Sub-canyon Scale Motions in Urban Turbulence: Influence of Flow Configurations

Using direct numerical simulation and ‘kinematic simulation’ (henceforth KS) of velocity fields, measurement, flow visualisation and novel kinematic analysis, the following aspects of small scale motions in turbulence were investigated: (i) Random advection and distortion of small scale motions by larger scale motions; (ii) the Lagrangian spectrum at high frequency of particles moving in small scale eddies and the effects of the time dependence of the eddies; (iii) the relative velocities Δu and the separation distance l between pairs of particles, to find the decorrelation time scales of Δu and the relation between the mean square separation \({\bar l^2}\) and the conditional displacements of single particles; (iv) how the forms of these motions can be inferred from the asymptotic forms of Fourier series and spectra; (v) the specific implications for Eulerian and Lagrangian spectra of the small scales being mostly associated with elongated regions of spiralling motions in which there are different orders of discontinuous derivatives of velocity normal to streamline surfaces. These studies suggest that small scale motion in isotropic turbulence has a characteristic spiralling structure, which is generally consistent with statistics, such as fractals, spectra and probability distributions.

<p>Burgers and Onsager were pioneers in using statistical mechanics in the theory of turbulent fluid motion. Their approach was, however, rather different. Whereas Onsager stayed close to the energy conserving Hamiltonian systems of classical mechanics, Burgers explicitly exploited the fact that turbulent motion is forced and dissipative. The basic assumption of Burgers' approach is that forcing and dissipation balance on average, an assumption that leads to interesting conclusions concerning the statistics of turbulent flow but also to a few problems. A compilation and assessment of his work can be found in [1].</p><p>We have taken up the thread of Burgers' approach and rephrased it in terms of Jaynes' principle of maximum entropy. The principle of maximum entropy yields a  statistical description in terms of a probability density function that is as noncommittal as possible while reproducing any given expectation values. In the spirit of Burgers, these expectation values are the average energy as well as the average of the first and higher order time-derivatives of the energy (or other global quantities). In [2] the method was applied to a system devised by Lorenz . By using constraints on the average energy and its first and second order time-derivatives a satisfying description was produced of the system's statistics, including covariances between the different variables. </p><p>Burgers' approach can also be applied to the parametrization problem, i.e., the problem of how to deal statistically with scales of motion that cannot be resolved explicitly. Quite recently we showed this for two-dimensional turbulence on a doubly periodic flow domain, a system that is relevant as a first-order approximation of large-scale balanced flow in the atmosphere and oceans. Using a spectral description of the system it is straightforward to separate between resolved and unresolved scales and by using a reference model with high resolution it is possible to study how well a parametrization performs by implementing it in the same model with a lower resolution. Based on two studies [3, 4] we will show how well the principle of maximum entropy works in tackling the problem of unresolved turbulent scales.  </p><p>[1] F.T.M. Nieuwstadt and J.A. Steketee, Eds., 1995: Selected Papers of J.M. Burgers. Kluwer Academic, 650 pp. </p><p>[2] W.T.M. Verkley and C.A. Severijns, 2014: The maximum entropy principle applied to a dynamical system proposed by Lorenz. Eur. Phys. J. B, 87:7, https://doi.org/10.1140/epjb/e2013-40681-2 (open access).  </p><p>[3] W.T.M. Verkley, P.C. Kalverla and C.A. Severijns, 2016: A maximum entropy approach to the parametrization of subgrid processes in two-dimensional flow. Quarterly Journal of the Royal Meteorological Society, 142, 2273-2283, https://doi.org/10.1002/qj.2817</p><p>[4] W.T.M. Verkley, C.A. Severijns and B.A. Zwaal, 2019: A maximum entropy approach to the interaction between small and large scales in two-dimensional turbulence. Quarterly Journal of the Royal Meteorological Society, 145, 2221-2236, https://doi.org/10.1002/qj.3554</p>

Atmospheric motions in clouds and cloud surroundings have a wide range of scales, from several kilometers to centimeters. These motions have different impacts on cloud dynamics and microphysics. Larger-scale motions (hereafter referred to as convective motions) are responsible for mass transport over distances comparable with cloud scale, while motions of smaller scales (hereafter referred to as turbulent motions) are stochastic and responsible for mixing and cloud dilution. This distinction substantially simplifies the analysis of dynamic and microphysical processes in clouds. The present research is Part I of the study aimed at describing the method for separating the motion scale into a convective component and a turbulent component. An idealized flow is constructed, which is a sum of an initially prescribed field of the convective velocity with updrafts in the cloud core and downdrafts outside the core, and a stochastic turbulent velocity field obeying the turbulent properties, including the −5/3 law and the 2/3 structure function law. A wavelet method is developed allowing separation of the velocity field into the convective and turbulent components, with parameter values being in a good agreement with those prescribed initially. The efficiency of the method is demonstrated by an example of a vertical velocity field of a cumulus cloud simulated using the System for Atmospheric Modeling (SAM) with bin microphysics and resolution of 10 m. It is shown that vertical velocity in clouds indeed can be represented as a sum of convective velocity (forming zone of cloud updrafts and subsiding shell) and a stochastic velocity obeying laws of homogeneous and isotropic turbulence.

Simulation of vortex shedding from an oscillating circular cylinder

Performance of time-frequency representation techniques to measure blood flow turbulence with pulsed-wave Doppler ultrasound

The nonclosure of surface energy balance remains an outstanding problem in eddy covariance (EC) measurements of land‐surface fluxes of heat, water vapor, and CO2. Here data collected from an EC tower over a semiarid sagebrush ecosystem indicate that under unstable atmospheric conditions, the nonclosure becomes increased with increasing instability, consistent with many other studies. It is demonstrated that the increased nonclosure is not caused by the inadequate sampling of large‐scale turbulent motions using a 30‐min averaging interval, though the scales of turbulent motions dominating sensible and latent heat fluxes become enlarged with increasing instability. Quadrant analysis is then used to reveal that the flux contributions from ejections remain nearly constant with increasing instability, whereas the flux contributions from sweeps are reduced and their time fractions increase. Our results imply that the increased nonclosure of surface energy balance is associated with changes in turbulent structures including their dominant time scales and flux contributions of ejections and sweeps as the atmospheric instability increases, which require further studies using vertically distributed observations and/or large eddy simulations.

A number of important technical applications rely on diusers where the o w is decelerated in the presence of an associated adverse pressure gradient, resulting in rapid boundary layer growth, potentially o w separation, and unsteadiness (both, small and large scale turbulent motion). Simulations of high Reynolds number o ws with strong adverse pressure gradient and o w separation are computationally challenging because standard turbulence models are dicult to calibrate for such o ws and simulations that resolve all scales of the turbulent motion can become prohibitively expensive. For validation purposes we computed two well documented turbulent channel o w cases using steady Reynolds-averaged Navier-Stokes. In collaboration with J. Eaton at Stanford University we then started simulations of an asymmetric diuser at an ino w Reynolds number based on channel height and bulk velocity of 10,000 using Reynolds-averaged Navier-Stokes, direct numerical simulations, and a hybrid turbulence modeling approach, the o w simulation methodology. The capability of the various approaches to accurately predict time-averaged properties of the o w are discussed. Although at this point none of the dieren t approaches is entirely satisfactory, the current results provide valuable hints and insights of how to proceed with such o w simulations so that more reliable results can be obtained.

We study star cluster formation in a low-metallicity environment using three-dimensional hydrodynamic simulations. Starting from a turbulent cloud core, we follow the formation and growth of protostellar systems with different metallicities ranging from 10−6 to 0.1 Z⊙. The cooling induced by dust grains promotes fragmentation at small scales and the formation of low-mass stars with M* ∼ 0.01–0.1 M⊙. While the number of low-mass stars increases with metallicity, when Z/Z⊙ ≳ 10−5, the stellar mass distribution is still top-heavy for Z/Z⊙ ≲ 10−2 compared to the Chabrier initial mass function (IMF). In these cases, star formation begins after the turbulent motion decays and a single massive cloud core monolithically collapses to form a central massive stellar system. The circumstellar disc preferentially feeds the mass to the central massive stars, making the mass distribution top-heavy. When Z/Z⊙ = 0.1, collisions of the turbulent flows promote the onset of the star formation and a highly filamentary structure develops owing to efficient fine-structure line cooling. In this case, the mass supply to the massive stars is limited by the local gas reservoir and the mass is shared among the stars, leading to a Chabrier-like IMF. We conclude that cooling at the scales of the turbulent motion promotes the development of the filamentary structure and works as an important factor leading to the present-day IMF.

Assuming local thermodynamic equilibrium in the fluid, an expression is derived for the rate of destruction of the mean square of the temperature fluctuations by radiative transfer of heat. This takes a particularly simple form (a) if the fluid is effectively transparent over distances equal to the scale of the turbulent motion, when the effect appears as a decay time for temperature fluctuations from the mean, and (b) if the fluid is effectively opaque, when the effect is of an increased conductivity due to radiation. A theory of the interaction of the temperature and velocity fields developed in a previous paper shows that, if the radiative effects are relatively weak, a sudden collapse of the turbulent motion occurs while the flux Richardson number is still less than one. If the radiative effects are strong, the turbulent intensity approaches zero as the flux Richardson number approaches one. The effects of radiation are always to increase the critical value of the ordinary Richardson number. Criteria for fully turbulent motion of an unrestricted flow are given in terms of the gradients of mean velocity and mean temperature and of the rate of radiative cooling. The relevance of these calculations to motions of the atmosphere is briefly discussed.

The probability dΓ, that at location and time t contaminant fluid with concentration between Γ and Γ + dΓwill be encountered, is investigated. When a finite quantity of contaminant material is released in a large-Reynolds-number flow, and while the contaminant cloud so formed remains of smaller dimension than the energy containing scales of turbulent motion, it is argued that will be of self-similar form over the range of Γ that is indicative of values in the strands of contaminant fluid of which the cloud is comprised. A nondimensional stringiness factor S(t) is defined, using , as a measure of the extent to which contaminant material has been pulled out by the convective turbulent motion into long threads. S(t) is shown to relate the average of the median value of concentration throughout each realization of the cloud to the ensemble-average concentration . It is suggested that many of the results of the paper apply in a more general category of diffusion problems, and some experimental results are reviewed.

We investigate turbulent gas motions in spiral galaxies and their importance to star formation in far outer disks, where the column density is typically far below the critical value for spontaneous gravitational collapse. Following the methods of Burkhart et al. on the Small Magellanic Cloud, we use the third and fourth statistical moments, as indicators of structures caused by turbulence, to examine the neutral hydrogen (H i) column density of a sample of spiral galaxies selected from The H i Nearby Galaxy Survey. We apply the statistical moments in three different methods—the galaxy as a whole, divided into a function of radii and then into grids. We create individual grid maps of kurtosis for each galaxy. To investigate the relation between these moments and star formation, we compare these maps with their far-ultraviolet images taken by the Galaxy Evolution Explorer satellite.We find that the moments are largely uniform across the galaxies, in which the variation does not appear to trace any star-forming regions. This may, however, be due to the spatial resolution of our analysis, which could potentially limit the scale of turbulent motions that we are sensitive to greater than ∼700 pc. From comparison between the moments themselves, we find that the gas motions in our sampled galaxies are largely supersonic. This analysis also shows that the Burkhart et al. methods may be applied not just to dwarf galaxies but also to normal spiral galaxies.

Numerical ability of hyperbolic flux solvers to compute 2D shear layers in turbulent shallow flows

A case-study comparison is made of simultaneous airborne gust probe and dual-Doppler radar measurements of motions associated with roll vortices in the optically clear planetary boundary layer. Inter-comparison of the cross-roll component of motion is emphasized. Some similarities and some differences in the data obtained with the two systems are discussed. Considering the differences in measurement techniques, agreement is good between the independent depictions of the roll structure and quantitative determinations of the intensities and predominant scales of eddy motion. The observed roll vortices fit descriptions and cause-effect relationships from certain models and other observations.

1 Multiple scales in rivers

The influence of the different scales of turbulent motion on plume dispersion in the atmospheric convective boundary layer (CBL) is studied by means of a large-eddy simulation (LES). In particular, the large-scale (meandering) and small-scale (relative diffusion) contributions are separated by analyzing dispersion in two reference systems: the absolute (fixed) coordinate system and the coordinate system relative to the plume’s instantaneous center of mass. In the relative coordinate system, the (vertically) inhomogeneous meandering motion is removed, and only the small-scale, homogeneous turbulent motion contributes to the dispersion process. First, mean plume position, dispersion parameters (variance), and skewness of the plume position are discussed. The analysis of the third-order moments shows how the structure and the symmetry of scalar distribution are affected with respect to the turbulent characteristics of the CBL (inhomogeneity of the large-scale vertical motion) and the presence of the boundary conditions (surface and top of the CBL). In fact, the reflection of the plume by the CBL boundaries generates the presence of nonlinear cross-correlation terms in the balance equation for the third-order moments of the plume position. As a result, the third-order moment of the absolute position is not balanced by the sum of the third-order moments of the meandering and relative plume position. Second, mean concentration and concentration fluctuations are calculated and discussed in both coordinate systems. The intensity of relative concentration fluctuation icr, which quantifies the internal (in plume) mixing, is explicitly calculated. Based on these results, a parameterization for the probability distribution function (PDF) of the relative concentration is proposed, showing very good agreement with the LES results. Finally, the validity of Gifford’s formula, which relates the absolute concentration’s high-order moments to the relative concentration and the PDF of the plume centerline, is studied. It is found that due to the presence of the CBL boundaries, Gifford’s formula is not able to reproduce correctly the value of the absolute mean concentration near the ground. This result is analyzed by showing that, when the plume is reflected by the CBL boundaries, the instantaneous relative plume width z′2r(t) departs from its mean value σ2r. By introducing the skewness of the relative plume position into a parameterization for the relative mean concentration, the results for the calculated mean concentration are improved.