arXiv subjects

Michael Heisel

Publications and source records attributed to Michael Heisel.

12 recordsLinked to original sources

arXiv2026

On the large-scale vertical velocity intermittency of turbulent wall flows

Large-scale intermittency in the vertical velocity (LSI) has received significant attention in studies of coherent structures and their detection using data-driven approaches. However, a theory that predicts the origin of LSI from the Navier-Stokes equations or some approximated version of them at very high Reynolds numbers is yet to be achieved. This letter proposes such a theory for a neutrally stratified wall-bounded turbulent flow based on a dominant balance between inertial and pressure forces. Using multiple flume and wind tunnel experiments, it is shown that the flatness factor ($FF_w$) measuring LSI collapses to a universal trend for all flow configurations within the inertial sublayer (ISL) before reaching a common minimum value above the ISL. A theory that predicts $FF_w$ using second-order statistics and explicitly accommodates large-scale energy anisotropy is tested against a wide range of Reynolds numbers from laboratory to field settings with varied surface roughness conditions. The theory also demonstrates why $FF_w$ cannot be described using down-gradient closure approximations routinely employed in large-scale meteorological and climate models.

physics.flu-dyn↗

arXiv2025

On the wall-normal velocity variance in canonical wall-bounded turbulence

The variance and spectra of wall-normal velocities are investigated for direct numerical simulations of turbulent flow in a channel, pipe, and zero-pressure-gradient boundary layer across a decade of friction Reynolds numbers. Spectra along the spanwise wavenumber have a pronounced peak well described by the turbulent dissipation rate and the local shear stress throughout the bottom half of the boundary layer. Deviations in the local stress from the surface shear velocity $U_\tau$ account for almost all of the differences in wall-normal velocity variance observed across different canonical flows, including for plane Couette flow. The dependence on the local stress is attributed to the fact that wall-normal motions are predominately `active' per Townsend's attached eddy hypothesis and directly contribute to the local shear stress, noting this hypothesis assumes simplified ideal conditions with constant turbulent shear stress. A semi-empirical fit applied to the Reynolds number dependence of the variance matches the simulations across the lower half of the boundary layer and aligns with observed values in the literature. The fit extrapolates to a value between 1.45 and 1.65 times the local shear stress in the high-Reynolds-number limit, consistent with previous predictions relative to $U_\tau$ including for the vertical velocity in the near-neutral atmospheric boundary layer. However, universality in the exact proportional constant is precluded by small discrepancies in the variances corresponding to dissimilarity in the low-wavenumber contributions across different flow configurations and wall-normal positions. We speculate the dissimilarity is due to relatively weak `inactive' wall-normal motions that are excluded from Townsend's original hypothesis.

physics.flu-dyn↗

arXiv2024

The vertical velocity skewness in the atmospheric boundary layer without buoyancy and Coriolis effects

One of the main statistical features of near-neutral atmospheric boundary layer (ABL) turbulence is the positive vertical velocity skewness $Sk_w$ above the roughness sublayer or the buffer region in smooth-walls. The $Sk_w$ variations are receiving renewed interest in many climate-related parameterizations of the ABL given their significance to cloud formation and to testing sub-grid schemes for Large Eddy Simulations (LES). The vertical variations of $Sk_w$ are explored here using high Reynolds number wind tunnel and flume experiments collected above smooth, rough, and permeable-walls in the absence of buoyancy and Coriolis effects. These laboratory experiments form a necessary starting point to probe the canonical structure of $Sk_w$ as they deal with a key limiting case (i.e. near-neutral conditions) that has received much less attention compared to its convective counterpart in atmospheric turbulence studies. Diagnostic models based on cumulant expansions, realizability constraints, and the now-popular constant mass flux approach routinely employed in the convective boundary layer as well as prognostic models based on third-order budgets are used to explain variations in $Sk_w$ for the idealized laboratory conditions. The failure of flux-gradient relations to model $Sk_w$ from the gradients of the vertical velocity variance $\sigma_w^2$ are explained and corrections based on models of energy transport offered. Novel links between the diagnostic and prognostic models are also featured, especially for the inertial term in the third order budget of the vertical velocity fluctuation. The co-spectral properties of $w'/\sigma_w$ versus $w'^2/\sigma_w^2$ are also presented for the first time to assess the dominant scales governing $Sk_w$ in the inner and outer layers, where $w'$ is the fluctuating vertical velocity and $\sigma_w$ is the vertical velocity standard deviation.

physics.ao-ph↗

arXiv2024

The vertical-velocity skewness in the inertial sublayer of turbulent wall flows

We provide empirical evidence that within the inertial sub layer of adiabatic turbulent flows over smooth walls, the skewness of the vertical velocity component $Sk_w$ displays universal behaviour, being constant and constrained within the range $Sk_w \approx 0.1-0.16$, regardless of flow configuration and Reynolds number. A theoretical model is proposed to explain the observed behaviour, including the observed range of variations of $Sk_w$. The model clarifies why $Sk_w$ cannot be predicted from down-gradient closure approximations routinely employed in meteorological and climate models whereby $Sk_w$ impacts cloud formation and dispersion processes. The model also offers an alternative and implementable approach.

physics.flu-dyn↗

arXiv2024

Stochastic modelling of the instantaneous velocity profile in rough-wall turbulent boundary layers

The statistical properties of Uniform Momentum Zones (UMZs) are extracted from laboratory and field measurements in rough wall turbulent boundary layers to formulate a set of stochastic models for the simulation of instantaneous velocity profiles. A spatio-temporally resolved velocity dataset, covering a field of view of $8 \times 9$ m$^2$, was obtained in the atmospheric surface layer using super-large-scale particle image velocimetry (SLPIV), as part of the Grand-scale Atmospheric Imaging Apparatus (GAIA). Wind tunnel data from a previous study are included for comparison \citep{heisel2020mixing}. The probability density function of UMZ attributes such as their thickness, modal velocity, and averaged vertical velocity are built at varying elevations and modeled using log-normal and Gaussian distributions. Inverse transform sampling of the distributions is used to generate synthetic step-like velocity profiles that are spatially and temporally uncorrelated. Results show that in the wide range of wall-normal distances and $Re_\tau$ up to $ \sim O(10^6)$ investigated here, shear velocity scaling is manifested in the velocity jump across shear interfaces between adjacent UMZs, and attached eddy behavior is observed in the linear proportionality between UMZ thickness and their wall normal location. These very same characteristics are recovered in the generated instantaneous profiles, using both a fully stochastic and a data-driven hybrid stochastic models, which address, in different ways, the coupling between modal velocities and UMZ thickness. Our method provides a stochastic approach for generating an ensemble of instantaneous velocity profiles, consistent with the structural organization of UMZs, where the ensemble reproduces the logarithmic mean velocity profile and recovers significant portions of the Reynolds stresses and thus of the streamwise and vertical velocity variability.

physics.flu-dyn↗

arXiv2023

On the departure from Monin-Obukhov surface similarity and transition to the convective mixed layer

Large-eddy simulations are used to evaluate mean profile similarity in the convective boundary layer (CBL). Particular care is taken regarding the grid sensitivity of the profiles and the mitigation of inertial oscillations in the simulation spin-up. The nondimensional gradients $\phi$ for wind speed and air temperature generally align with Monin-Obukhov similarity across cases but have a steeper slope than predicted within each profile. The same trend has been noted in several other recent studies. The Businger-Dyer relations are modified here with an exponential cutoff term to account for the decay in $\phi$ to first-order approximation, yielding improved similarity from approximately 0.05$z_i$ to above 0.3$z_i$, where $z_i$ is the CBL depth. The necessity for the exponential correction is attributed to an extended transition from surface scaling to zero gradient in the mixed layer, where the departure from Monin-Obukhov similarity may be negligible at the surface but becomes substantial well below the conventional surface layer height of 0.1$z_i$.

physics.flu-dyn↗

arXiv2022

Evidence of mixed scaling for mean profile similarity in the stable atmospheric surface layer

A new mixed scaling parameter $Z=z/\sqrt{Lh}$ is proposed for similarity in the stable atmospheric surface layer, where $z$ is the height, $L$ is the Obukhov length, and $h$ is the boundary layer depth. Compared to the parameter $\zeta = z/L$ from Monin-Obukhov similarity theory (MOST), the new parameter $Z$ leads to improved mean profile similarity for wind speed and air temperature in large-eddy simulations. It also yields the same linear similarity relation for CASES-99 field measurements, including in the strongly stable (but still turbulent) regime where large deviations from MOST are observed. Results further suggest that similarity for turbulent energy dissipation rate depends on both $Z$ and $\zeta$. The proposed mixed scaling of $Z$ and relevance of $h$ can be explained by physical arguments related to the limit of z-less stratification that is reached asymptotically above the surface layer. While the presented evidence and fitted similarity relations are promising, the results and arguments are limited to a small sample of idealized stationary stable boundary layers. Corroboration is needed from independent datasets and analyses, including for complex and transient conditions not tested here.

physics.ao-ph↗

arXiv2022

Turbulence organization and mean profile shapes in the stably stratified boundary layer: zones of uniform momentum and air temperature

A persistent spatial organization of eddies is identified in the lowest portion of the stably-stratified planetary boundary layer. The analysis uses flow realizations from published large-eddy simulations (Sullivan et al., J Atmos Sci 73(4):1815-1840, 2016) ranging in stability from neutral to nearly z-less stratification. The coherent turbulent structure is well approximated as a series of uniform momentum zones (UMZs) and uniform temperature zones (UTZs) separated by thin layers of intense gradients that are significantly greater than the mean. This pattern yields stairstep-like instantaneous flow profiles whose shape is distinct from the mean profiles that emerge from long-term averaging. However, the scaling of the stairstep organization is closely related to the resulting mean profiles. The differences in velocity and temperature across the thin gradient layers remain proportional to the surface momentum and heat flux conditions regardless of stratification. The vertical thickness of UMZs and UTZs is proportional to height above the surface for neutral and weak stratification, but becomes thinner and less dependent on height as the stability increases. Deviations from the logarithmic mean profiles for velocity and temperature observed under neutral conditions are therefore predominately due to the reduction in zone size with increasing stratification, which is empirically captured by existing Monin-Obukhov similarity relations for momentum and heat. The zone properties are additionally used to explain trends in the turbulent Prandtl number, thus providing a connection between the eddy organization, mean profiles, and turbulent diffusivity in stably stratified conditions.

physics.flu-dyn↗

arXiv2021

Self-similar geometries within the inertial subrange of scales in boundary layer turbulence

The inertial subrange of turbulent scales is commonly reflected by a power law signature in ensemble statistics such as the energy spectrum and structure functions - both in theory and from observations. Despite promising findings on the topic of fractal geometries in turbulence, there is no accepted image for the physical flow features corresponding to this statistical signature in the inertial subrange. The present study uses boundary layer turbulence measurements to evaluate the self-similar geometric properties of velocity isosurfaces and investigate their influence on statistics for the velocity signal. The fractal dimension of streamwise velocity isosurfaces, indicating statistical self-similarity in the size of "wrinkles" along each isosurface, is shown to be constant only within the inertial subrange of scales. For the transition between the inertial subrange and production range, it is inferred that the largest wrinkles become increasingly confined by the overall size of large-scale coherent velocity regions such as uniform momentum zones. The self-similarity of isosurfaces yields power law trends in subsequent one-dimensional statistics. For instance, the theoretical 2/3 power law exponent for the structure function can be recovered by considering the collective behavior of numerous isosurface level sets. The results suggest that the physical presence of inertial subrange eddies is manifested in the self-similar wrinkles of isosurfaces.

physics.flu-dyn↗

arXiv2021

Effect of finite Reynolds number on self-similar crossing statistics and fractal measurements in turbulence

Stochastic simulations are used to create synthetic one-dimensional telegraph approximation (TA) signals based on turbulent zero crossings, where the interval between crossings is governed by a power law probability distribution with exponent $\alpha$. The power law exponent is determined for statistics of simulated TA signals, namely the box-counting fractal dimension $D_1$, energy spectrum exponent $\beta_{TA}$, and an intermittency exponent $\mu_{TA}$. For the binary TA signal with no variability in amplitude, the parameters are related linearly as $D_1 = 2 - \beta_{TA} = 1 - \mu_{TA}$. The relations are unchanged if the crossing interval distribution has a finite power law region (i.e. inertial subrange) representing a flow with finite Reynolds number. However, the finite distribution yields statistics that are not truly scale-invariant, and distorts the linear relation between the statistic exponents and $\alpha$. The behavior is due to finite-size effects apparent from the survival function, or the complementary cumulative distribution, which for finite Reynolds number is only approximately self-similar and has an effective exponent differing from $\alpha$. An expression presented for the effective exponent recovers the expected relations between $\alpha$ and the TA statistics. The findings demonstrate how a finite Reynolds number can affect indicators of self-similarity, fractality, and intermittency observed from single-point measurements.

physics.data-an↗

arXiv2020

Settling and Clustering of Snow Particles in Atmospheric Turbulence

The effect of turbulence on snow precipitation is not incorporated into present weather forecasting models. Here we show evidence that turbulence is in fact a key influence on both fall speed and spatial distribution of settling snow. We consider three snowfall events under vastly different levels of atmospheric turbulence. We characterize the size and morphology of the snow particles, and we simultaneously image their velocity, acceleration, and relative concentration over vertical planes about 30 m2 in area. We find that turbulence-driven settling enhancement explains otherwise contradictory trends between the particle size and velocity. The estimates of the Stokes number and the correlation between vertical velocity and local concentration indicate that the enhanced settling is rooted in the preferential sweeping mechanism. When the snow vertical velocity is large compared to the characteristic turbulence velocity, the crossing trajectories effect results in strong accelerations. When the conditions of preferential sweeping are met, the concentration field is highly non-uniform and clustering appears over a wide range of scales. These clusters, identified for the first time in a naturally occurring flow, display the signature features seen in canonical settings: power-law size distribution, fractal-like shape, vertical elongation, and large fall speed that increases with the cluster size. These findings demonstrate that the fundamental phenomenology of particle-laden turbulence can be leveraged towards a better predictive understanding of snow precipitation and ground snow accumulation. They also demonstrate how environmental flows can be used to investigate dispersed multiphase flows at Reynolds numbers not accessible in laboratory experiments or numerical simulations.

physics.flu-dyn↗

arXiv2019

On the mixing length eddies and logarithmic mean velocity profile in wall turbulence

Since the introduction of the logarithmic law of the wall more than 80 years ago, the equation for the mean velocity profile in turbulent boundary layers has been widely applied to model near-surface processes and parameterise surface drag. Yet the hypothetical turbulent eddies proposed in the original logarithmic law derivation and mixing length theory of Prandtl have never been conclusively linked to physical features in the flow. Here, we present evidence that suggests these eddies correspond to regions of coherent streamwise momentum known as uniform momentum zones (UMZs). The arrangement of UMZs results in a step-like shape for the instantaneous velocity profile, and the smooth mean profile results from the average UMZ properties, which are shown to scale with the friction velocity and wall-normal distance in the logarithmic region. These findings are confirmed across a wide range of Reynolds number and surface roughness conditions from the laboratory scale to the atmospheric surface layer.

physics.flu-dyn↗