Vertical Velocity Fluctuations Research Articles

Dominant heat transfer mechanism with conical roughness in a cubical box in turbulent Rayleigh–Bénard convection

In the present study, we numerically investigate the effect of Prandtl number on the heat transfer mechanism in turbulent Rayleigh–Bénard convection inside a cubical box endowed with conical roughness elements. The Rayleigh number is kept fixed at Ra=108, while the Prandtl number (Pr) varies from 1 to 50. In contrast to the monotonic increasing trend of the Nusselt number (Nu∼Pr0.27) in the two-dimensional (2D) roughness explored previously [Sharma et al., “Influence of Prandtl number in turbulent Rayleigh-Bénard convection over rough surfaces,” Phys. Rev. Fluids 7, 104609 (2022)], it assumes an invariant behavior (∼Pr0.012) for three dimensional (3D), though it is approximately 50% higher than its smooth counterpart. Flow intensity, measured in terms of Reynolds number (Re), drops with increasing Pr showing consistently lower magnitude for the 3D configuration. The addition of roughness elements is observed to disrupt the preferred orientation of large-scale circulation (LSC). The effect is predominant for lower Pr, where the roughness interferes most with the natural bias of LSC toward the diagonal planes of the cubical box. The analysis of plume statistics reveals that both coverage and intensity of plumes are augmented for the roughened cell. Increased homogeneity in the flow at higher Pr is reflected by the emergence of a more pronounced and distinguishable peak in probability density functions of temperature and velocity. Temporal spectra and variance data substantiate augmented intensity of fluctuations in the rough cell, while behavioral differences in the flow at different Pr are elucidated by using cross correlation of vertical velocity and temperature fluctuations.

Can Recurrence Quantification Analysis Be Useful in the Interpretation of Airborne Turbulence Measurements?

AbstractIn airborne data or model outputs, clouds are often defined using information about Liquid Water Content (LWC). Unfortunately LWC is not enough to retrieve information about the dynamical boundary of the cloud, that is, volume of turbulent air around the cloud. In this work, we propose an algorithmic approach to this problem based on a method used in time series analysis of dynamical systems, namely Recurrence Plot (RP) and Recurrence Quantification Analysis (RQA). We construct RPs using time series of turbulence kinetic energy, vertical velocity and temperature fluctuations as variables important for cloud dynamics. Then, by studying time series of laminarity (LAM), a variable which is calculated using RPs, we distinguish between turbulent and non‐turbulent segments along a horizontal flight leg. By selecting a single threshold of this quantity, we are able to reduce the number of subjective variables and their thresholds used in the definition of the dynamical cloud boundary.

Effect of isothermal rough boundaries on the statistics of velocity and temperature fluctuations in turbulent Rayleigh–Bénard convection

Using direct numerical simulations, we investigate the effect of surface roughness on the statistics of fluctuations in a 2D rectangular cell of aspect ratio Γ = 2 with air as the working fluid. We consider roughly two decades of Rayleigh number, 108≤Ra≤4.64×109, with three roughness configurations of R1, R2, and R3 characterized by their maximum heights of 5%, 10%, and 20% of the cell height, respectively. We show that roughened cells trigger stronger fluctuations, which further gets augmented with increasing Ra. Vertical variations of velocity and temperature fluctuations show different trends. While the temperature fluctuation becomes homogeneous in the bulk, it exhibits strong inhomogeneous vertical velocity fluctuations. The comparison of global heat flux with smooth case shows a significant increment beyond Ra=2.15×108. Surface roughness impacts local heat flux through augmented plumes, which is qualitatively ascertained by instantaneous temperature field. Furthermore, probability distribution functions reveal no particular trend for the taller roughness configurations, though the magnitude is amplified. Through identification of plumes and background regions, we show their behavior as a function of Ra for different rough cases. Finally, we decompose the shear production into its three components (based on the nature of mechanical forces) to understand the energy interaction between the mean flow and fluctuating flow field.

Modeling wind-driven seed dispersal using a coupled Lagrangian particle tracking and 1-D [formula omitted]-[formula omitted] turbulence model

We present a one-dimensional k-ɛ model and a Markov chain stochastic Lagrangian particle tracking model to study wind-driven dispersal of forest and grassland seeds. The turbulence model within and above the canopy is implemented for transient winds so that time series of profiles of mean velocity, turbulence kinetic energy, dissipation rate, and the root-mean-square of fluctuating velocity components can be modeled. We validate the model for steady state conditions using observations in a wide range of canopies, and apply the model for predicting time series of seed dispersal of Andropogon gerardii in a tall grass prairie in Missouri, United States. The stochastic seed dispersal model is validated against experimental data from a Quercus-Carya (oak-hickory) forest where seeds were released from different heights for a range of wind speeds. Using the model, we explore the detailed seed movement trajectories, instantaneous velocities, and investigate the relationship between dispersal distance and the seed falling duration and the mean fluctuating velocity during the falling. Moreover, examining the role of individual turbulent velocity components, we elucidate the different roles of horizontal and vertical velocity fluctuations, i.e., the horizontal component mainly contributes to the seed spreading in the wind direction, while the vertical component enhances the long tail of the distribution in the downstream direction, i.e., promoting long-distance-dispersal of seeds by wind.

Experimental and numerical investigation of a disc-attached cylinder near a wall

An experimental and numerical study is carried out to investigate the flow up- and downstream of a disc-attached cylinder near a wall with a Reynolds number of Re=U0d/ν=5.4⋅104 (U0 is the mean upstream flow velocity, d is the diameter of the cylinder, and ν is the kinematic viscosity). Laser Doppler Velocimetry measurements were conducted to obtain statistical flow parameters such as the mean velocity and turbulent kinetic energy. The experimental results show that the mean flow can be characterized as two-dimensional at a transverse distance of more than d away from the disc. Furthermore, it is shown that the effect of the disc and the cylinder fades away downstream. Analysis of a power spectrum of the vertical velocity fluctuations shows that vortex shedding is disturbed downstream of the disc. The numerical simulation is performed using a Reynolds-Averaged Navier–Stokes model. The turbulent kinetic energy and mean velocities are well-predicted by the numerical model. An increase in the peak amplitudes of the power spectra obtained from the vertical velocity fluctuations is found at a transverse distance of 3.75d from the centerline of the disc for both the experimental and numerical study, caused by vortices being transported by a transverse flow related to the disc.

The Impact of Internal Gravity Waves on the Spectra of Turbulent Fluctuations of Vertical Wind Velocity in the Stable Atmospheric Boundary Layer

The wave turbulence interactions in the stable boundary layer (SBL) of the atmosphere are studied based on data from lidar measurements of the vertical component of wind velocity during the propagation of internal gravity waves (IGWs). It is shown that as an IGW appears, the amplitude of the spectra of turbulent fluctuations of vertical wind velocity nearby the frequency of quasi-harmonic oscillations induced by an IGW increases significantly, sometimes by several orders of magnitude, compared to the spectra in the absence of an IGW. Since IGW energy is transferred to small-scale turbulence, the amplitude of spectra with the Kolmogorov–Obukhov −5/3 power-law frequency dependence in the inertial frequency range increases. The slope of the spectra in the low-frequency range between the frequency of IGW-induced oscillations and the frequency of the lower boundary of the inertial range exceeds the slope, corresponding to the −5/3 power-law dependence. In this frequency range, the spectra obey the power-law dependence on the frequency with the exponent ranging from −4.2 to −1.9. The average value of the exponent −3 is consistent with a low-frequency slope caused by IGWs in turbulent spectra in the lower SBL.

Aerodynamic noise reduction of a blunt flat plate by trailing-edge blowing

This study investigates the influence of air blowing on the aerodynamic noise generated by a flat plate with a blunt trailing edge. The uniform blowing was applied through evenly spaced holes along the span at the base of the flat plate. Acoustic pressure measurements were conducted in an anechoic wind tunnel using a free-field microphone at Reynolds numbers ranging from 2.8×105 to 6.5×105. Particle image velocimetry measurements were performed to obtain time-resolved evolution and statistics of the flow velocity field, providing a detailed understanding of the noise reduction mechanisms. The results demonstrated that air blowing effectively reduces both the amplitude and bandwidth of tonal and broadband noise within a limited frequency range. This phenomenon was attributed to the stabilization of separated shear layers over a longer distance by air blowing and a decrease in turbulent kinetic energy in the near-wake region. It was shown that air blowing suppresses the tonal peak of vertical velocity fluctuations and narrows the wake width, which accounts for the increase of vortex shedding frequency and a potential drag reduction. Generally, the effects of air blowing on vortex shedding at the blunt trailing edge are analogous to those of a splitter plate. The unaffected convective velocity of the large-scale vortex structures and the enhanced spanwise coherence in the vortex formation region provide further evidence to this analogy.

Study of interscale interactions for turbulence over the obstacle arrays from a machine learning perspective

Investigating interactions between large- and small-scale motions is essential for understanding turbulence over rough boundaries. The present work applies XGBoost models to predict the spatial distribution of ejections and sweeps and quantify their statistical dependence on scale-decomposed velocity fields. Based on large eddy simulation, the models are trained and validated at 20 horizontal planes in turbulence over two types of obstacle arrays. At each height, a default XGBoost model X0 and four comparison models ( X u L , w L , X u L , w S , X u S , w L, and X u S , w S) are trained. The model X0 is trained by the set with four scale-decomposed velocity fields { u L , u S , w L , w S }, where u and w are the streamwise and vertical velocity fluctuations and subscripts L and S refer to above-canyon and sub-canyon scales, while the comparison models are trained by subsets of the scale-decomposed velocity fields. The results indicate that the model X0 predicts the spatial distributions of both ejection and sweep events well, with the structure underestimation being less than 8% within the canopy layer and 3% above it. Along the vertical direction, the relative importance of scale-decomposed velocity fields on the prediction of ejections and sweeps is quantified by the feature importance and prediction errors. The feature importance profiles reveal that both sweeps and ejections are most strongly related to w S within the canopy, but ejections have a stronger dependence on u L well above the canopy. For the comparison models, those trained with w S (namely, X u L , w S and X u S , w S) give better predictions within the canopy layer, whereas those trained with u L (namely, X u L , w S and X u L , w L) perform better above the canopy. This study shows that a machine-learning-based approach can be designed to quantify the relative importance of different scale-decomposed velocity fields on predicting ejections and sweeps and to detect vertical changes of such relative importance.

Scale-by-scale analysis of interscale scalar transfer in grid turbulence with mean scalar gradient

Direct numerical simulations were carried out on grid turbulence with a mean scalar gradient to reveal interscale scalar transport. Two-point statistical analysis using the structure function and the scale-by-scale scalar equation was performed. Results show that the third-order structure function becomes negative at large scales in the upstream region (inverse cascade occurs), while such distributions do not appear for turbulence energy. This phenomenon in scalars gradually disappears in the downstream region. Budget analysis of the structure function reveals that this is mainly caused by the non-linear scalar transfer term in the direction of the mean scalar gradient (vertical direction here). When the separation distance is smaller than Taylor's microscale, where the interscale scalar transfer is normal (large to small scales), the direction of the scalar flux is determined by the vertical velocity fluctuation difference between two points. However, when separation is larger than Taylor's microscale and inverse cascading occurs, the direction is determined by derivative of the scalar fluctuation rather than the velocity fluctuation difference. Further analysis reveals that the existence of fluid mass with an unmixed scalar plays an important role in the inverse cascade phenomenon.

Experimental Study of Turbulent Wake Flow Around Trapezoidal Cylinders With Varying Streamwise Aspect Ratios

AbstractThe effects of streamwise aspect ratio (AR) on the asymmetric wake flow over and behind right-angled trapezoidal cylinders with AR (= upper cylinder length to height ratio) = 1, 2, 3, 4, and 5 were investigated using particle image velocimetry. The Reynolds number based on the freestream velocity and cylinder height was 14700. The flow characteristics are examined in terms of the mean velocity flow, Reynolds stresses, probability density function (PDF), and two-point correlations. The results show that the primary vortex in the AR1 and AR2 trapezoidal cases extends into the wake region but is confined to the surface of the longer cases and two asymmetrical wake vortexes are only observed in the longer cases. Dual peaks of elevated streamwise Reynolds stresses are observed in the wake region, regardless of the aspect ratios. The magnitudes of the Reynolds stresses and turbulent kinetic energy are higher in the shorter cases (AR1, AR2, and AR3 cases) compared to the longer cases. The PDF distributions show a bimodal asymmetrical shape in the shorter cases but a nearly Gaussian distribution in the AR5 case. Two-point autocorrelations of the streamwise and vertical velocity fluctuations revealed that the spatial coherency of the turbulent structures is highly sensitive to the streamwise aspect ratio and reference locations. Systematic comparison between the present asymmetric results and symmetric wakes generated by rectangular cylinders with similar aspect ratios and Reynolds number shows significant differences between the asymmetric and symmetric wakes, especially at smaller aspect ratios.

Gap ratio effects on the coherent structures surrounding a near-wall square cylinder

Turbulent flow around a square cylinder offset at different heights from an upstream rough wall are investigated using time-resolved particle image velocimetry. The Reynolds number based on the freestream velocity and cylinder height was 12750 and the incoming turbulent boundary layer thickness was 7.2 times the cylinder height. The examined gaps beneath the cylinder were 0.0, 0.3, 0.5, 1.0, 2.0, 4.0, and 8.0 times the cylinder height. The results show that the mean recirculation length remains relatively constant for cases with a gap size greater than or equal to 1.0 times the cylinder height. Flow acceleration through the gap under the cylinder is strongest with a gap size of 2.0 times cylinder height. Downstream of the cylinder, the vertical velocity fluctuations contribute strongly to the production of turbulent kinetic energy by interacting with mean wall-normal velocity gradient in the vertical direction. The dominant frequency embedded in the incoming turbulent boundary layer persists in the wake of the cylinder when the gap size is less than 1.0 cylinder height. Kelvin-Helmholtz vortices originating from the top leading edge of cylinder occur at Strouhal numbers of 2.77-3.11 for the cases with gap ratio ranging from 0.3-8.0 cylinder heights, while spectral migration towards lower frequencies is observed for cases with gap sizes equal to 0.3 and 0.5 cylinder heights. The spatial trajectory of top Kelvin-Helmholtz vortices extends further away from the cylinder as the gap size increases. Spectral proper orthogonal decomposition analysis shows that the von Kármán vortex shedding structures possess the highest spectral energy for all offset cases despite regular vortex shedding being disrupted when the gap size is 0.3 times the cylinder height.

Fast Atmospheric Response to a Cold Oceanic Mesoscale Patch in the North‐Western Tropical Atlantic

AbstractLow‐level clouds over the tropical and sub‐tropical oceans play a crucial role in the planetary radiative energy budget. However, they are challenging to model in climate simulations because they are affected by local processes that are still partially unknown. The control that mesoscale sea surface temperature (SST) structures have on the dynamics of the lower atmosphere on daily scales is emerging to be non‐negligible and calls for more effort to be understood. During the EUREC4A field campaign, two of the research vessels (R/Vs) involved in the experiment sampled the edge of a cold mesoscale SST patch in the north‐western tropical Atlantic, crossing a gradient of roughly 0.75°C/100 km. The comprehensive set of instruments carried by the R/Vs allows an unprecedented characterization of the atmospheric response to the cold water forcing. The cold ocean patch weakens the vertical atmospheric mixing, reducing the boundary layer depth of roughly 200 m and the horizontal wind intensity of approximately 3 m s−1. At the same time, the humidity content in the sub‐cloud layer increases and these conditions decrease the latent heat flux (by roughly 80 W m−2) and reduce vertical velocity fluctuations, making it less likely that moisture exceeds the lifting condensation level. As a consequence, fewer and thinner low‐level clouds form over cold water. Independent satellite measurements are found to agree with the in situ observations. The observed link between sea temperature and low‐level clouds highlights its importance in the puzzle of modeling the sea‐air‐cloud interactions.

Componentwise influence of upstream turbulence on the far-wake dynamics of wind turbines

Wake meandering and turbulent kinetic energy (TKE) generation in the far-wake region of wind turbines significantly affect the power production and aerodynamic loads of wind farms. This work thus aims at understanding the componentwise influence of upstream turbulence and roles of different mechanisms on the far-wake dynamics to guide the development of wind-farm wake models. We find that the wake meandering is mainly caused by the upstream spanwise (v′) and vertical (w′) velocity fluctuations, supporting the passive wake meandering mechanism. However, our results also show a scale-dependence of the wake meandering that should be accounted in wake models. We find that v′ and w′ cause greater TKE generation than the streamwise velocity fluctuations (u′). We then use simulation- and resolvent-based componentwise input–output analyses to explain that this is because the shear instability in turbine wakes is more receptive to the transverse forcing relative to the streamwise forcing. This highlights the importance of implementing the shear instability mechanism in wake models for accurate TKE estimations. Finally, we find that u′ cause the thrust fluctuations, which can lead to near-wake corrections and hence influence the far-wake evolution.

Gravitational effect on the nonlinear dynamics of a buoyant turbulent flame.

This study numerically examines the gravitational effect on the nonlinear dynamics of a buoyant turbulent flame utilizing analytical methods based on complex networks and dynamical systems. A dense (sparse) network structure is formed in the near (far) field in low gravity, as shown by the degree and cluster coefficient in the spatial network. The global dynamics of the vertical flow velocity fluctuations in the intermittent luminous zone is synchronous with that of the temperature fluctuations in low gravity. The synchronized state disappears as the gravity level is increased, leading to a desynchronized state. These behaviors are clearly identified by the symbolic recurrence plots.

On the Non-monotonic Variation of the Entrainment Buoyancy Flux with Wind Shear

The magnitude of the entrainment buoyancy flux, and hence the growth rate of the convective boundary layer, does not increase monotonically with wind shear. Explanations for this have previously been based on wind-shear effects on the turbulence kinetic energy. By distinguishing between turbulent and non-turbulent regions, we provide an alternative explanation based on two competing wind-shear effects: the initial decrease in the correlation between buoyancy and vertical velocity fluctuations, and the increase in the turbulent area fraction. The former is determined by the change in the dominant forcing; without wind shear, buoyancy fluctuations drive vertical velocity fluctuations and the two are thus highly correlated; with wind shear, vertical velocity fluctuations are partly determined by horizontal velocity fluctuations via the transfer of kinetic energy through the pressure–strain correlation, thus reducing their correlation with the buoyancy field. The increasing turbulent area fraction, on the other hand, is determined by the increasing shear production of turbulence kinetic energy inside the entrainment zone. We also show that the dependence of these conditional statistics on the boundary-layer depth and on the magnitude of the wind shear can be captured by a single non-dimensional variable, which can be interpreted as an entrainment-zone Froude number.

Types of Vertical Structure of the Nocturnal Boundary Layer

The vertical structure of the observed stable boundary layer often deviates substantially from textbook profiles. Even over flat homogeneous surfaces, the turbulence may not be completely related to the surface conditions and instead generated by elevated sources of turbulence such as low-level jets and transient modes. In stable conditions, even modest surface heterogeneity can alter the vertical structure of the stable boundary layer. With clear skies and low wind speeds, cold-air drainage is sometimes generated by very weak slopes and induces a variety of different vertical structures. Our study examines the vertical structure of the boundary layer at three contrasting tower sites. We emphasize low wind speeds with strong stratification. At a given site, the vertical structure may be sensitive to the surface wind direction. Classification of vertical structures is posed primarily in terms of the profile of the heat flux. The nocturnal boundary layer assumes a variety of vertical structures, which can often be roughly viewed as layering of the heat-flux divergence (convergence). The correlation coefficient between the temperature and vertical velocity fluctuations provides valuable additional information for classification of the vertical structure.

On the wake of an isolated rotating wheel: An experimental and numerical investigation

The wake of an isolated, rotating wheel of a geometry typical of those used in open-wheel motorsport, is investigated. The CFD is validated by comparing the wake data gathered from this method with the data from the PIV wind tunnel experiments, where analysis of the data showed a good agreement between the two methods. A comparison of the mean and instantaneous flow-fields obtained from the CFD shows significant differences in the wake topology. The time-averaged illustration of the flow shows an inverted “T” shape, and consists of a pair of upper and lower counter-rotating vortices that merge downstream, with the upper being dominant. The instantaneous wake follows the same fundamental shape, but consists of incoherent macro-scale eddies, together with these counter-rotating vortices in a deformed state. Analysis of the unsteadiness of the wake via proper orthogonal decomposition reveals significant transverse and vertical velocity fluctuations. The transverse velocity fluctuations are driven by both the contraction and expansion of the contact patch wake and the instability of the merged counter-rotating vortex pair that eventually lead to a transverse flapping motion of the bulk wake. The instability of these vortices also leads to vertical velocity fluctuations in the vortex-induced downwash region.

Spectral proper orthogonal decomposition of coupled hydrodynamic and acoustic fields: Application to impinging jet configurations (draft)

A large variety of flow configurations involve an aero-acoustic coupling and the complexity of the interaction can make the analysis difficult. In the purpose to decompose these flows in simpler phenomena, the spectral proper orthogonal decomposition (SPOD) algorithm can be used. Compared to POD, this method adds up a discrete Fourier transform before the singular value decomposition. A theoretical framework for the weighting of the flow field variables used in the SPOD has been proposed to identify hydrodynamic modes by Schmidt et al. However, in flow configurations where both the hydrodynamic and acoustic fields interact, without additional data processing, only hydrodynamic modes that are generally dominants would be identified by the SPOD. This paper proposes a general framework based on a few pre-processing steps applied to the input aero-acoustic fields to facilitate the identification of both the hydrodynamic and acoustic fields by the SPOD, the purpose being to analyze how the hydrodynamic waves lead to the acoustic ones and the possible feedback process. This framework is applied to large-eddy simulations of supersonic ideally expanded impinging planar jet of infinite extent characterized by different nozzle-to-plate distances and incidence angles of the flat plate. The analysis shows that the SPOD algorithm is able to capture two important aero-acoustic feedback loops of impinging jet configurations: the one closed by sound waves traveling upstream (related to the jet impingement on the flat plate) and the one characterized by neutral wave modes of the jet shear layer itself. The analysis has also shown that the symmetrical/anti-symmetrical acoustic patterns radiated with respect to the jet main axis and due to the jet impingement are mainly correlated to the axial velocity fluctuations structures in the jet for the normally impinging cases. For the cases with flat plate incidence, the acoustic radiated is mainly correlated to vertical velocity fluctuations structures developing in the upper shear layer of the jet.

Investigation of flow dynamics and heat transfer mechanism in turbulent Rayleigh–Bénard convection over multi-scale rough surfaces

We present a two-dimensional numerical study of turbulent Rayleigh–Bénard convection with air as the working fluid over a multi-scale randomly roughened surface in a rectangular box of aspect ratio 2 over three decades of Rayleigh number ( $10^8 \leq {\textit {Ra}} \leq 10^{11}$ ). With varied response of the roughness elements at different ${\textit {Ra}}$ , enhanced heat transfer scaling ( $\gamma =0.41$ ) is retained throughout the explored ${\textit {Ra}}$ range. The plume emission process is triggered from the taller roughness elements at a lower ${\textit {Ra}}$ , while smaller elements contribute significantly at higher ${\textit {Ra}}$ . Increased plume emission frequency compared to the smooth case is reflected from the enhanced volume fraction and thermal dissipation rate of plumes. The tip of the roughness elements exhibits the highest temperature and vertical velocity fluctuations, while washing out of the trapped fluid in the throat region holds the key to enhanced heat flux at higher ${\textit {Ra}}$ . Increased localized pockets of fluid at higher ${\textit {Ra}}$ indicate better inter-scale energy transfer, which is reflected in higher energy content at all scales in the computed temperature spectra. The decomposition of the flow field into orthogonal modes reveals that heat transfer enhancement at higher ${\textit {Ra}}$ is associated with multiple small-scale structures. Owing to better energy transfer and intense localized fluctuations, modal distribution of energy is less severe for higher ${\textit {Ra}}$ , and stable twin large-scale rolls do not favour an efficient heat transport process.

Anomalous vertical sound propagation and the ground-blocking of turbulence

Scattering by turbulence leads to random scintillations and coherence loss of sound waves, among other impacts. In a recent experiment involving transmissions from a 130-m tower to microphones on the ground [Kamrath et al., J. Acoust. Soc. Am. 149(3), 2055–2071 (2021)], the turbulence impacts on phase variances were shown to be considerably smaller for vertical and slanted paths than theoretically predicted. The primary cause is likely ground blocking of the turbulence: since the sound waves are impacted most strongly by the turbulent velocity fluctuations in the direction of propagation, and the ground blocks large vertical motions, the turbulence impacts are relatively weakened for vertical paths. An approach is described for including the ground blocking in the turbulence spectrum and, thus, in acoustic scattering calculations. The anisotropic propagation effect could possibly be used to measure the relative strengths of vertical and horizonal velocity fluctuations in the near-ground atmosphere.