One-dimensional Velocity Spectra Research Articles

Characteristics of mean flow and turbulence in bubble-in-chain induced flows

Mean flow and turbulence in bubble-in-chain induced flows are experimentally observed at various release frequencies and flow rates. We find that horizontal water velocity profiles collapse to a universal Gaussian distribution and one-dimensional velocity spectra to a consistent slope of \ensuremath{-}3.

The Effect of Aerosol Radiative Heating on Turbulence Statistics and Spectra in the Atmospheric Convective Boundary Layer: A Large-Eddy Simulation Study

Turbulence statistics and spectra in a radiatively heated convective boundary layer (CBL) under aerosol pollution conditions are less investigated than their counterparts in the clear CBL. In this study, a large-eddy simulation (LES) coupled with an aerosol radiative transfer model is employed to determine the impact of aerosol radiative heating on CBL turbulence statistics. One-dimensional velocity spectra and velocity–temperature cospectra are invoked to characterize the turbulence flow in the CBL with varying aerosol pollution conditions. The results show that aerosol heating makes the profiles of turbulent heat flux curvilinear, while the total (turbulent plus radiative) heat flux profile retains the linear relationship with height throughout the CBL. The horizontal and vertical velocity variances are reduced significantly throughout the radiatively heated CBL with increased aerosol optical depth (AOD). The potential temperature variance is also reduced, especially in the entrainment zone and near the surface. The velocity spectral density tends to be smaller overall, and the peak of the velocity spectra is shifted toward larger wavenumbers as AOD increases. This shift reveals that the energy-containing turbulent eddies become smaller, which is also supported by visual inspection of the vertical velocity pattern over horizontal planes. The modified CBL turbulence scales for velocity and temperature are found to be applicable for normalizing the corresponding profiles, indicating that a correction factor for aerosol radiative heating is needed for capturing the general features of the CBL structure in the presence of aerosol radiative heating.

Simplification and Validation of a Spectral-Tensor Model for Turbulence Including Atmospheric Stability

A spectral-tensor model of non-neutral, atmospheric-boundary-layer turbulence is evaluated using Eulerian statistics from single-point measurements of the wind speed and temperature at heights up to 100 m, assuming constant vertical gradients of mean wind speed and temperature. The model has been previously described in terms of the dissipation rate epsilon , the length scale of energy-containing eddies mathcal {L}, a turbulence anisotropy parameter varGamma , the Richardson number Ri, and the normalized rate of destruction of temperature variance eta _theta equiv epsilon _theta /epsilon . Here, the latter two parameters are collapsed into a single atmospheric stability parameter z / L using Monin–Obukhov similarity theory, where z is the height above the Earth’s surface, and L is the Obukhov length corresponding to {Ri,eta _theta }. Model outputs of the one-dimensional velocity spectra, as well as cospectra of the streamwise and/or vertical velocity components, and/or temperature, and cross-spectra for the spatial separation of all three velocity components and temperature, are compared with measurements. As a function of the four model parameters, spectra and cospectra are reproduced quite well, but horizontal temperature fluxes are slightly underestimated in stable conditions. In moderately unstable stratification, our model reproduces spectra only up to a scale sim 1 km. The model also overestimates coherences for vertical separations, but is less severe in unstable than in stable cases.

Comparison of Convective Boundary Layer Velocity Spectra Retrieved from Large- Eddy-Simulation and Weather Research and Forecasting Model Data

AbstractAs computing capabilities expand, operational and research environments are moving toward the use of finescale atmospheric numerical models. These models are attractive for users who seek an accurate description of small-scale turbulent motions. One such numerical tool is the Weather Research and Forecasting (WRF) model, which has been extensively used in synoptic-scale and mesoscale studies. As finer-resolution simulations become more desirable, it remains a question whether the model features originally designed for the simulation of larger-scale atmospheric flows will translate to adequate reproductions of small-scale motions. In this study, turbulent flow in the dry atmospheric convective boundary layer (CBL) is simulated using a conventional large-eddy-simulation (LES) code and the WRF model applied in an LES mode. The two simulation configurations use almost identical numerical grids and are initialized with the same idealized vertical profiles of wind velocity, temperature, and moisture. The respective CBL forcings are set equal and held constant. The effects of the CBL wind shear and of the varying grid spacings are investigated. Horizontal slices of velocity fields are analyzed to enable a comparison of CBL flow patterns obtained with each simulation method. Two-dimensional velocity spectra are used to characterize the planar turbulence structure. One-dimensional velocity spectra are also calculated. Results show that the WRF model tends to attribute slightly more energy to larger-scale flow structures as compared with the CBL structures reproduced by the conventional LES. Consequently, the WRF model reproduces relatively less spatial variability of the velocity fields. Spectra from the WRF model also feature narrower inertial spectral subranges and indicate enhanced damping of turbulence on small scales.

Influence of confinement on obstacle-free turbulent wakes

Large-eddy simulations (LESs) of obstacle-free wakes, in a channel like geometry with an homogeneous transverse direction, are carried out in order to investigate the influence of confinement on turbulent wakes. The numerical solver makes use of a multi-domain Fourier–Chebyshev spectral method and the LES capability is implemented through a spectral vanishing viscosity technique. A top hat like velocity profile is imposed at the inlet and both no slip and free slip conditions are considered at the confining walls. Prescribing the velocity ratio, defined as the ratio of the velocity gap to the mean velocity, we study the influence of confinement on such flows at the Reynolds number Re=5000. Several quantities are analyzed, as one-dimensional velocity spectra, third order-velocity structure function, turbulent kinetic energy and its dissipation rate. It turns out that for obstacle-free wakes confinement increases the intensity of turbulence and its three-dimensional feature, as e.g. pointed out by Lumley diagrams, in agreement with numerical and experimental results obtained for confined cylinder wake flows. Finally, comparing no slip simulation results with free slip ones, we also point out the role of boundary layers.

Large eddy simulations of confined turbulent wake flows

The influence of confinement on turbulent obstacle-free wake is numerically investigated by means of large eddy simulations (LES). The numerical solver makes use of a multi-domain Fourier-Chebyshev spectral method and the LES capability is implemented through a spectral vanishing viscosity technique. The geometry is channel like and the transverse direction is homogeneous. A top hat like velocity profile is assumed at the inlet and no slip conditions are considered at the confining walls. Prescribing the velocity ratio, defined as the ratio of the velocity gap to the mean velocity, we study the influence of confinement on such flows at the Reynolds number Re = 5000. Several quantities are analyzed, as one-dimensional velocity spectra, third-order structure function, turbulent kinetic energy and its dissipation rate. It turns out that for obstacle-free wakes confinement increases the intensity of turbulence and its three-dimensional feature.

Anisotropy of velocity spectra in quasistatic magnetohydrodynamic turbulence

We consider homogeneous magnetohydrodynamic turbulence subject to a uniform magnetic field B at low magnetic Reynolds number. The flow, which is computed with direct simulations, is statistically stationary. By examining one-dimensional velocity spectra, we show that the anisotropy induced by B is scale dependent; at small scales, the velocity component parallel to B is more attenuated than that perpendicular to B. Although in contrast with results in the literature based on three-dimensional spectra, the present conclusion is demonstrated to be consistent with the effective turbulent energy distribution in Fourier space and the definition of the one-dimensional spectrum. Further, it is found that the anisotropy is minimum in a range of length scales about the size of the Taylor microscale. It is argued that this range is the vestige of the inertial range, which is gradually destroyed as B increases.

The effect of cross flow on one-dimensional spectra measured using hot wires

Expressions were developed to estimate the cross-flow error that occurs in the one-dimensional velocity spectra determined by applying Taylor’s frozen field hypothesis to measurements with single- and cross-wire probes. The cross-flow error and the error caused by the unsteady convection of the small-scale motions were evaluated for typical measurements. It was found that the cross-flow error could be significant in inertial range of the measured one-dimensional spectra, and was much larger than the error caused by the unsteady convection of the small-scale motions in the one-dimensional spectra of the cross-stream velocity components, \( F^{2}_{{22}} {\left( {k_{1} } \right)} \) and \( F^{1}_{{33}} {\left( {k_{1} } \right)} \). The results indicate that the one-dimensional spectra of the streamwise velocity component \( F^{1}_{{11}} {\left( {k_{1} } \right)} \) measured with a single-wire probe should be significantly more accurate than the spectra measured with a cross-wire probe. The cross-flow error in the one-dimensional spectra also becomes much less important in the dissipation range of the measured spectra.

Investigation of Clear Air Convective Structures in the PBL Using a Dual Doppler Radar and a Doppler Sodar

Abstract In August 1979, the Dual Doppler Radar (Ronsard System) and the Doppler Sodar system of CNET were simultaneously used during an experiment on clear air convection. It provided the opportunity to develop a method for the spatial study of atmospheric structures in the PBL: the mean characteristics of the flow structures at scales larger than one kilometer (wind velocity and variance profiles, one-dimensional velocity spectra) are studied. Spatial properties of the atmosphere are then investigated, showing a heterogeneity of the horizontal wind field inside the observed area. Finally, a predominant alignment of the convective cells along the same direction is found in every case.

Measurement of fluid turbulence based on pulsed ultrasound techniques. Part 1. Analysis

The pulsed ultrasonic Doppler velocimeter has been used extensively in transcutaneous measurement of the velocity of blood in the human body. It would be useful to evaluate turbulent flow with this device in both medical and non-medical applications. However, the complex behaviour and limitations of the pulsed Doppler velocimeter when applied to random flow have not yet been fully investigated.In this study a three-dimensional stochastic model of the pulsed ultrasonic Doppler velocimeter for the case of a highly focused and damped transducer and isotropic turbulence is presented. The analysis predicts the correlation and spectral functions of the Doppler signal and the detected velocity signal. The analysis addresses specifically the considerations and limitations of measuring turbulent intensities and one-dimensional velocity spectra.Results show that the turbulent intensity can be deduced from the broadening of the spectrum of the Doppler signal and a mathematical description of the effective sample-volume directivity.In the measurement of one-dimensional velocity spectra at least two major complicacations are identified and quantified. First, the presence of a time-varying, broad-band random process (the Doppler ambiguity process) obscures the spectrum of the random velocity. This phenomenon is similar to that occurring in laser anemometry, but the ratio of the level of the ambiguity spectrum to the largest detected velocity spectral component can be typically two to three orders of magnitude greater for ultrasonic technique owing to the much greater wavelength.Secondly, the spatial averaging of the velocity field in the sample volume causes attenuation in the measured velocity spectrum. For the ultrasonic velocimeter, this effect is very significant.The influence of the Doppler ambiguity process can be reduced by the use of two sample volumes on the same acoustic beam. The signals from the two sample volumes are cross-correlated, removing the Doppler ambiguity process, while retaining the random velocity. The effects of this technique on the detected velocity spectrum are quantified explicitly in the analysis for the case of a three-dimensional Gaussianshaped sample-volume directivity.

Measurement of fluid turbulence based on pulsed ultrasound techniques. Part 2. Experimental investigation

An extensive experimental programme in both laminar and turbulent flow was undertaken to examine the validity of all of the major implications of the model of the pulsed ultrasonic Doppler velocimeter for turbulent flow developed in part 1 of this investigation. The turbulence measurements were made in fully developed flow at the centre of a 6·28 cm diameter pipe. The Reynolds number of the flow ranged from 6000 to 40000. The carrier frequency of the ultrasonic velocimeter was 4·7 MHz.Measurements of the turbulence intensity and of the one-dimensional velocity spectra made with the ultrasonic velocimeter are compared with the analysis and with the actual quantities as measured by a hot-film anemometer. The experimental results are in agreement with theoretical predictions.Measurements of one-dimensional turbulence spectra with reduced ambiguity spectra made by the two sample volume methods described in part 1 are presented. The results verify the analysis and indicate that an improvement in the useful dynamic range of the velocity power spectrum of nearly three orders of magnitude can realistically be achieved.

The scaling of velocity fluctuations in the surface mixed layer

Turbulent velocity fluctuations in the upper portions of the wind-driven mixed layer of oceans or lakes appear to have a velocity scale proportional to the friction velocity and a length scale proportional to the distance below the free surface, as is usual in shear flows near a boundary. A number of one-dimensional velocity spectra have been measured in aquatic mixed layers, and these spectra, when they are scaled with the surface stress and the distance from the free surface, have been compared with turbulent boundary layer measurements. The good agreement suggests that the surface wave orbital velocities act merely as ‘inactive’ motions and do not interfere with the lower-frequency stress-carrying eddies.