Velocity Power Spectra Research Articles

LES grid resolution requirements for the modelling of gravity currents

The influence of the grid resolution on the large eddy simulation (LES) of a lock-exchange turbidity current is investigated. The simulations are performed using a finite volume Boussinesq code with a Smagorinsky turbulence model for a range of buoyancy Reynolds numbers, ranging from transitional currents (Reb=1,000) to fully-developed turbulence (Reb=60,000). The general features of the flow and the relative independence of the current front for Reb>10,000 are correctly predicted. In agreement with previous research, the spanwise two-point correlations are found to be the most useful quantities to assess the mesh resolution. In addition, velocity power spectrum densities are used to provide information on the maximum cell size required to ensure the LES filter cutoff wavelength is inside the inertial range of the turbulence spectra. We show that at low Reynolds numbers, the turbulence model is too restrictive and direct resolution (DNS) is preferable. For 10,000<Reb<60,000, the combination of the different criteria lead to a minimum resolution of 1140 × 37 × 74 cells for coarse LES, and 1925 × 62 × 125 cells for well-resolved LES, regardless of the Reynolds number. Finally, recommendations are made on how to achieve a well-resolved LES based on examination of the vertical profiles of the ratio of SGS viscosity to molecular viscosity, and of the SGS shear-stress to the resolved Reynolds stress.

N-oxide Derivatives: Car-Parrinello Molecular Dynamics and Electron Localization Function Study on Intramolecular Hydrogen Bonds.

First-principle molecular dynamics simulations (CPMD) and electron localization function (ELF) topological analysis were performed for two N-oxides, 2-[( N, N-dimethylamino- N-oxy)methyl]-4,6-dimethylphenol (I) and 5,5'-dibromo-3-[(diethylamino)methyl]-2,2'-biphenol N-oxide (II). Special attention was paid to hydrogen bond dynamics and spectroscopic features. Simulations were carried out in vacuo and in the crystalline phase. It was found that for compound I proton transfer phenomena do not occur spontaneously. An opposite situation was noticed for one of the two intramolecular hydrogen bonds of compound II. The influence of the neighboring molecules (including microsolvation) and the crystal field on the hydrogen bond properties cannot be neglected. Hydrogen bond spectroscopic signatures were quite well reproduced by power spectra of atomic velocity. Metric and spectroscopic theoretical findings were compared with experimental data available, especially in a view of the fact that experimental X-ray diffraction and FT-IR data of compound II indicate strong delocalization of the N-oxide bridge proton. ELF analysis showed that for compound II the N-oxide bridge belongs to the topological category of strong hydrogen bonds with the separate ELF basin for the bridged hydrogen atom.

On the forward modeling of radar Doppler spectrum width from LES: Implications for model evaluation.

Large-eddy simulations of an observed single-layer Arctic mixed-phase cloud are analyzed to study the value of forward modeling of profiling millimeter-wave cloud radar Doppler spectral width for model evaluation. Individual broadening terms and their uncertainties are quantified for the observed spectral width and compared to modeled broadening terms. Modeled turbulent broadening is narrower than the observed values when the turbulent kinetic energy dissipation rate from the subgrid-scale model is used in the forward model. The total dissipation rates, estimated with the subgrid-scale dissipation rates and the numerical dissipation rates, agree much better with both the retrieved dissipation rates and those inferred from the power spectra of the simulated vertical air velocity. The comparison of the microphysical broadening provides another evaluative measure of the ice properties in the simulation. To accurately retrieve dissipation rates as well as each broadening term from the observations, we suggest a few modifications to previously presented techniques. First, we show that the inertial subrange spectra filtered with the radar sampling volume is a better underlying model than the unfiltered -5/3 law for the retrieval of the dissipation rate from the power spectra of the mean Doppler velocity. Second, we demonstrate that it is important to filter out turbulence and remove the layer-mean reflectivity-weighted mean fall speed from the observed mean Doppler velocity to avoid overestimation of shear broadening. Finally, we provide a method to quantify the uncertainty in the retrieved dissipation rates, which eventually propagates to the uncertainty in the microphysical broadening.

Experimental investigation of the aeroacoustics of synthetic jet actuators in quiescent conditions

In this paper, the aeroacoustic characteristics of a circular orifice, synthetic jet actuator in quiescent conditions is investigated. Electromagnetic actuation, in the form of a shaker-driven actuator with latex diaphragm, proved to be desirable over piezoelectric actuation for this work due to the reduced diaphragm noise contribution to overall actuator self-noise, hence making it easier to identify jet-related noise. Acoustic and velocity data, collected from microphone measurements in an anechoic chamber and hotwire measurements respectively, were compared for correlation. Schlieren visualization was also used to show synthetic jet development near the orifice. Flow-induced sound in the form of an audible whistling was found to occur for a Strouhal number range of 0.24<St<0.50. A threshold in the jet Reynolds number of 600 < Rej<750 was established for the onset of whistling from the actuator for all drive voltages. Coherence between the acoustic spectra and velocity power spectra is shown, with evidence of a feedback mechanism consisting of vortices shed at a frequency that coincides with acoustic modes of the actuator.

Interaction between the atmospheric boundary layer and a stand-alone wind turbine in Gansu—Part II: Numerical analysis

To analyze the interaction between wind turbines and the atmospheric boundary layer, we integrated a large-eddy simulation with an actuator line model and examined the characteristics of wind-turbine loads and wakes with reference to a corresponding experiment in Gansu. In the simulation, we set the wind turbine to have a rotor diameter of 14.8 m and a tower height of 15.4 m in the center of an atmospheric boundary layer with a 10.6A degrees yaw angle. The results reveal an obviously skewed wake structure behind the rotor due to the thrust component normal to the flow direction. The power spectra of the inflow fluctuation velocity exhibit a region of -5/3 slope, which confirms the ability of large-eddy simulations to reproduce the energy cascade from larger to smaller scales. We found there to be more energy in the power spectrum of the axial velocity, which shows that coherent turbulence structures have more energy in the horizontal direction. By the conjoint analysis of atmospheric turbulence and windturbine loads, we found that when the inflow wind direction changes rapidly, the turbulence kinetic energy and coherent turbulence kinetic energy in the atmospheric turbulence increase, which in turn causes fluctuations in the wind turbine load. Furthermore, anisotropic atmospheric turbulence causes an asymmetric load cycle, which imposes a strike by the turbine blade on the shaft, thereby increasing the fatigue load on the shaft. Our main conclusion is that the atmospheric boundary layer has a strong effect on the evolution of the wake and the structural response of the turbine.

Experimental Investigation of Three‐Dimensional Flow Structure and Turbulent Flow Mechanisms Around a Nonsubmerged Spur Dike With a Low Length‐to‐Depth Ratio

AbstractFlume experiments were conducted to investigate the three‐dimensional flow structure and turbulent flow mechanisms around a nonsubmerged, sidewall‐attached rectangular spur dike with a low length‐to‐depth ratio. Velocity measurements show that the wake of the spur dike in the middepth region consists of a single, large recirculation zone, while that in the near‐bed region is composed of a horizontal recirculation zone and a corner vortex with its axis perpendicular to the flume sidewalls. A horseshoe vortex system observed in front of the spur dike is found to interact with the downstream recirculation zone, which results in the increase in lateral turbulent mixing especially in near‐bed regions. Another vortex, which rotates in the opposite direction to the horseshoe vortex, is found beneath the free surface in front of the spur dike, which is associated with increased free surface elevation and its fluctuation. Power spectra of the transverse velocity show evidence of a periodic behavior of the near‐wake shear layer emanating from the tip of the spur dike with a Strouhal number of about 2. It is also shown that the two experiments conducted at different Reynolds and Froude numbers show very similar flow fields in spite of large differences in free surface elevations, which indicates that the effects of free surface deformation on mean velocities and Reynolds stresses are marginal.

Wind characteristics in wind farms situated on a hilly terrain

Wind characteristics in wind farms situated on a hilly terrain are considerably different than on a flat terrain. This issue is particularly important in strong-wind situations, when the wind velocity exceeds 25 m/s. In those situations, wind turbines are designed to remain in the parking position (no rotation of rotor blades) to prevent damage or even collapse of wind turbines. The present wind-tunnel study thus focuses on flow and turbulence characteristics in wind farms situated on a hilly terrain subjected to strong winds. A particular emphasis is on wind conditions for wind turbines placed at various positions in wind farms, as well as on a distance between a hill and a wind farm. The hill model is observed to strongly influence flow and turbulence characteristics at the wind-turbine model position in the wind-farm model. The most prominent aerodynamic features are flow retardation and turbulence enhancement, whereas the velocity power spectra show different trends along the height of the wind-turbine tower model. These experimental results present an important input for engineers attempting to design more robust and reliable wind turbines for hilly terrains.

The VIMOS Public Extragalactic Redshift Survey (VIPERS)

We used the VIMOS Public Extragalactic Redshift Survey (VIPERS) final data release (PDR-2) to investigate the performance of colour-selected populations of galaxies as tracers of linear large-scale motions. We empirically selected volume-limited samples of blue and red galaxies as to minimise the systematic error on the estimate of the growth rate of structure fσ8 from the anisotropy of the two-point correlation function. To this end, rather than rigidly splitting the sample into two colour classes we defined the red or blue fractional contribution of each object through a weight based on the (U − V) colour distribution. Using mock surveys that are designed to reproduce the observed properties of VIPERS galaxies, we find the systematic error in recovering the fiducial value of fσ8 to be minimised when using a volume-limited sample of luminous blue galaxies. We modelled non-linear corrections via the Scoccimarro extension of the Kaiser model (with updated fitting formulae for the velocity power spectra), finding systematic errors on fσ8 of below 1–2%, using scales as small as 5 h−1 Mpc. We interpret this result as indicating that selection of luminous blue galaxies maximises the fraction that are central objects in their dark matter haloes; this in turn minimises the contribution to the measured ξ(rp,π) from the 1-halo term, which is dominated by non-linear motions. The gain is inferior if one uses the full magnitude-limited sample of blue objects, consistent with the presence of a significant fraction of blue, fainter satellites dominated by non-streaming, orbital velocities. We measured a value of f σ8 = 0.45 ± 0.11 over the single redshift range 0.6 ≤ z ≤ 1.0, corresponding to an effective redshift for the blue galaxies 〈z〉=0.85. Including in the likelihood the potential extra information contained in the blue-red galaxy cross-correlation function does not lead to an appreciable improvement in the error bars, while it increases the systematic error.

Large eddy simulations of the all-speed turbulent jet flow using 3-D CFD code GASFLOW-MPI

Turbulent flow at a wide range of Mach numbers may occur during design based accidents (DBA) or severe accidents in nuclear power plants (NPPs), for instinct, incompressible gas mixing flow (subsonic), gas mixture critical flow (transonic) or detonation (supersonic). All of them need to be simulated in safety analysis of NPP containments, therefore we need the computer code to have the capability to simulate all-speed flow. GASFLOW-MPI is a well-developed parallel all-speed CFD software used to predict gas turbulent mixing, chemical combustion and other related thermal-hydraulic phenomena in containments of NPPs. In order to validate the all-speed turbulent flow capability of GASFLOW-MPI, four turbulent jet cases over a broad range of Mach number have been performed in this paper. The large eddy simulation (LES) turbulent model is employed to capture more details of turbulence and flow features in this study. The standard Smagorinsky sub-grid scale model is utilized to model the unresolved turbulent behaviors at sub-grid scale. Both the instantaneous and time-averaged flow fields are analyzed as well as turbulent statistics to compare with the experimental data sets. The simulation results are in good agreement with the experimental data sets available in the literature. The shear layer instability is observed in the instantaneous flow field which leads to the end of the potential core and then the centerline velocity begins to decay. The size of the potential core and the decay rate of the centerline velocity are consistent well with the experiments. The turbulence intensity in the fully developed region agree well with the experimental data and the velocity power spectrum reveals the -5/3 law. Simulation results show that the compressibility has a significant effect on a free shear layer growing rate which is consistent with the experiments. The complex shock wave structure is also captured exactly by the second-order total variation diminishing (TVD) scheme. GASFLOW-MPI code has been successfully validated using the experimental data of turbulent jet flow at the wide regime of Mach numbers.

LES mesh resolution requirements for particledriven gravity currents

In this study we investigate the influence of grid resolution on a near-wall resolved LES model of a lock-exchange particle-driven gravity current. The simulations are performed using the finite volume Boussinesq code SnS with a Smagorinsky turbulence model for a buoyant Reynolds number of 60,000 on 4 grid sizes. According to previous studies, two-point correlations are most appropriate to estimate LES resolution. With the largest scales of the flow being resolved by more than 20 cells, well-resolved LES is obtained for grid resolutions of 1925×62×125 and finer. In addition, in order to apply the turbulence model correctly, we show that the velocity power spectrum densities provide useful information for the maximum cell size. The ratio of the subgrid scale viscosity to the molecular viscosity and the subgrid scale shear-stress to the resolved Reynolds stress show good convergence with grid refinement. The ratios vSGS / &lt;0.3 above the current and τSGS (u'v')ave &lt; 0.05 inside the mixing layer, are chosen as threshold values, based on our evaluation study.

Modified singular spectrum analysis for despiking acoustic Doppler velocimeter (ADV) data

Spectral investigation of spike contaminated velocity time series recorded by acoustic Doppler velocimeter (ADV) remains a challenging task. In this paper, we propose a singular spectrum analysis (SSA) method with novel grouping criteria to remove spikes from highly contaminated velocity time series. The proposed technique is tested on the highly contaminated experimentally observed velocity time series data in the vegetated sand bed channel. The performance of this method is assessed by the power spectral density of clean ADV time series data. Special importance is placed to produce the accurate power spectral density in streams with high energy fluctuation. The trends show that the reconstructed velocity time series is free from spikes and noise components. Furthermore, the velocity power spectra of the filtered AVD time series data satisfy the Kolmogorov −5/3 law in inertial sub range.

Shape of the acoustic gravitational wave power spectrum from a first order phase transition

We present results from large-scale numerical simulations of a first order thermal phase transition in the early Universe, in order to explore the shape of the acoustic gravitational wave and the velocity power spectra. We compare the results with the predictions of the recently proposed sound shell model. For the gravitational wave power spectrum, we find that the predicted k−3 behavior, where k is the wave number, emerges clearly for detonations. The power spectra from deflagrations show similar features, but exhibit a steeper high-k decay and an extra feature not accounted for in the model. There are two independent length scales: the mean bubble separation and the thickness of the sound shell around the expanding bubble of the low temperature phase. It is the sound shell thickness which sets the position of the peak of the power spectrum. The low wave number behavior of the velocity power spectrum is consistent with a causal k3, except for the thinnest sound shell, where it is steeper. We present parameters for a simple broken power law fit to the gravitational wave power spectrum for wall speeds well away from the speed of sound where this form can be usefully applied. We examine the prospects for the detection, showing that a LISA-like mission has the sensitivity to detect a gravitational wave signal from sound waves with an RMS fluid velocity of about 0.05c, produced from bubbles with a mean separation of about 10−2 of the Hubble radius. The shape of the gravitational wave power spectrum depends on the bubble wall speed, and it may be possible to estimate the wall speed, and constrain other phase transition parameters, with an accurate measurement of a stochastic gravitational wave background.

The effect of thermal velocities on structure formation in N-body simulations of warm dark matter

We investigate the impact of thermal velocities in N-body simulations of structure formation in warm dark matter models. Adopting the commonly used approach of adding thermal velocities, randomly selected from a Fermi-Dirac distribution, to the gravitationally-induced velocities of the simulation particles, we compare the matter and velocity power spectra measured from CDM and WDM simulations, in the latter case with and without thermal velocities. This prescription for adding thermal velocities introduces numerical noise into the initial conditions, which influences structure formation. At early times, the noise affects dramatically the power spectra measured from simulations with thermal velocities, with deviations of the order of ∼ \U0001d4aa(10) (in the matter power spectra) and of the order of ∼ \U0001d4aa(102) (in the velocity power spectra) compared to those extracted from simulations without thermal velocities. At late times, these effects are less pronounced with deviations of less than a few percent. Increasing the resolution of the N-body simulation shifts these discrepancies to higher wavenumbers. We also find that spurious haloes start to appear in simulations which include thermal velocities at a mass that is ∼3 times larger than in simulations without thermal velocities.

Beyond the growth rate of cosmic structure: Testing modified gravity models with an extra degree of freedom

In ``modified'' gravity the observed acceleration of the universe is explained by changing the gravitational force law or the number of degrees of freedom in the gravitational sector. Both possibilities can be tested by measurements of cosmological structure formation. In this paper we elaborate the details of such tests using the Galileon model as a case study. We pay attention to the possibility that each new degree of freedom may have stochastically independent initial conditions, generating different types of potential well in the early universe and breaking complete correlation between density and velocity power spectra. This ``stochastic bias'' can confuse schemes to parametrize the predictions of modified gravity models, such as the use of the growth parameter $f$ alone. Using data from the WiggleZ Dark Energy Survey we show that it will be possible to obtain constraints using information about the cosmological-scale force law embedded in the multipole power spectra of redshift-space distortions. As an example, we obtain an upper limit on the strength of the conformal coupling to matter in the cubic Galileon model, giving $|1/M|\ensuremath{\lesssim}200/{M}_{\mathrm{P}}$. This allows the fifth-force to be stronger than gravity, but is consistent with zero coupling.

Galaxy formation with BECDM - I. Turbulence and relaxation of idealized haloes.

We present a theoretical analysis of some unexplored aspects of relaxed Bose-Einstein condensate dark matter (BECDM) haloes. This type of ultralight bosonic scalar field dark matter is a viable alternative to the standard cold dark matter (CDM) paradigm, as it makes the same large-scale predictions as CDM and potentially overcomes CDM's small-scale problems via a galaxy-scale de Broglie wavelength. We simulate BECDM halo formation through mergers, evolved under the Schrödinger-Poisson equations. The formed haloes consist of a soliton core supported against gravitational collapse by the quantum pressure tensor and an asymptotic r-3 NFW-like profile. We find a fundamental relation of the core-to-halo mass with the dimensionless invariant Ξ ≡ |E|/M3/(Gm/ħ)2 or Mc/M ≃ 2.6Ξ1/3, linking the soliton to global halo properties. For r ≥ 3.5 rc core radii, we find equipartition between potential, classical kinetic and quantum gradient energies. The haloes also exhibit a conspicuous turbulent behaviour driven by the continuous reconnection of vortex lines due to wave interference. We analyse the turbulence 1D velocity power spectrum and find a k-1.1 power law. This suggests that the vorticity in BECDM haloes is homogeneous, similar to thermally-driven counterflow BEC systems from condensed matter physics, in contrast to a k-5/3 Kolmogorov power law seen in mechanically-driven quantum systems. The mode where the power spectrum peaks is approximately the soliton width, implying that the soliton-sized granules carry most of the turbulent energy in BECDM haloes.

2MTF – VI. Measuring the velocity power spectrum

We present measurements of the velocity power spectrum and constraints on the growth rate of structure $f\sigma_{8}$, at redshift zero, using the peculiar motions of 2,062 galaxies in the completed 2MASS Tully-Fisher survey (2MTF). To accomplish this we introduce a model for fitting the velocity power spectrum including the effects of non-linear Redshift Space Distortions (RSD), allowing us to recover unbiased fits down to scales $k=0.2\,h\,{\rm Mpc}^{-1}$ without the need to smooth or grid the data. Our fitting methods are validated using a set of simulated 2MTF surveys. Using these simulations we also identify that the Gaussian distributed estimator for peculiar velocities of \cite{Watkins2015} is suitable for measuring the velocity power spectrum, but sub-optimal for the 2MTF data compared to using magnitude fluctuations $\delta m$, and that, whilst our fits are robust to a change in fiducial cosmology, future peculiar velocity surveys with more constraining power may have to marginalise over this. We obtain \textit{scale-dependent} constraints on the growth rate of structure in two bins, finding $f\sigma_{8} = [0.55^{+0.16}_{-0.13},0.40^{+0.16}_{-0.17}]$ in the ranges $k = [0.007-0.055, 0.55-0.150]\,h\,{\rm Mpc}^{-1}$. We also find consistent results using four bins. Assuming scale-\textit{independence} we find a value $f\sigma_{8} = 0.51^{+0.09}_{-0.08}$, a $\sim16\%$ measurement of the growth rate. Performing a consistency check of General Relativity (GR) and combining our results with CMB data only we find $\gamma = 0.45^{+0.10}_{-0.11}$, a remarkable constraint considering the small number of galaxies. All of our results are completely independent of the effects of galaxy bias, and fully consistent with the predictions of GR (scale-independent $f\sigma_{8}$ and $\gamma\approx0.55$).

Very large scale motions and PM10 concentration in a high-Re boundary layer

In this letter, the concentration of particles with size less than 10 μm (PM10) and flow velocities are measured synchronously at different heights in a sand storm, a high-Reynolds number multi-phase turbulent boundary layer. It is revealed that the low-speed very large scale motions (VLSMs) are recurrent with a frequency dominating the streamwise velocity power spectra and modulate the streamwise distribution of PM10 concentration. In the logarithmic layer, the low-speed VLSMs correspond to weak shear stress on the bottom surface and hence decrease the PM10 upward flux. In the higher region, the high-speed VLSMs enhance both the streamwise and the upward transportation of PM10 because of the positive correlation between the velocity and the particle concentration perturbations.

Brownian motion as a new probe of wettability.

Understanding wettability is crucial for optimizing oil recovery, semiconductor manufacturing, pharmaceutical industry, and electrowetting. In this letter, we study the effects of wettability on Brownian motion. We consider the cases of a sphere in an unbounded fluid medium, as well as a sphere placed in the vicinity of a plane wall. For the first case, we show the effects of wettability on the statistical properties of the particles' motion, such as velocity autocorrelation, velocity, and thermal force power spectra over a large range of time scales. We also propose a new method to measure wettability based on the particles' Brownian motion. In addition, we compare the boundary effects on Brownian motion imposed by both no-slip and perfect-slip flat walls. We emphasize the surprising boundary effects on Brownian motion imposed by a perfect-slip wall in the parallel direction, such as a higher particle mobility parallel to a perfect flat wall compared to that in the absence of the wall, as well as compared to a particle near a no-slip flat wall.

Normalized dissipation rate in a moderate Taylor Reynolds number flow

Time-resolved velocity measurements are obtained using a hot-wire in a nearly homogeneous and isotropic flow downstream of an active grid for a range of Taylor Reynolds numbers from$191$to$659$. It is found that the dimensionless dissipation rate,$C_{\unicode[STIX]{x1D716}}$, is nearly a constant for sufficiently high values of Taylor Reynolds number,$R_{\unicode[STIX]{x1D706},u_{q}}$, and is approximately equal to$0.87$. This value is approximately$5\,\%$less than the value reported by Boset al.(Phys. Fluids, vol. 19 (4), 2007, 045101), which is obtained using DNS/LES (direct numerical simulation combined with large eddy simulation) for decaying homogeneous and isotropic turbulence, and is in excellent agreement with the active grid experiment of Thormann &amp; Meneveau (Phys. Fluids, vol. 26 (2), 2014, 025112.). The results presented herein show that deviation from isotropy may cause inconsistencies in the computation of$C_{\unicode[STIX]{x1D716}}$. As a result, it is suggested that the velocity scale be the square root of the turbulence kinetic energy. The integral length scale measurements obtained from the longitudinal velocity correlation are in close agreement with the integral length scale measured from the peak of the energy spectrum,$\unicode[STIX]{x1D705}E_{11}(\unicode[STIX]{x1D705})$, where$\unicode[STIX]{x1D705}$is the wavenumber and$E_{11}(\unicode[STIX]{x1D705})$is the one-dimensional power spectrum of the downstream velocity.

Another look on the structure of mountain waves: A spectral perspective

Linear wave solutions in the spectral space are analyzed to help understand the structure of mountain waves. Nonrotating and hydrostatic waves generated in wind with directional shear past a circular bell-shaped mountain are studied. The power spectra of perturbed vertical velocity and pressure are symmetrically distributed about the orientation of dominant wave component, which bisects the angle between surface wind and local wind directions. The maximum power spectrum increases with the horizontal wind speed but decreases with the wind turning angle. The power spectra of potential temperature and horizontal velocity exhibit an asymmetric distribution except at the surface, which are infinite for the wave components normal to the mean wind. These large-amplitude perturbations of potential temperature and horizontal velocity are advected downstream and the waves finally break, giving rise to the occurrence of turbulent wakes at various heights. All the wavefields rotate with height in the same direction of the mean wind. However, the perturbed vertical velocity and pressure turn at a rate slower than that of horizontal velocity and potential temperature. The application of spectral analysis to the wave momentum flux is discussed, which helps explain the misalignment of wave momentum flux with the surface wind.