Some Additional Coherence Data in the Inertial Subrange

1987 ◽  
Vol 26 (12) ◽  
pp. 1770-1773 ◽  
Author(s):  
Ann-Sofi Smedman
Keyword(s):  
Inertial Subrange

Structure of Turbulent Velocity and Temperature Fluctuations in Fully Developed Pipe Flow

1979 ◽  
Vol 101 (1) ◽  
pp. 15-22 ◽  
Author(s):  
M. Hishida ◽  
Y. Nagano
Keyword(s):  
Pipe Flow ◽  
Dominant Role ◽  
Temperature Fluctuations ◽  
Temperature Fields ◽  
Inertial Subrange ◽  
Wall Region ◽  
Turbulent Heat ◽  
Temperature Spectrum ◽  
Axial Heat ◽  
Heat Transport Process

An experimental investigation of the turbulent structure of velocity and temperature fields has been made in fully developed pipe flow of air. In the near-wall region, the coherent quasi-ordered structure plays a dominant role in the turbulent heat transport process. The turbulent axial heat flux as well as the intensities of velocity and temperature fluctuations reach their maximums in this region, but these maximum points are different. The nondimensional intensities of velocity and temperature fluctuations are well described with the “logarithmic law” in the turbulent part of the wall region where the velocity-temperature cross-correlation coefficient is nearly constant. In the turbulent core, the velocity and temperature fluctuations are less correlated. The spectra of velocity and temperature fluctuations present −1 slope at low wavenumbers in the wall region and −5/3 slope in the inertial subrange. The temperature spectrum for the inertial-diffusive subrange indicates the −8/3 power-law.

Observations of Small-Scale Turbulence and Energy Dissipation Rates in the Cloudy Boundary Layer

2006 ◽  
Vol 63 (5) ◽  
pp. 1451-1466 ◽  
Author(s):  
Holger Siebert ◽  
Katrin Lehmann ◽  
Manfred Wendisch
Keyword(s):  
Boundary Layer ◽  
Energy Dissipation ◽  
Wind Velocity ◽  
Turbulence Theory ◽  
Horizontal Wind ◽  
Inertial Subrange ◽  
Intermittent Flow ◽  
Small Scale ◽  
Dissipation Rates ◽  
Wide Range

Abstract Tethered balloon–borne measurements with a resolution in the order of 10 cm in a cloudy boundary layer are presented. Two examples sampled under different conditions concerning the clouds' stage of life are discussed. The hypothesis tested here is that basic ideas of classical turbulence theory in boundary layer clouds are valid even to the decimeter scale. Power spectral densities S( f ) of air temperature, liquid water content, and wind velocity components show an inertial subrange behavior down to ≈20 cm. The mean energy dissipation rates are ∼10−3 m2 s−3 for both datasets. Estimated Taylor Reynolds numbers (Reλ) are ∼104, which indicates the turbulence is fully developed. The ratios between longitudinal and transversal S( f ) converge to a value close to 4/3, which is predicted by classical turbulence theory for local isotropic conditions. Probability density functions (PDFs) of wind velocity increments Δu are derived. The PDFs show significant deviations from a Gaussian distribution with longer tails typical for an intermittent flow. Local energy dissipation rates ɛτ are derived from subsequences with a duration of τ = 1 s. With a mean horizontal wind velocity of 8 m s−1, τ corresponds to a spatial scale of 8 m. The PDFs of ɛτ can be well approximated with a lognormal distribution that agrees with classical theory. Maximum values of ɛτ ≈ 10−1 m2 s−3 are found in the analyzed clouds. The consequences of this wide range of ɛτ values for particle–turbulence interaction are discussed.

Forced Turbulent Convection Along Heated and Cooled Walls with Variable Fluid Properties

2021 ◽  
Author(s):  
Lorenzo Sufrà ◽  
Helfried Steiner
Keyword(s):  
Isotropic Turbulence ◽  
Turbulence Models ◽  
Turbulent Pipe Flow ◽  
Wall Friction ◽  
Effect Of Temperature ◽  
Inertial Subrange ◽  
Property Variation ◽  
Fluid Properties ◽  
Applied Approach ◽  
Heat And Momentum Transfer

Abstract The effect of temperature depending material properties on heat and momentum transfer along heated/cooled walls in turbulent pipe flow was investigated using direct numerical simulations (DNS). For the considered thermal wall conditions, always associated with a molecular Prandtl number well over unity Prw = 10, the significantly dampened/enhanced turbulent motion caused by the increase/decrease of the viscosity with distance to the heated/cooled wall, turned out to clearly dominate over the opposite trend of the enthalpy fluctuations. The Nusselt number and, quantitatively less pronounced, the wall friction coefficient are accordingly decreased/increased for the heated/cooled case. A comparison against a well established Nu-correlation unveils the limits of the generally applied approach, which is essentially based on uniform bulk flow conditions and subsequently modified accounting for material property variation, when applied to heated and cooled conditions. An enhanced disparity of the turbulent normal stresses is observed inside the inertial subrange for the heated case, indicating a stronger deviation from isotropic turbulence, which possibly challenges mostly isotropic standard turbulence models.

An Ocean Refractometer: Resolving Millimeter-Scale Turbulent Density Fluctuations via the Refractive Index

2006 ◽  
Vol 23 (1) ◽  
pp. 121-137 ◽  
Author(s):  
Matthew H. Alford ◽  
David W. Gerdt ◽  
Charles M. Adkins
Keyword(s):  
Refractive Index ◽  
Density Fluctuations ◽  
Inertial Subrange ◽  
Conductivity Measurements ◽  
Velocity Fluctuations ◽  
Fiber Motion ◽  
Turbulent Spectrum ◽  
Ocean Measurements ◽  
Fiberoptic Sensor ◽  
Better Than

Abstract A fiberoptic sensor has been constructed to measure oceanic density fluctuations via their refractive index signature. The resolution (Δz = 1 mm, Δt = 0.2 ms) and precision (Δn < 10−8, Δρ = 3.4 × 10−5 kg m−3) of the device are far better than other methods and are sufficient to resolve the entire turbulent spectrum. Spectra show the salinity Batchelor rolloff at levels undetectable via conductivity measurements. However, the low-wavenumber portion of the spectrum occupied by the turbulent inertial subrange (≈1 m–1 cm scales) is marred by noise resulting from fiber motion in response to turbulent velocity fluctuations. The technique is described, and the first ocean measurements are reported.

Turbulence, diffusion and patchiness in the sea

1994 ◽  
Vol 343 (1303) ◽  
pp. 11-18 ◽  
Keyword(s):  
Large Scale ◽  
Approximate Model ◽  
Inertial Subrange ◽  
Biological Processes ◽  
Two Dimensional ◽  
Predator Prey ◽  
Interacting Populations ◽  
Terrestrial Environments ◽  
Population Interactions ◽  
Passive Tracers

We explore the role that biological processes play in the patchiness of plankton populations in the sea. We ask how population interactions modify the variance in plankton density as a function of spatial scale (i.e. the variance spectrum) from that expected if the biota were merely passive tracers. Using an approximate model for two limiting cases of turbulence - the inertial subrange and two-dimensional turbulence - we consider a simple predator - prey formulation for interacting populations in a turbulent ocean. No simple generalizations emerge. T he interacting populations ‘redden’ (i.e. more variance at large scale) the spectrum of the passive tracers in the inertial subrange. Conversely, the interaction ‘whitens’ (i.e. less variance at large scale) the passive tracer spectrum for two-dimensional turbulence. This mirrors results in terrestrial environments.

Microscale temperature and velocity spectra in the atmospheric boundary layer

1977 ◽  
Vol 83 (3) ◽  
pp. 547-567 ◽  
Author(s):  
R. M. Williams ◽  
C. A. Paulson
Keyword(s):  
Reynolds Number ◽  
Prandtl Number ◽  
Temperature Fluctuations ◽  
Inertial Subrange ◽  
Velocity Fluctuations ◽  
One Dimensional ◽  
Temperature Spectra ◽  
The Mean ◽  
Velocity Spectra ◽  
The One

High-frequency fluctuations in temperature and velocity were measured at a height of 2 m above a harvested, nearly level field of rye grass. Conditions were both stably and unstably stratified. Reynolds numbers ranged from 370000 to 740000. Measurements of velocity were made with a hot-wire anemometer and measurements of temperature with a platinum resistance element which had a diameter of 0[sdot ]5 μm and a length of 1 mm. Thirteen runs ranging in length from 78 to 238 s were analysed.Spectra of velocity fluctuations are consistent with previously reported universal forms. Spectra of temperature, however, exhibit an increase in slope with increasing wavenumber as the maximum in the one-dimensional dissipation spectrum is approached. The peak of the one-dimensional dissipation spectrum for temperature fluctuations occurs at a higher wavenumber than that of simultaneous spectra of the dissipation of velocity fluctuations. It is suggested that the change in slope of the temperature spectra and the dissimilarity between temperature and velocity spectra may be due to spatial dissimilarity in the dissipation of temperature and velocity fluctuations. The temperature spectra are compared with a theoretical prediction for fluids with large Prandtl number, due to Batchelor (1959). Even though air has a Prandtl number of 0[sdot ]7, the observations are in qualitative agreement with predictions of the theory. The non-dimensional wavenumber at which the increase in slope occurs is about 0[sdot ]02, in good agreement with observations in the ocean reported by Grantet al. (1968).For the two runs for which the stratification was stable, the normalized spectra of the temperature derivative fall on average slightly below the mean of the spectra of the remaining runs in the range in which the slope is approximately one-third. Hence the Reynolds number may not have always been sufficiently high to satisfy completely the conditions for an inertial subrange.Universal inertial-subrange constants were directly evaluated from one-dimensional dissipation spectra and found to be 0[sdot ]54 and 1[sdot ]00 for velocity and temperature, respectively. The constant for velocity is consistent with previously reported values, while the value for temperature differs from some of the previous direct estimates but is only 20% greater than the mean of the indirect estimates. This discrepancy may be explained by the neglect in the indirect estimates of the divergence terms in the conservation equation for the variance of temperature fluctuations. There is weak evidence that the one-dimensional constant, and hence the temperature spectra, may depend upon the turbulence Reynolds number, which varied from 1200 to 4300 in the observations reported.

scholarly journals Observation of turbulent dispersion of artificially released SO<sub>2</sub> puffs with UV cameras

2018 ◽  
Vol 11 (11) ◽  
pp. 6169-6188 ◽  
Author(s):  
Anna Solvejg Dinger ◽  
Kerstin Stebel ◽  
Massimo Cassiani ◽  
Hamidreza Ardeshiri ◽  
Cirilo Bernardo ◽  
...  
Keyword(s):  
Concentration Distribution ◽  
Concentration Field ◽  
Turbulent Dispersion ◽  
Relative Dispersion ◽  
Inertial Subrange ◽  
Centre Of Mass ◽  
Dispersion Parameters ◽  
Data Set ◽  
Atmospheric Flow ◽  
Depth Analysis

Abstract. In atmospheric tracer experiments, a substance is released into the turbulent atmospheric flow to study the dispersion parameters of the atmosphere. That can be done by observing the substance's concentration distribution downwind of the source. Past experiments have suffered from the fact that observations were only made at a few discrete locations and/or at low time resolution. The Comtessa project (Camera Observation and Modelling of 4-D Tracer Dispersion in the Atmosphere) is the first attempt at using ultraviolet (UV) camera observations to sample the three-dimensional (3-D) concentration distribution in the atmospheric boundary layer at high spatial and temporal resolution. For this, during a three-week campaign in Norway in July 2017, sulfur dioxide (SO2), a nearly passive tracer, was artificially released in continuous plumes and nearly instantaneous puffs from a 9 m high tower. Column-integrated SO2 concentrations were observed with six UV SO2 cameras with sampling rates of several hertz and a spatial resolution of a few centimetres. The atmospheric flow was characterised by eddy covariance measurements of heat and momentum fluxes at the release mast and two additional towers. By measuring simultaneously with six UV cameras positioned in a half circle around the release point, we could collect a data set of spatially and temporally resolved tracer column densities from six different directions, allowing a tomographic reconstruction of the 3-D concentration field. However, due to unfavourable cloudy conditions on all measurement days and their restrictive effect on the SO2 camera technique, the presented data set is limited to case studies. In this paper, we present a feasibility study demonstrating that the turbulent dispersion parameters can be retrieved from images of artificially released puffs, although the presented data set does not allow for an in-depth analysis of the obtained parameters. The 3-D trajectories of the centre of mass of the puffs were reconstructed enabling both a direct determination of the centre of mass meandering and a scaling of the image pixel dimension to the position of the puff. The latter made it possible to retrieve the temporal evolution of the puff spread projected to the image plane. The puff spread is a direct measure of the relative dispersion process. Combining meandering and relative dispersion, the absolute dispersion could be retrieved. The turbulent dispersion in the vertical is then used to estimate the effective source size, source timescale and the Lagrangian integral time. In principle, the Richardson–Obukhov constant of relative dispersion in the inertial subrange could be also obtained, but the observation time was not sufficiently long in comparison to the source timescale to allow an observation of this dispersion range. While the feasibility of the methodology to measure turbulent dispersion could be demonstrated, a larger data set with a larger number of cloud-free puff releases and longer observation times of each puff will be recorded in future studies to give a solid estimate for the turbulent dispersion under a variety of stability conditions.

scholarly journals An analytical theory of the buoyancy–Kolmogorov subrange transition in turbulent flows with stable stratification

2013 ◽  
Vol 371 (1982) ◽  
pp. 20120212 ◽  
Author(s):  
Semion Sukoriansky ◽  
Boris Galperin
Keyword(s):  
Spatial Scales ◽  
Stable Stratification ◽  
Temperature Fields ◽  
Inertial Subrange ◽  
Langevin Equations ◽  
Small Scale ◽  
Recursive Procedure ◽  
Theoretical Understanding ◽  
Scale Turbulence ◽  
Buoyancy Subrange

The buoyancy subrange of stably stratified turbulence is defined as an intermediate range of scales larger than those in the inertial subrange. This subrange encompasses the crossover from internal gravity waves (IGWs) to small-scale turbulence. The energy exchange between the waves and small-scale turbulence is communicated across this subrange. At the same time, it features progressive anisotropization of flow characteristics on increasing spatial scales. Despite many observational and computational studies of the buoyancy subrange, its theoretical understanding has been lagging. This article presents an investigation of the buoyancy subrange using the quasi-normal scale elimination (QNSE) theory of turbulence. This spectral theory uses a recursive procedure of small-scale modes elimination based upon a quasi-normal mapping of the velocity and temperature fields using the Langevin equations. In the limit of weak stable stratification, the theory becomes completely analytical and yields simple expressions for horizontal and vertical eddy viscosities and eddy diffusivities. In addition, the theory provides expressions for various one-dimensional spectra that quantify turbulence anisotropization. The theory reveals how the dispersion relation for IGWs is modified by turbulence, thus alleviating many unique waves' features. Predictions of the QNSE theory for the buoyancy subrange are shown to agree well with various data.

scholarly journals Stratified Inertial Subrange Inferred from In Situ Measurements in the Bottom Boundary Layer of the Rockall Channel

2010 ◽  
Vol 40 (11) ◽  
pp. 2401-2417 ◽  
Author(s):  
Pascale Bouruet-Aubertot ◽  
Hans van Haren ◽  
M. Pascale Lelong
Keyword(s):  
Boundary Layer ◽  
Energy Levels ◽  
Deep Ocean ◽  
Energy Dissipation Rate ◽  
Bottom Boundary Layer ◽  
Inertial Subrange ◽  
Buoyancy Frequency ◽  
Bottom Boundary ◽  
Wide Range ◽  
Taylor Hypothesis

Abstract Deep-ocean high-resolution moored temperature data are analyzed with a focus on superbuoyant frequencies. A local Taylor hypothesis based on the horizontal velocity averaged over 2 h is used to infer horizontal wavenumber spectra of temperature variance. The inertial subrange extends over fairly low horizontal wavenumbers, typically within 2 × 10−3 and 2 × 10−1 cycles per minute (cpm). It is therefore interpreted as a stratified inertial subrange for most of this wavenumber interval, whereas in some cases the convective inertial subrange is resolved as well. Kinetic energy dissipation rate ε is inferred using theoretical expressions for the stratified inertial subrange. A wide range of values within 10−9 and 4 × 10−7 m2 s−3 is obtained for time periods either dominated by semidiurnal tides or by significant subinertial variability. A scaling for ε that depends on the potential energy within the inertio-gravity waves (IGW) frequency band PEIGW and the buoyancy frequency N is proposed for these two cases. When semidiurnal tides dominate, ε ≃ (PEIGWN)3/2, whereas ε ≃ PEIGWN in the presence of significant subinertial variability. This result is obtained for energy levels ranging from 1 to 30 times the Garrett–Munk energy level and is in contrast with classical finescale parameterization in which ε ∼ (PEIGW)2 that applies far from energy sources. The specificities of the stratified bottom boundary layer, namely a weak stratification, may account for this difference.

Statistical features of heat transfer in grid-generated turbulence: constant-gradient case

1978 ◽  
Vol 86 (3) ◽  
pp. 513-543 ◽  
Author(s):  
K. S. Venkataramani ◽  
R. Chevray
Keyword(s):  
Heat Transfer ◽  
Temperature Profile ◽  
Vertical Component ◽  
Joint Probability ◽  
Inertial Subrange ◽  
Joint Moments ◽  
Integral Scale ◽  
Molecular Diffusivity ◽  
Mean Temperature ◽  
Normal Law

Turbulence produced by a grid which simultaneously imparts a mean temperature profile varying linearly with height was investigated in a specially constructed wind tunnel. While the mean temperature profile is preserved downstream of the grid in accordance with the theory of Corrsin (1952), the downstream evolution of the r.m.s. temperature fluctuation is at variance with his prediction. The reason for this discrepancy is shown to lie in the neglect of molecular diffusivity, which leads to unbounded growth of the fluctuations. Along with conventional correlations and spectra, the filtered heat-transfer correlation is presented. About 60% of the heat transport is accomplished by the low wavenumber components having length scales equal to or larger than the integral scale. An intriguing feature of the present experiments is the presence of an inertial-convective subrange for the temperature field notwithstanding the low Reynolds number and the consequent absence of an inertial subrange for the velocity field. Experimental results show that the temperature has a positive skewness everywhere in contrast to the velocity components, which are symmetrically distributed. Measurements of the joint probability density function of the vertical component of the velocity and the temperature indicate that, while the assumption of joint normality is not uniformly valid, the conditional expectations nearly follow the normal law. Marginal and joint moments of up to fourth order are presented. Odd-order joint moments are clearly sensitive to the skewness of the temperature.

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