat unclear. Here, digital particle imaging velocimetry type measurements on towed-sphere wakes are described, so that the development of anisotropy can be measured by the time development of turbulence profiles in horizontal and vertical centerplanes. The observed anisotropies can be associated with energy transfer to internal wave modes, and suppression of other vertical displacements, that contrasts with sphere wakes at similar Re in a homogeneous fluid. Maximum Reynolds stresses occur at the boundary of a sinuous undulation of the wake, which increases in amplitude up to Nt≈60 (N is the buoyancy frequency that characterizes the strength of the stratification). Although an intrinsic wake profile instability cannot be excluded, the observed wake element spacings can be accounted for by known spiral and Kelvin–Helmholtz instabilities in the near wake.

Asymmetric mixing transport: A horizontal transport mechanism for sinking plankton and sediment in tidal flows

A mechanism is described for the net horizontal transport of sinking plankton or sediment by oscillatory tidal flows. The mean motion of the plankton or particles is driven by the modulation of vertical mixing between flood and ebb. Cold water forced over warm water on the flood tide creates enhanced vertical mixing and resuspension of sinking particles higher into the water column. On ebb, the converse occurs, and sinking particles are lower in the water column. Since friction retards the tidal flow near the bottom, this leads to a net horizontal transport toward the less dense water. Because less dense water tends to be shallower, this will tend to move sinking plankton and sediment toward the crest of banks, toward the coast, and up embayments, even in the absence of any mean currents. A one‐dimensional Eulerian model of this horizontal transport is developed and is compared to particle motion in a fully nonlinear two‐dimensional model with an advanced turbulence closure scheme. The Eulerian model can, in most circumstances, predict the net horizontal motion of the particles as a function of their sinking speed and observable oceanographic properties. The mean horizontal speed of sinking particles is greatest when the sinking speed of the particles is about one‐seventieth of the tidal velocities, or equivalently, about one‐third of the mean turbulent velocity scale u*. This horizontal transport of plankton and particles requires no behavior more complicated than simple sinking to achieve net horizontal speeds of several kilometers per day for realistic planktonic sinking speeds. It is possible that such a mechanism is a factor in larval recruitment and retention in coastal regions, for example, scallop larvae on Georges Bank.

An Algebraic Model of Turbulence for Flows with a Maximum of Tangential Stress Inside the Boundary Layer

The two-layer Klauser scheme of turbulent boundary layer is used to construct a new algebraic model of turbulence for a fairly wide class of flows characterized by the presence of a maximum of tangential stress inside the layer. A distinguishing feature of the model is the method of determination of the velocity scale of turbulence in the outer region of the boundary layer, based on the use of the Bradshow–Ferriss–Atwell (BFA) equation for turbulent stresses. This provides the possibility of taking into account the effect on the scale of both the external factors (longitudinal pressure gradient, injection, suction, transverse curvature of the surface) and the basic mechanisms of transport of turbulent tangential stresses (convection, diffusion, generation, and dissipation). In the final analysis, this defines the rather wide capabilities of the model confirmed by the results of its testing on the basis of experimental data for boundary layers with a positive differential pressure, injection, and transverse curvature of the surface.

Turbulent Jet Issuing from a Quasi Two-Dimensional Nozzle with a Rectangular Notch at the Midspan. Streamwise Variation of Turbulent Flowfield.

The turbulent flowfield of a turbulent air jet issuing from a quasi two-dimensional nozzle with a rectangular notch at the midspan, has been measured using linearized constant temperature anemometers. The aim of this study is to examine the streamwise variation of the turbulent quantities and the turbulent scales, and to clarify the asymptotic process of the present jet toward the two-dimensional jet. Throughout this experiment, Reynolds number based on the nozzle width and the exit velocity, was kept constant 13000. From this experiment, in the upstream region of the quasi two dimensional jet, it is revealed that the development of the turbulent kinetic energy is suppressed by means of the rectangular notch. In the far downstream region, the decreasing rate of the turbulent velocity scale at the jet center region approaches to that of the two-dimensional jet. Furthermore, the turbulent kinetic energy flux in the interactive region takes the minimum value at the section of x/d=15 due to the inward secondary flow.

A Lagrangian Solution To The Relationship Between A Distributed Source And Concentration Profile

A new solution is presented to the problem ofrelating source strength and concentration profiles within a plant canopy. The solution is based on the Lagrangian dispersion theory developed by G. I. Taylor in 1921. A dispersion matrix is derived that relates the source and concentration profiles based on profiles of the turbulent length and velocity scales. The matrix translates the effects of persistence (a temporal effect) into spatialcoordinates and represents the change from near-field to far-field in acontinuous fashion, successfully accounting for both regimes. A test ofthe new model using wind-tunnel data showed excellent quantitative agreement between model and measurements. A comparison was also made withM. R. Raupach's localized near-field theory, which underestimated the near-field effect in the wind-tunnel data and relative to the new model.

A thickened flame model for large eddy simulations of turbulent premixed combustion

A subgrid scale model for large eddy simulations of turbulent premixed combustion is developed and validated. The approach is based on the concept of artificially thickened flames, keeping constant the laminar flame speed sl0. This thickening is simply achieved by decreasing the pre-exponential factor of the chemical Arrhenius law whereas the molecular diffusion is enhanced. When the flame is thickened, the combustion–turbulence interaction is affected and must be modeled. This point is investigated here using direct numerical simulations of flame–vortex interactions and an efficiency function E is introduced to incorporate thickening effects in the subgrid scale model. The input parameters in E are related to the subgrid scale turbulence (velocity and length scales). An efficient approach, based on similarity assumptions, is developed to extract these quantities from the resolved velocity field. A specific operator is developed to exclude the dilatational part of the velocity field from the estimation of turbulent fluctuations. The combustion model is then implemented in a compressible parallel finite volume–element solver able to handle hybrid grids to simulate a lateral injections combustor (LIC). Results are in agreement with the available experimental data.

Growth of Ceratium hirundinella in a subtropical Australian reservoir: the role of vertical migration

A study into the photophysiology, growth and migration of Ceratium hirundinella in Chaffey Reservoir in subtropical northern New South Wales, Australia, revealed that a proportion of cells formed subsurface accumulations at depths that optimized light intensity (212-552 µmol photons m -2 s -1 ) for photosynthesis and cell growth. At high incident irradiance, Ceratium migrated downwards from the near-surface waters, avoiding high-light-induced, slow-recovering non-photochemical quenching of photosystem II. Overnight deepening of the surface mixed layer by convective cooling produced homogeneous distributions of Ceratium with a significant proportion of the population below the depth where light saturation of photosynthesis occurred. Ceratium migrated towards the surface from suboptimal light intensities, at a velocity of 1.6-2.7 � 10 -4 m s -1 . Subsurface accumu- lations occurred under a variety of turbulence intensities; however, accumulation was significantly reduced when the turbulent velocity scale in the mixed layer was >5 � 10-3 m s-1, beyond which turbulent diffusion dominated advection by swimming. The formation of subsurface accumulations with increased computed water column integral photosynthesis by 35% compared to a uniform cell distribution.

Methods for calculating the response of structures to inhomogeneous turbulent flows

Problems involving the response of structures to turbulent flows are usually modeled using a linear approach. The incoming turbulence is described using a Von Karman or Liepmann spectrum using typical turbulence velocity and length scales. However, these models only apply to homogeneous turbulence and so inhomogeneous flows can only be treated in an approximate manner. This paper will describe an alternative approach in which the turbulent flow is decomposed into a set of uncorrelated modes using proper orthogonal decomposition. The response of the structure to each mode can then be considered independently and the results summed incoherently to give the complete response. However, to obtain the proper orthogonal modes the flow must be measured in great detail. It will be shown that this requirement can be reduced if measurements are limited to the most energetic parts of the flow.

Numerical simulation of turbulent propane–air combustion with nonhomogeneous reactants

High-resolution two-dimensional numerical simulations have been performed for premixed turbulent propane–air flames propagating into regions of nonhomogeneous reactant stoichiometry. Simulations include complex chemical kinetics, realistic molecular transport, and fully resolved hydrodynamics (no turbulence model). Aerothermochemical conditions (pressure, temperature, stoichiometry, and turbulence velocity scale) approach those in an automotive gasoline direct-injection (GDI) engine at a low-speed, part-load operating condition. Salient findings are as follows: (1) There is no leakage of the primary fuel (propane) behind an initial thin premixed heat-release zone. This “primary premixed flame” can be described using a monotonic progress variable and laminar premixed flamelet concepts. (2) For the conditions simulated, differences in global heat release and flame area (length) between homogeneous and nonhomogeneous reactants having the same overall stoichiometry are small. (3) Beyond three-to-four flame thicknesses behind the primary flame, practically all hydrocarbon fuel has broken down into CO and H 2. (4) The rate of heat release in the “secondary reaction zone” behind the primary premixed flame is governed by turbulent mixing and the kinetics of CO 2 production. Mixture-fraction-conditioned secondary heat release, CO, and CO 2 production rates are qualitatively similar to results from a first-order conditional moment closure (CMC) model; CMC gives poor results for H 2, H 2O, and radical species. Description of the secondary heat release using steady laminar diffusion flamelet concepts is problematic. (5) Of the chemical species considered, HCO mass fraction or the product of CH 2O and OH mass fractions correlates best with local heat-release rate [1]. (6) Computational considerations demand modifications to chemical mechanisms involving C 3H 7 and CH 3CO. Specific changes are proposed to strike a satisfactory balance between accuracy and computational efficiency over a broad range of reactant stoichiometry.

Near Surface Characterization of an Impinging Elliptic Jet Array

In this study naturally occurring large-scale structures and some turbulence characteristics within an impinging jet array are investigated. The dynamics of a three-by-three elliptic jet array are analyzed relative to the flow structures within the array. With applications to electronic component cooling, low Reynolds number conditions, Re = 300 to 1500, are presented. Two jet aspect ratios are used, 2 and 3, with identical jet hydraulic diameters and jet-to-jet space. The effects of impinging distance are studied in the range of one to six jet hydraulic diameters. Flow visualization and PIV are used for the identification of structures and quantitative analysis. These results are used to evaluate the integrated surface layer vorticity, Γ*, which is shown to depend on the jet aspect ratio and impingement distance. Also, a transport coefficient is presented, based on a turbulence velocity and length scales. This coefficient is shown to experience a maximum value versus impingement distance that coincides with the location of axis switching.

Modeling Deep Ocean Convection: Large Eddy Simulation in Comparison with Laboratory Experiments

A large-eddy simulation model (LES) has been applied to study deep convective processes in a stratified ocean driven by the energetic cooling at the ocean surface. Closely related to a recent laboratory experiment, the numerical experiment deals with the inverted problem of the growth of a convective mixed layer driven by a localized source of bottom heating in a rotating, stably stratified fluid. In general, good agreement is found between numerical and laboratory results. After onset of the heating a well-mixed layer forms above the heated circular surface. Although small-scale turbulence quantities like rms velocities and length scale can be best described by the nonrotating turbulent velocity and length scales, they are also found to differ significantly from a nonrotating control run, which indicates that rotation affects but does not control the turbulence. Due to the horizontal radial temperature gradient between the mixed layer and the ambient fluid a rim current develops around the periphery of the heated surface. Its near-surface maximum can be well described by a simple thermal wind law. The strong counterrotating current also observed in the laboratory at greater heights above the surface is found to be mainly driven by surface friction and should not be observed in the ocean. As time progresses, the rim current becomes unstable, eventually generating a field of baroclinic eddies that stop the mixed layer growth by causing some horizontal exchange between the convective layer and its cooler surrounding. The wavelength of the instabilities slowly increases with time and is clearly related to the local Rossby radius.

A first order mixing–condensation scheme for nocturnal stratocumulus

A simple closure scheme for nocturnal stratocumulus is proposed. The scheme is formulated in conserved variables. Cloud fraction and cloud water amount are diagnosed assuming a top-hat distribution for total water. Conversion of cloud water into rain water is parameterized in terms of cloud water and the incoming rain flux. Turbulence transport in the cloud layer is accounted for by a first-order vertical diffusion scheme with a profile-type diffusivity. The length scale corresponds to the thickness of the cloud layer. The turbulent velocity scale is directly related to the long wave radiative flux divergence in the cloud. Entrainment at cloud top is implicitly treated by extending the in-cloud mixing profile slightly beyond cloud top. The excess height is derived from the buoyancy frequency at cloud top and a radiative–convective velocity scale. The scheme is capable of simulating realistic profiles of the conserved variables and cloud parameters for a case of nocturnal stratocumulus prepared on the basis of ASTEX data.

An inertial‐dissipation method for estimating turbulent flux in buoyancy‐driven, convective boundary layers

A method is developed for using wavenumber spectra of scalar contaminants in a boundary layer dominated by buoyancy‐driven convection to estimate the magnitude of vertical turbulent fluxes. The technique is analogous to the conventional inertial‐dissipation method (IDM) for obtaining fluxes from variance spectral density levels in the inertial subrange but differs in the way that turbulence scales are combined to provide an “eddy density diffusivity” for relating flux magnitude to variance dissipation rate. The method is illustrated using spectra and direct flux covariance data from the oceanic boundary layer at the edge of a freezing lead during the 1992 Lead Experiment in the Arctic Ocean. There, density was controlled almost exclusively by salinity, and it is argued that the turbulent length and velocity scales governing vertical exchange were the inverse of the wavenumber at the peak in the weighted salinity spectrum (considerably less than the mixed layer depth) and the cube root of the product of turbulent length scale and the buoyancy flux magnitude, respectively. The sign of the skewness of temperature or salinity time series is shown to be a robust indicator of the (negative) direction of vertical flux. The “free convection” approach is valid (i.e., should be used instead of the conventional IDM) only if the convective turbulent scale velocity is appreciably larger than friction velocity (square root of the Reynolds stress), so that turbulent kinetic energy dissipation is approximately equal to buoyancy production.

Turbulence-induced contact rates of plankton:the question of scale

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 166:307-310 (1998) - doi:10.3354/meps166307 Turbulence-induced contact rates of plankton: the question of scale André W. Visser*, Brian R. MacKenzie Danish Institute for Fisheries Research, Department of Marine and Coastal Ecology, Kavalergården, DK-2920 Charlottenlund, Denmark *E-mail: awv@dfu.min.dk Modelling encounter rates between planktonic predators and prey in turbulent waters requires an estimate of a spatial scale. One spatial scale proposed in the literature based on prey concentration is shown to be systematically inconsistent and its use is shown to imply that plankton sampling methodology can bias encounter rate estimates in turbulent situations. We show that a scale based on the predator's reactive distance is more appropriate, as it has clear theoretical support, and is consistent with other mathematical treatments of encounter problems. Applying the reactive distance as the length scale produces encounter rates for small (e.g. 4 to 10 mm) fish larvae 2- to 3-fold lower than those using prey separation distance. Turbulence · Plankton · Predation · Encounter rate · Turbulent velocity scale · Spatial scale Full text in pdf format PreviousExport citation RSS - Facebook - Tweet - linkedIn Cited by Published in MEPS Vol. 166. Publication date: May 28, 1998 Print ISSN:0171-8630; Online ISSN:1616-1599 Copyright © 1998 Inter-Research.

On convective turbulence and the influence of rotation

A series of experiments were performed in a rotating cylindrical tank over a wide range of rotation rates in which convective turbulence was generated by a bottom-mounted heated plate in both homogeneous and stratified fluids. Measurements were made of the turbulent velocities in all three axes over the full depth of the chamber, and of the temperatures at the mid-depth near the centre of the tank. For even small rotation rates, the measurements showed that the turbulent velocities were weakly affected by rotation at all depths, but as the rotation rate increased, the deviation from the non-rotational scaling slowly and progressively increased until eventually the turbulent velocities were fully rotationally controlled. The results indicated that there was no sudden transition of the turbulent field from the non-rotational state (a function only of the surface buoyancy flux B and the depth z ) to the rotational state (where the strength of the turbulent field is a function of only B and the Coriolis parameter f ). Rather the transition was a smooth asymptotic one from one state to the other. Nevertheless, it was possible to parametrize this transition by a single value of the turbulent or small scale Rossby number, defined by Ro = (B/f 3 z 2 ) 1 3 . Our measurements suggested a critical value of Ro c ≈ 0.1, below which the turbulence was fully rotationally controlled and which was equivalent to a critical depth z c = (35 ± 15)(B/f 3 ) 1 2 . Using typical oceanic values for B and f , the oceanic turbulence driven by surface cooling events becomes rotationally controlled only for depths greater than about 10 km, a depth which is greater than that of the bulk of the world's oceans. Thus, convective turbulence actively being generated by cooling of the ocean surface is best described by non-rotating turbulent velocity and length scales and is a function only of the surface buoyancy flux and the depth.

The Measurement of Turbulent Energy Budget of the Two-Dimensional Mixing Layer. 1st Report. Evaluation of the Dissipation Rate Assuming Local Isotropy.

Measurements of the turbulent velocity field have been performed in a newly designed low-speed two-dimensional mixing layer facility Mean and fluctuating velocity in the streamwise direction are measured by an I-type hot-wire anemometer, and the dissipation rate is evaluated from the time derivative of the fluctuating velocity signal based on the Taylor hypothesis and under the assumption of local isotropy of turbulence. The moments of velocity fluctuation up to the third order agree well with previous experiments and DNS, when normalized by the local turbulence velocity scale, the region of self-similarity in terms of the relative turbulence structure is found to be larger than the conventional definition of the global self similarity region where the turbulence velocity scale no longer varies in the streamwise direction. The dissipation rate can also be well correlated with the recent DNS result, when the Taylor micro length scale and local turbulence velocity scale are chosen as the characteristic length and velocity scales, respectively.

Unsteady, Turbulent Convection into a Rotating, Linearly Stratified Fluid: Modeling Deep Ocean Convection

Abstract A laboratory experiment has been constructed to Model the deep convective processes in a stratified ocean driven by the energetic cooling at the ocean surface. For convenience in the laboratory the authors have examined the analogous but inverted problem of the growth of a convective mixed layer generated by a localized source of bottom heating in a rotating, thermally stratified fluid. The heating is provided by a heat exchanger mounted beneath a central circular plate of a diameter smaller than that of the main cylindrical tank. Following the initiation of the heating, a cylinder of well-mixed fluid forms above the heated plate and as it grows upward it steadily erodes the overlying ambient stratification. Measurements of the root-mean-square velocities in the mixed layer indicate that rotation affects but does not control the turbulence, and the nonrotating turbulent velocity and length scales are thus appropriate to describe the small-scale turbulence. Rotation initially confines the heated f...

A theoretical investigation of boundary layer flow and bottom shear stress for smooth, transitional, and rough flow under waves

Velocity and shear stress distributions and the relationship between maximum near‐bottom orbital velocity uom and maximum shear velocity u*m in an oscillatory boundary layer are computed for hydraulically smooth, transitional, and rough turbulent flow using unsteady boundary layer theory and a single, continuous expression for eddy viscosity K. Velocity profiles over a half wave cycle calculated using a time‐independent form of K compare favorably with available measured profiles in smooth, transitional, and rough turbulent flows; computed shear stress profiles agree reasonably well with measured stress profiles. Use of a time‐dependent eddy viscosity generally improves the agreement between measured and computed velocity and shear stress near the bed but not in the outer boundary layer. Maximum computed bottom shear stress, however, does not differ significantly from values calculated with a time‐independent K owing to the choice of u*m as the turbulent velocity scale in K. The ratio of maximum orbital velocity to maximum shear velocity is computed as a function of two nondimensional parameters, a Reynolds number Re*=u*mδw/ν and an inverse Rossby number ξ0=ωz0/u*m; δW is wave boundary layer thickness, ω is wave frequency, ν is kinematic viscosity, and z0 is the bottom roughness parameter. These independent variables of the nondimensional unsteady boundary layer equation can be related to the more commonly used wave boundary layer parameters which are expressed in terms of orbital velocity instead of shear velocity. At the fully rough and fully smooth turbulent flow limits, u*m/uom is given by a single curve as a function of ξ0 or Re*, respectively. These curves compare favorably with available measurements and expressions for wave friction factor. The nondimensional equations also yield the dependence of u*m/uom on ξ0 and Re* for transitionally rough turbulent flow.

Modelling the Effect of Turbulence on the Collision of Cloud Droplets

From an analysis of scales in the cloud droplet collision problem, the authors infer that a trajectory model that is to be capable of predicting collisions between droplets of all possible sizes should be of second-order, that is should explicitly model particle acceleration. But for collisions between large droplets (radius about 50 µm or larger), which are still much smaller than raindroplets, a first-order model is appropriate. The relative motion of large droplets are studied with a first-order, two particle trajectory model. Turbulence is found to be unimportant (relative to differential gravitational settling) if the (large) droplet sizes are sufficiently distinct. Zeroth-order two-particle models, of the type hitherto applied to be problem, deteriorate in accuracy as the influence of turbulence on the droplet separation increases, that is, for large σv/v′, where σv is the turbulent velocity scale and v′ is the droplet still-air terminal velocity. Under no circumstance is a single-particle model applicable.

A comparison of boundary layer diffusion schemes in unstable conditions over land

We compare the results of a local and a nonlocal scheme for vertical diffusion in the atmospheric boundary layer with observations at the 200 m tower at Cabauw. This is done for a 12 h period during daytime on 31 May 1978, which is characterised by strong insolation, clear skies, moderately strong winds and weak advection. The local diffusion scheme uses an eddy diffusivity determined independently at each point along the vertical based on local vertical gradients of wind and virtual potential temperature, similar to the usual approach in atmospheric models. The nonlocal scheme determines an eddy diffusivity profile based on a diagnosed boundary-layer height and a turbulent velocity scale. It also incorporates nonlocal (vertical) transport effects for heat and moisture. The boundary-layer diffusion schemes are forced with the locally observed fluxes for heat and moisture. The outputs of the scheme are compared with the observed mean structure along the Cabauw tower, and the radiosonde profile at a nearby location (De Bilt). Overall, the nonlocal scheme transports moisture away from the surface more rapidly than the local scheme, and deposits the moisture at higher levels. The local scheme tends to saturate the lowest model levels unrealistically in comparison with the observations. We also compare the outputs of the two diffusion schemes with the results of a transilient model simulation. Subsequently, we study the impact on the model behaviour by varying important parameters in both diffusion schemes and we investigate the sensitivity to uncertainty in the environmental conditions. Finally, we study the interaction of the diffusion schemes with a simple surface flux scheme.