Vertical Velocity Fluctuations Research Articles

Influence of atmospheric stratification on the integral scale and fractal dimension of turbulent flows

Abstract. In this work the relation between integral scale and fractal dimension and the type of stratification in fully developed turbulence is analyzed. The integral scale corresponds to that in which energy from larger scales is incoming into a turbulent regime. One of the aims of this study is the understanding of the relation between the integral scale and the bulk Richardson number, which is one of the most widely used indicators of stability close to the ground in atmospheric studies. This parameter will allow us to verify the influence of the degree of stratification over the integral scale of the turbulent flows in the atmospheric boundary layer (ABL). The influence of the diurnal and night cycles on the relationship between the fractal dimension and integral scale is also analyzed. The fractal dimension of wind components is a turbulent flow characteristic, as has been shown in previous works, where its relation to stability was highlighted. Fractal dimension and integral scale of the horizontal (u′) and vertical (w′) velocity fluctuations have been calculated using the mean wind direction as a framework. The scales are obtained using sonic anemometer data from three elevations 5.8, 13 and 32 m above the ground measured during the SABLES 98 field campaign (Cuxart et al., 2000). In order to estimate the integral scales, a method that combines the normalized autocorrelation function and the best Gaussian fit (R2 ≥ 0.70) has been developed. Finally, by comparing, at the same height, the scales of u′ and w′ velocity components, it is found that the turbulent flows are almost always anisotropic.

Bed shear stress estimation on an open intertidal flat using in situ measurements

Accurate estimations for the bed shear stress are essential to predict the erosion and deposition processes in estuaries and coasts. This study used high-frequency in situ measurements of water depths and near-bed velocities to estimate bed shear stress on an open intertidal flat in the Yangtze Delta, China. To determine the current-induced bed shear stress (τc) the in situ near-bed velocities were first decomposed from the turbulent velocity into separate wave orbital velocities using two approaches: a moving average (MA) and energy spectrum analysis (ESA). τc was then calculated and evaluated using the log-profile (LP), turbulent kinetic energy (TKE), modified TKE (TKEw), Reynolds stress (RS), and inertial dissipation (ID) methods. Wave-induced bed shear stress (τw) was estimated using classic linear wave theory. The total bed shear stress (τcw) was determined based on the Grant–Madsen wave–current interaction model (WCI). The results demonstrate that when the ratio of significant wave height to water depth (Hs/h) is greater than 0.25, τcw is significantly overestimated because the vertical velocity fluctuations are contaminated by the surface waves generated by high winds. In addition, wind enhances the total bed shear stress as a result of the increases in both τw and τc generated by the greater wave height and reinforcing of vertical turbulence, respectively. From a comparison of these various methods, the TKEw method associated with ESA decomposition was found to be the best approach because: (1) this method generates the highest mean index of agreement; (2) it uses vertical velocities that are less affected by Doppler noise; and (3) it is less sensitive to the near-bed stratification structure and uncertainty in bed location and roughness.

Acoustic measurements of vertical velocity and temperature fluctuations of a hydrothermal plume with comparisons to large eddy simulations

The acoustic scintillation method is used to study the hydrothermal plume of Dante within the Main Endeavour vent field (MEF) at the Endeavour segment of the Juan de Fuca Ridge. Forty days of vertical velocity and temperature fluctuations were obtained from the rising plume above the Dante edifice in an environment where the flow is dominated by strong (5cm/s) semi-diurnal tidal currents and a northerly mean residual current (3cm/s). These acoustic measurements provide a window on deep-sea hydrothermal plume dynamics in strong oscillatory cross flows. A large eddy simulation, parameterized with anisotropic mixing coefficients, taking into account ambient stratification and time-dependent background flows and calibrated by the acoustic measurements, yields insight into turbulent processes, entrainment, plume bending, rise height, and, inferentially, mound heat flux. The turbulent dissipation rates for kinetic energy (ε) and thermal variance (εθ) is approximated by computing the Reynolds averaged sub-grid scale turbulent production from shear and buoyancy (ε = P-B) and from temperature fluxes (εθ = Pθ), respectively, which are needed to compare to the acoustic derived turbulence levels. A new cabled observatory reciprocal acoustic scintillation system on the NEPTUNE observatory that will allow real time measurements of mean and turbulent flow of a hydrothermal plume will also be introduced.

Application of the modeling probability distribution functions for Lagrangian simulation of a passive tracer in the atmospheric boundary layer

The numerical stochastic Lagrangian modeling of the passive tracer in a convective atmospheric boundary layer (CABL) was performed based on the random walk and Langevinmodels of turbulent dispersion. The statistical structure of turbulence is modeled by the probability density function (PDF) of vertical velocity fluctuations, which is recovered by the calculated statistical moments of the vertical velocity fluctuations. Four models of the PDF reconstruction were tested and the results of simulations are compared with the experimental data in CABL. The superiority of Langevin model over the random-walk models is demonstrated.

Effect of cloud‐scale vertical velocity on the contribution of homogeneous nucleation to cirrus formation and radiative forcing

AbstractIce nucleation is a critical process for the ice crystal formation in cirrus clouds. The relative contribution of homogeneous nucleation versus heterogeneous nucleation to cirrus formation differs between measurements and predictions from general circulation models. Here we perform large‐ensemble simulations of the ice nucleation process using a cloud parcel model driven by observed vertical motions and find that homogeneous nucleation occurs rather infrequently, in agreement with recent measurement findings. When the effect of observed vertical velocity fluctuations on ice nucleation is considered in the Community Atmosphere Model version 5, the relative contribution of homogeneous nucleation to cirrus cloud occurrences decreases to only a few percent. However, homogeneous nucleation still has strong impacts on the cloud radiative forcing. Hence, the importance of homogeneous nucleation for cirrus cloud formation should not be dismissed on the global scale.

Resolution and domain‐size sensitivity in implicit large‐eddy simulation of the stratocumulus‐topped boundary layer

AbstractAs a complement to measurements, numerical modeling facilitates improved understanding of the complex turbulent processes in the stratocumulus‐topped boundary layer (STBL). Due to limited computational resources simulations are often run at too coarse resolutions to resolve details of cloud‐top turbulence and potentially in computational domains too small to account for the largest scales of boundary layer circulations. The effects of such deficiencies are not fully understood. Here the influence of resolution/anisotropy of the computational grid and domain size in under‐resolved implicit large‐eddy simulation of the STBL is investigated. The performed simulations are based on data from the first research flight of the DYCOMS‐II campaign. Regarding cloud cover and domain‐averaged liquid water path, simulations with horizontal/vertical grid spacing of 35/5 m, 70/10 m, and 105/15 m are found to agree better with measurements than more computationally expensive simulations with isotropic grid boxes, e.g., with 10/10 m or 15/15 m grid spacing. While decreasing the vertical grid spacing allows more representative simulation of the thin, turbulent, stably stratified interfacial layer between the STBL and the free troposphere, coarsening the horizontal resolution dampens vertical velocity fluctuations in this region and mimics the observed anisotropy of stably stratified small‐scale turbulence near the cloud top. The size of the computational domain is found to have almost no impact on mean cloud properties. However, increasing it from to does lead to the occurrence of larger coherent updraft structures. Increasing it further to shows little or no increase in the updraft size.

Temporal Scales of the Nocturnal Flow Within and Above a Forest Canopy in Amazonia

Multiresolution decomposition is applied to 10 months of nocturnal turbulence observations taken at eight levels within and above a forest canopy in Central Amazonia. The aim is to identify the contributions of different temporal scales of the flow above and within the canopy. Results show that turbulence intensity in the lower canopy is mostly affected by the static stability in the upper canopy. Horizontal velocity fluctuations peak at time scales longer than 100 s within the canopy, which correspond to the scale of non-turbulent submeso motions above the canopy. In the vertical velocity spectrum near the surface, the peak occurs at time scales around 100 s, which are larger than the time scales of the turbulent flow above the canopy. Heat-flux cospectra within the canopy peak at the same temporal scales as the vertical velocity fluctuations at that level, suggesting the existence of buoyancy driven turbulence. Case studies are presented as evidence that low-frequency fluctuations propagate towards the canopy interior more easily than does turbulence.

Lagrangian temperature and vertical velocity fluctuations due to gravity waves in the lower stratosphere

AbstractWave‐induced Lagrangian fluctuations of temperature and vertical velocity in the lower stratosphere are quantified using measurements from superpressure balloons (SPBs). Observations recorded every minute along SPB flights allow the whole gravity wave spectrum to be described and provide unprecedented information on both the intrinsic frequency spectrum and the probability distribution function of wave fluctuations. The data set has been collected during two campaigns coordinated by the French Space Agency in 2010, involving 19 balloons over Antarctica and 3 in the deep tropics. In both regions, the vertical velocity distributions depart significantly from a Gaussian behavior. Knowledge on such wave fluctuations is essential for modeling microphysical processes along Lagrangian trajectories. We propose a new simple parameterization that reproduces both the non‐Gaussian distribution of vertical velocities (or heating/cooling rates) and their observed intrinsic frequency spectrum.

A Numerical Study of Sea-Spray Aerosol Motion in a Coastal Thermal Internal Boundary Layer

A three-dimensional large-eddy simulation model is applied to the study of sea-spray aerosol transport, dispersion and settling in the coastal thermal internal boundary layer (IBL) formed by cool airflow from the open sea to the warm land. An idealized situation with constant inflow from the ocean and constant heat flux over the coastal land is considered. The numerical results confirm that the thickness of the coastal thermal IBL increases with the distance from the coastline until the outer edge of the IBL penetrates into the capping inversion layer. The thickness increases also with time until a fully-developed thermal boundary layer is formed. In addition, the thickness of the coastal thermal IBL increases more rapidly when the heat flux over the land is greater. Existence of large-scale eddies within the thermal IBL is identified and the turbulence intensity within the thermal IBL is also found to be significantly higher than that above. It is also indicated that the vertical position of the maximum concentration does not occur at the surface but increases as sea-spray aerosols are transported inland. The vertical position of the maximum flux of sea-spray aerosols within the coastal thermal IBL is shown to coincide with that of the maximum vertical velocity fluctuations when the coastal thermal IBL is fully developed with increased distance in the airflow direction.

Velocity Jumps in Road-Vehicle Dynamics

Vehicles on roads are excited to vertical vibrations and velocity fluctuations as the consequence of the random up and down of road surfaces. For resonant car vibrations in case of critical velocities effected by the constant driving force, the one-modular velocity density bifurcates into bi-modular distributions with two peaks; i.e. the car velocity is fluctuating around two mean values with permanent jumps between both. These effects are derived by means of quarter car models and second order stochastic roads which are non-linearly coupled to the along and across dynamics of the vehicle.

Near-ground turbulence of the Bora wind in summertime

Bora is a strong, temporally and spatially variable downslope wind that blows along the Eastern Adriatic Coast and many other dynamically similar places around the world. Bora mean velocity rarely exceeds 20m/s, while its strong gusts create significant problems for engineering structures, traffic and agriculture. Previous meteorological and geophysical studies laid foundations on Bora large- and mesoscale motions, but further research is necessary to fully understand and resolve Bora turbulence in a form usable for engineers. In this study, unique high-frequency measurements, carried out simultaneously in three heights on a meteorological tower in the hinterland of the city of Split, Croatia, are analyzed for a single summertime Bora episode. Time histories and vertical profiles are studied for turbulence intensity, Reynolds shear stress and turbulence length scales in comparison with values recommended in major international wind engineering standards. Turbulence intensity and Reynolds shear stress proved to be not that sensitive to meandering of the mean wind velocity, as the observed values remain within the same range during the time record. This trend applies on mean wind velocities larger than 5m/s, as for smaller velocities the spread of values increases considerably. Turbulence length scales are observed to increase with increasing mean wind velocity and vice versa. With increasing height from the ground, turbulence intensity and absolute Reynolds shear stress decrease, turbulence length scales increase, all in agreement with the atmospheric physics. However, while turbulence intensity, Reynolds shear stress and longitudinal turbulence length scales generally agree well with the values recommended in international standards for the respective terrain type, turbulence length scales related to lateral and vertical velocity fluctuations are much larger than the standard values.

A Clustering Method to Characterize Intermittent Bursts of Turbulence and Interaction with Submesomotions in the Stable Boundary Layer

Abstract Atmospheric boundary layers with stable stratification include a variety of small-scale nonturbulent motions such as waves, microfronts, and other complex structures. When the thermal stratification becomes strong, the presence of such motions could affect the turbulent mixing to a large extent, and common similarity theory that is used to describe weakly stable conditions may become unreliable. The authors apply a statistical clustering methodology based on a bounded variation, finite-element method (FEM-BV) to characterize the interaction between small-scale nonturbulent motions and turbulence. The clustering methodology achieves a multiscale representation of nonstationary turbulence data by approximating them through an optimal sequence of locally stationary multivariate autoregressive factor model (VARX) processes and some slow hidden process switching between them. The clustering method is used to separate periods with different influence of the nonturbulent motions on the vertical velocity fluctuations. The methodology can be used in a later stage to derive a stochastic parameterization for the interactions between nonturbulent and turbulent motions.

Dependence of Turbulent Velocities on Wind Speed and Stratification

We examine the dependence of several turbulence quantities on the wind speed and stability using nocturnal data from the Shallow Cold Pool Experiment. The turbulent quantities (velocities) are defined in terms of the standard deviation of the horizontal and vertical velocity fluctuations, two different calculations of the friction velocity, and two turbulent velocities based on the heat flux. The dependence of the turbulent velocities on the wind speed shows a transition between the weak-wind regime of small slope and the stronger wind regime of larger slope, as found in previous studies. This transition occurs for all of the turbulent velocities examined and occurs for a wide range of averaging times. Although this study concentrates primarily on data over a flat surface above the valley, the transition also occurs at the other 18 stations that have non-zero local slopes up to about 10 %. At the same time, the relationship between the turbulence and the wind speed cannot be universal because of the influence of stratification and site-dependent non-stationarity in the weak-wind regime. The wind speed of the transition increases with increasing stratification at a rate that is an order of magnitude slower than that predicted by a constant transition bulk Richardson number. For the weakest winds, the impact of stratification is unexpectedly small.

Three-dimensional flow structure in highly buoyant jet by scanning stereo PIV combined with POD analysis

The flow characteristics and the structure of highly buoyant jet of low density fluid issuing into a stagnant surrounding of high density fluid is studied by scanning stereo PIV combined with proper orthogonal decomposition (POD) analysis. The experiment is carried out at Froude number of 0.3 and Reynolds number of 200, which satisfies the inflow condition due to the unstable density gradient near the nozzle exit. An increase in the maximum mean velocity occurs and the vertical velocity fluctuation is highly amplified near the nozzle exit, which suggests the influence of inflow due to the unstable density gradient. The POD analysis indicates that the vertical velocity fluctuation is the major source of fluctuating energy contributing to the development of the highly buoyant jet. The examination of the POD modes show that the longitudinal structure of the vertical velocity fluctuation is generated along the jet axis having the opposite sign of velocity fluctuation on both sides of the jet axis. The vertical scale of the POD mode decreases with increasing the mode number and results in the frequent appearance of cross-flow across the buoyant jet. The reconstruction flow from the POD modes indicates that the vortex structure is caused by the highly sheared layer between the upward and downward velocity and the inflow is induced by the vortex structure. The magnitude of the vortex structure seems to be weakened with an increase in the distance from the nozzle and the buoyant jet approaches to an asymptotic state in the further downstream.

Multi-platform Observations Characterizing the Afternoon-to-Evening Transition of the Planetary Boundary Layer in Northern Alabama, USA

Observations from the University of Alabama in Huntsville campus and ground-based scanning radar for over 140 total spring, summer, and autumn cases are studied to contribute to the relative scarcity of long-term datasets documenting the afternoon-to-evening transition of the planetary boundary layer. A sunset relative frame of reference is employed, focusing on the period 3 h before to 2 h after astronomical sunset, and several findings are consistent with previous investigations. Fluctuating components of wind and temperature computed from nearly collocated surface, Doppler wind profiler, and vertically pointing Doppler lidar measurements show a consistent decline as turbulence intensity diminishes through the transition. When normalized by their initial values, a pattern emerges: temperature variances decline slowly at first then quite abruptly after about 90 min before sunset. After the temperature variances begin to wane, vertical velocity fluctuations decrease, and the rate of their decay increases as vigorous thermal structures diminish. The fastest decline of the horizontal wind variance occurs after an accelerated vertical wind variance decrease, and the horizontal wind fluctuations display the slowest rate of decrease among these quantities. Near-surface humidity measurements show increases in mean water vapour mixing ratio as a steady rise generally beginning about 80 min prior to sunset. Composites of mean lidar vertical motion show final convective-type towers of upward motion occur about an hour before sunset and are coherent through 800 m (all heights a.g.l.). Lidar vertical motion variance at 195 m decreases by more than an order of magnitude approaching sunset, then remains below 0.01 m\(^{2}\) s\(^{-2}\) for the rest of the studied time frame. Subtle, but steady, increases in both horizontal wind speed and radar-derived horizontal wind convergence above the surface layer (at 300 m) span the entire 5-h time frame. While the convergence results show a broad range, an increase in the mean is clear and found to be statistically significant. Implications for possible transition-effect enhancements to pre-existing low-level convergence areas are briefly noted.

MAGNETIC FLUX CONCENTRATION AND ZONAL FLOWS IN MAGNETOROTATIONAL INSTABILITY TURBULENCE

Accretion disks are likely threaded by external vertical magnetic flux, which enhances the level of turbulence via the magnetorotational instability (MRI). Using shearing-box simulations, we find that such external magnetic flux also strongly enhances the amplitude of banded radial density variations known as zonal flows. Moreover, we report that vertical magnetic flux is strongly concentrated toward low-density regions of the zonal flow. Mean vertical magnetic field can be more than doubled in low-density regions, and reduced to nearly zero in high density regions in some cases. In ideal MHD, the scale on which magnetic flux concentrates can reach a few disk scale heights. In the non-ideal MHD regime with strong ambipolar diffusion, magnetic flux is concentrated into thin axisymmetric shells at some enhanced level, whose size is typically less than half a scale height. We show that magnetic flux concentration is closely related to the fact that the magnetic diffusivity of the MRI turbulence is anisotropic. In addition to a conventional Ohmic-like turbulent resistivity, we find that there is a correlation between the vertical velocity and horizontal magnetic field fluctuations that produces a mean electric field that acts to anti-diffuse the vertical magnetic flux. The anisotropic turbulent diffusivity has analogies to the Hall effect, and may have important implications for magnetic flux transport in accretion disks. The physical origin of magnetic flux concentration may be related to the development of channel flows followed by magnetic reconnection, which acts to decrease the mass-to-flux ratio in localized regions. The association of enhanced zonal flows with magnetic flux concentration may lead to global pressure bumps in protoplanetary disks that helps trap dust particles and facilitates planet formation.

Coherence and Reynolds stresses in the turbulent wake behind a curved circular cylinder

The turbulent wake behind a curved circular cylinder is investigated based on data obtained from a direct numerical simulation. Here, emphasis is placed in the assessment of two approaches for simplified modelling: reduced-order modelling (ROM) and Reynolds-averaged Navier–Stokes equations. To this end, the instantaneous vortical structures, the proper orthogonal decomposition (POD) of the flow, and relevant Reynolds stress components have been analysed. The results show that despite the complexity of the instantaneous vortical structures, the wake dynamics are governed by the quasi-periodic shedding of primary vortices. Between 24% and 50% of the kinetic energy in the POD is captured by the two most energetic modes, and about 200 modes are needed to capture 90% of the kinetic energy. These findings suggest that, as long as the large-scale structures of the von Kármán vortex shedding are concerned, the present case can be approached by ROM; but a detailed representation of the flow dynamics without an eddy viscosity model that accounts for the unresolved turbulent fluctuations would require a large amount of degrees of freedom. Concerning the Reynolds stresses, their magnitude varies considerably depending on the depth at which they have been sampled. This dependence is related to the strength of the vortex shedding, and the intensity of the secondary flows induced by the curvature of the cylinder. As a consequence of the combination of these two effects, the correlation between streamwise and vertical velocity fluctuations is highest in the wake behind the midspan of the curved cylinder, and the correlation between cross-flow and vertical velocity fluctuations reaches large values in the lower wake.

Comparison of PDFs, closure schemes and turbulence parameterisations in Lagrangian stochastic models

Six one–dimensional models, based on the Ito–type stochastic equation, are presented and compared. Four of these take into account up to the fourth order moment of vertical velocity fluctuations, and two up to the third order moment. Four models make use of a bi–Gaussian probability density function (PDF) and the other two are based on a Gram–Charlier series expansion truncated to the third or fourth order. All the models were run with a parameterisation of input turbulence (i.e. w2, w3, and τ profiles). Concerning the fourth order moment w4, two different parameterisations were considered. Comparisons are made between ground–level concentrations, plume height and plume width observed in the Willis and Deardorff water tank experiments and those predicted by the different models here considered. The goal of this study was to find the models that give greater confidence in their applicability in dispersion studies and to verify the importance of considering the fourth order moment. The main conclusions are: simulation results largely depend on the turbulence parameterisation chosen; the Gram–Charlier PDF gives the best agreement with observations; some combinations of models and turbulence parameterisations perform well in simulating the shape of the ground–level concentration (g.1.c.) trend but fail in correctly simulating the form of the plume (plume height and vertical width); in the case of the Gram–Charlier PDF, the fourth order model reproduced the vertical plume width better than the third order one, whereas the two schemes yielded similar g.1.c. distributions.

Turbulence comes in bursts in stably stratified flows

There is a clear distinction between simple laminar and complex turbulent fluids; however, in some cases, as for the nocturnal planetary boundary layer, a stable and well-ordered flow can develop intense and sporadic bursts of turbulent activity that disappear slowly in time. This phenomenon is ill understood and poorly modeled and yet it is central to our understanding of weather and climate dynamics. We present here data from direct numerical simulations of stratified turbulence on grids of 20483 points that display the somewhat paradoxical result of measurably stronger events for more stable flows, not only in the temperature and vertical velocity derivatives as commonplace in turbulence, but also in the amplitude of the fields themselves, contrary to what happens for homogenous isotropic turbulent flows. A flow visualization suggests that the extreme values take place in Kelvin-Helmoltz overturning events and fronts that develop in the field variables. These results are confirmed by the analysis of a simple model that we present. The model takes into consideration only the vertical velocity and temperature fluctuations and their vertical derivatives. It indicates that in stably stratified turbulence, the stronger bursts can occur when the flow is expected to be more stable. The bursts are generated by a rapid nonlinear amplification of energy stored in waves and are associated with energetic interchanges between vertical velocity and temperature (or density) fluctuations in a range of parameters corresponding to the well-known saturation regime of stratified turbulence.

Turbulent Wake of a Bridge Pier in a Tidal Current

The evolution of a large Reynolds number O(10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> ) wake was investigated using data from a ship-mounted acoustic Doppler current profiler (ADCP). The ADCP was a custom configured 600-kHz Teleydyne RD Instruments Workhorse augmented to have a fifth beam that was nominally vertical. The test was conducted in Narragansett Bay, RI, USA, using a large support pier of the Newport Bridge as the turbulent source in the bay's tidal flow. The turbulence was manifested as a vigorously fluctuating wake in the lee of the bridge pier. A series of wake crossings between x = 10-100 D were made during the ebb of the tidal cycle, where x and D are, respectively, the downstream distance and bridge pier diameter. The data set serves as one of a handful where wake evolution has been documented for a large Reynolds number system, and is unique in that high-horizontal resolution vertical velocity profiles were taken with the vertical fifth beam of the ADCP. A range of scales was observed in the vertical velocity field within the wake, including small-scale turbulence O(2-10 m) and large vortex structures O(20-40 m). When cast in terms of nondimensional wake age ( N τ), where N and τ are, respectively, the buoyancy frequency and wake age, the decay of root mean square vertical velocity fluctuations was observed to be proportional to (N τ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-0.82</sup> , faster than the decay of an unstratified 2-D plane wake.