Some statistical properties of small scale turbulence in an atmospheric boundary layer

1970 ◽  
Vol 41 (1) ◽  
pp. 141-152 ◽  
Author(s):  
R. W. Stewart ◽  
J. R. Wilson ◽  
R. W. Burling
Keyword(s):  
Boundary Layer ◽  
Lognormal Distribution ◽  
A Priori ◽  
Inertial Subrange ◽  
Small Scale ◽  
Order Structure ◽  
Third Order ◽  
The Difference ◽  
Scale Turbulence ◽  
Derivatives Of

Derivatives of velocity signals obtained in a turbulent boundary layer are examined for correspondence to the lognormal distribution. It is found that there is rough agreement but that unlikely events at high values are much less common in the observed fields than would be inferred from the lognormal distribution. The actual distributions correspond more to those obtained from a random walk with a limited number of steps, so the difference between these distributions and the lognormal may be related to the fact that the Reynolds number is finite.The third-order structure function is examined, and found to be roughly consistent with the existence of an inertial subrange of a Kolmogoroff equilibrium reacute;gime over a range of scale which is a priori reasonable but which is far less extensive than the $-\frac{5}{3}$ region of the spectrum.

Structure functions of turbulence in the atmospheric boundary layer over the ocean

1970 ◽  
Vol 44 (1) ◽  
pp. 145-159 ◽  
Author(s):  
C. W. Van Atta ◽  
W. Y. Chen
Keyword(s):  
Boundary Layer ◽  
Atmospheric Boundary Layer ◽  
Fourth Order ◽  
Structure Functions ◽  
Inertial Subrange ◽  
Order Structure ◽  
Third Order ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Order Quantities

Structure functions of turbulent velocity fluctuations up to fourth order have been measured at several heights in the atmospheric boundary layer over the open ocean, and the results are compared with theoretical predictions for separations in the inertial subrange. The behaviour of second- and third-order quantities shows substantial agreement with the predictions of Kolmogorov's original theory over a wide range of separations, but the results of a recent modification of the theory, attempting to account for intermittency in the local dissipation rate, are also consistent with the data over somewhat shorter separation intervals. The behaviour of the measured fourth-order structure function disagrees with that predicted from Kolmogorov's original work, but good agreement is found with the results of the modified theory.

Observations of Small-Scale Turbulence and Energy Dissipation Rates in the Cloudy Boundary Layer

2006 ◽  
Vol 63 (5) ◽  
pp. 1451-1466 ◽  
Author(s):  
Holger Siebert ◽  
Katrin Lehmann ◽  
Manfred Wendisch
Keyword(s):  
Boundary Layer ◽  
Energy Dissipation ◽  
Wind Velocity ◽  
Turbulence Theory ◽  
Horizontal Wind ◽  
Inertial Subrange ◽  
Intermittent Flow ◽  
Small Scale ◽  
Dissipation Rates ◽  
Wide Range

Abstract Tethered balloon–borne measurements with a resolution in the order of 10 cm in a cloudy boundary layer are presented. Two examples sampled under different conditions concerning the clouds' stage of life are discussed. The hypothesis tested here is that basic ideas of classical turbulence theory in boundary layer clouds are valid even to the decimeter scale. Power spectral densities S( f ) of air temperature, liquid water content, and wind velocity components show an inertial subrange behavior down to ≈20 cm. The mean energy dissipation rates are ∼10−3 m2 s−3 for both datasets. Estimated Taylor Reynolds numbers (Reλ) are ∼104, which indicates the turbulence is fully developed. The ratios between longitudinal and transversal S( f ) converge to a value close to 4/3, which is predicted by classical turbulence theory for local isotropic conditions. Probability density functions (PDFs) of wind velocity increments Δu are derived. The PDFs show significant deviations from a Gaussian distribution with longer tails typical for an intermittent flow. Local energy dissipation rates ɛτ are derived from subsequences with a duration of τ = 1 s. With a mean horizontal wind velocity of 8 m s−1, τ corresponds to a spatial scale of 8 m. The PDFs of ɛτ can be well approximated with a lognormal distribution that agrees with classical theory. Maximum values of ɛτ ≈ 10−1 m2 s−3 are found in the analyzed clouds. The consequences of this wide range of ɛτ values for particle–turbulence interaction are discussed.

Aero-optics of subsonic turbulent boundary layers

2012 ◽  
Vol 696 ◽  
pp. 122-151 ◽  
Author(s):  
Kan Wang ◽  
Meng Wang
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Dominant Role ◽  
Elevation Angle ◽  
Turbulent Boundary Layers ◽  
Density Field ◽  
Small Scale ◽  
Number Range ◽  
Scale Turbulence

AbstractCompressible large-eddy simulations are carried out to study the aero-optical distortions caused by Mach 0.5 flat-plate turbulent boundary layers at Reynolds numbers of ${\mathit{Re}}_{\theta } = 875$, 1770 and 3550, based on momentum thickness. The fluctuations of refractive index are calculated from the density field, and wavefront distortions of an optical beam traversing the boundary layer are computed based on geometric optics. The effects of aperture size, small-scale turbulence, different flow regions and beam elevation angle are examined and the underlying flow physics is analysed. It is found that the level of optical distortion decreases with increasing Reynolds number within the Reynolds-number range considered. The contributions from the viscous sublayer and buffer layer are small, while the wake region plays a dominant role, followed by the logarithmic layer. By low-pass filtering the fluctuating density field, it is shown that small-scale turbulence is optically inactive. Consistent with previous experimental findings, the distortion magnitude is dependent on the propagation direction due to anisotropy of the boundary-layer vortical structures. Density correlations and length scales are analysed to understand the elevation-angle dependence and its relation to turbulence structures. The applicability of Sutton’s linking equation to boundary-layer flows is examined, and excellent agreement between linking equation predictions and directly integrated distortions is obtained when the density length scale is appropriately defined.

scholarly journals Modulation of Small-Scale Turbulence by Ducted Gravity Waves in the Nocturnal Boundary Layer

2008 ◽  
Vol 65 (4) ◽  
pp. 1414-1427 ◽  
Author(s):  
Y. P. Meillier ◽  
R. G. Frehlich ◽  
R. M. Jones ◽  
B. B. Balsley
Keyword(s):  
Boundary Layer ◽  
Gravity Waves ◽  
Richardson Number ◽  
Potential Temperature ◽  
Nocturnal Boundary Layer ◽  
Small Scale ◽  
Temperature Structure ◽  
Turbulence Measurements ◽  
Gradient Richardson Number ◽  
Scale Turbulence

Abstract Constant altitude measurements of temperature and velocity in the residual layer of the nocturnal boundary layer, collected by the Cooperative Institute for Research in Environmental Sciences (CIRES) Tethered Lifting System (TLS), exhibit fluctuations identified by previous work (Fritts et al.) as the signature of ducted gravity waves. The concurrent high-resolution TLS turbulence measurements (temperature structure constant C2T and turbulent kinetic energy dissipation rate ɛ) reveal the presence of patches of enhanced turbulence activity that are roughly synchronized with the troughs of the temperature and velocity fluctuations. To investigate the potentially dominant role ducted gravity waves might play on the modulation of atmospheric stability and therefore, on turbulence, time series of the wave-modulated gradient Richardson number (Ri) and of the vertical gradient of potential temperature ∂θ/∂z(t) are computed numerically and compared to the TLS small-scale turbulence measurements. The results of this study agree with the predictions of previous theoretical studies (i.e., wave-generated fluctuations of temperature and velocity modulate the gradient Richardson number), resulting in periodic enhancements of turbulence at Ri minima. The patches of turbulence observed in the TLS dataset are subsequently identified as convective instabilities generated locally within the unstable phase of the wave.

scholarly journals An analytical theory of the buoyancy–Kolmogorov subrange transition in turbulent flows with stable stratification

2013 ◽  
Vol 371 (1982) ◽  
pp. 20120212 ◽  
Author(s):  
Semion Sukoriansky ◽  
Boris Galperin
Keyword(s):  
Spatial Scales ◽  
Stable Stratification ◽  
Temperature Fields ◽  
Inertial Subrange ◽  
Langevin Equations ◽  
Small Scale ◽  
Recursive Procedure ◽  
Theoretical Understanding ◽  
Scale Turbulence ◽  
Buoyancy Subrange

The buoyancy subrange of stably stratified turbulence is defined as an intermediate range of scales larger than those in the inertial subrange. This subrange encompasses the crossover from internal gravity waves (IGWs) to small-scale turbulence. The energy exchange between the waves and small-scale turbulence is communicated across this subrange. At the same time, it features progressive anisotropization of flow characteristics on increasing spatial scales. Despite many observational and computational studies of the buoyancy subrange, its theoretical understanding has been lagging. This article presents an investigation of the buoyancy subrange using the quasi-normal scale elimination (QNSE) theory of turbulence. This spectral theory uses a recursive procedure of small-scale modes elimination based upon a quasi-normal mapping of the velocity and temperature fields using the Langevin equations. In the limit of weak stable stratification, the theory becomes completely analytical and yields simple expressions for horizontal and vertical eddy viscosities and eddy diffusivities. In addition, the theory provides expressions for various one-dimensional spectra that quantify turbulence anisotropization. The theory reveals how the dispersion relation for IGWs is modified by turbulence, thus alleviating many unique waves' features. Predictions of the QNSE theory for the buoyancy subrange are shown to agree well with various data.

Triadic scale interactions in a turbulent boundary layer

2015 ◽  
Vol 767 ◽  
Author(s):  
Subrahmanyam Duvvuri ◽  
Beverley J. McKeon
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Small Scale ◽  
Velocity Signal ◽  
Small Scales ◽  
Amplitude Modulation Coefficient ◽  
Scale Turbulence ◽  
Scale Motion ◽  
Phase Relationships

AbstractA formal relationship between the skewness and the correlation coefficient of large and small scales, termed the amplitude modulation coefficient, is established for a general statistically stationary signal and is analysed in the context of a turbulent velocity signal. Both the quantities are seen to be measures of phase in triadically consistent interactions between scales of turbulence. The naturally existing phase relationships between large and small scales in a turbulent boundary layer are then manipulated by exciting a synthetic large-scale motion in the flow using a spatially impulsive dynamic wall roughness perturbation. The synthetic scale is seen to alter the phase relationships, or the degree of modulation, in a quasi-deterministic manner by exhibiting a phase-organizing influence on the small scales. The results presented provide encouragement for the development of a practical framework for favourable manipulation of energetic small-scale turbulence through large-scale inputs in a wall-bounded turbulent flow.

Fractal reconstruction of the subgrid scales in turbulence models in applications to cloud microphysics

2020 ◽  
Author(s):  
Emmanuel Akinlabi ◽  
Marta Waclawczyk ◽  
Szymon Malinowski
Keyword(s):  
Climate Models ◽  
A Priori ◽  
Turbulence Models ◽  
Random Variable ◽  
Fractal Model ◽  
Cloud Microphysics ◽  
Small Scale ◽  
Mixing Processes ◽  
Subgrid Scales ◽  
Scale Turbulence

<p>Modelling of small-scale turbulence in the atmosphere play a significant role in improving our understanding of cloud processes, thereby contributing to the development of better parameterization of climate models. One of the important problems is related to the transport of cloud particles, their activation and growth, which are influenced by small-scale turbulence motions. The idea presented in this work is to use fractal interpolation to reconstruct structures which are typically not resolved in the Large Eddy Simulations (LES) of clouds. Known filtered values of velocities on LES are basis of the reconstruction. The reconstructed small scales depend on the stretching parameter <em>d</em>, which is related to the fractal dimension of the signal. In many previous studies, the stretching parameter values were assumed to be constant in space and time. We modify this approach by treating the stretching parameter as a random variable with a prescribed probability density function (pdf). This function can be determined from <em>a priori</em> analysis of numerical or experimental data and within a certain range of wavenumbers it has a universal form, independent of the Reynolds number. We show, such modification leads to improvement in terms of reconstruction of two-point statistics of turbulent velocities. Preliminary results of simulations with Lagrangian particles (superdroplets) in the reconstructed field show the fractal model properly mimics the turbulent mixing processes at subgrid scales.</p>

Passive Manipulation of Separation-Bubble Transition Using Surface Modifications

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Brian R. McAuliffe ◽  
Metin I. Yaras
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Layer ◽  
Separation Bubble ◽  
Surface Modifications ◽  
Small Scale ◽  
Two Dimensional ◽  
Vortex Pairing ◽  
Separated Shear Layer ◽  
Scale Turbulence

Through experiments using two-dimensional particle-image velocimetry (PIV), this paper examines the nature of transition in a separation bubble and manipulations of the resultant breakdown to turbulence through passive means of control. An airfoil was used that provides minimal variation in the separation location over a wide operating range, with various two-dimensional modifications made to the surface for the purpose of manipulating the transition process. The study was conducted under low-freestream-turbulence conditions over a flow Reynolds number range of 28,000–101,000 based on airfoil chord. The spatial nature of the measurements has allowed identification of the dominant flow structures associated with transition in the separated shear layer and the manipulations introduced by the surface modifications. The Kelvin–Helmholtz (K-H) instability is identified as the dominant transition mechanism in the separated shear layer, leading to the roll-up of spanwise vorticity and subsequent breakdown into small-scale turbulence. Similarities with planar free-shear layers are noted, including the frequency of maximum amplification rate for the K-H instability and the vortex-pairing phenomenon initiated by a subharmonic instability. In some cases, secondary pairing events are observed and result in a laminar intervortex region consisting of freestream fluid entrained toward the surface due to the strong circulation of the large-scale vortices. Results of the surface-modification study show that different physical mechanisms can be manipulated to affect the separation, transition, and reattachment processes over the airfoil. These manipulations are also shown to affect the boundary-layer losses observed downstream of reattachment, with all surface-indentation configurations providing decreased losses at the three lowest Reynolds numbers and three of the five configurations providing decreased losses at the highest Reynolds number. The primary mechanisms that provide these manipulations include: suppression of the vortex-pairing phenomenon, which reduces both the shear-layer thickness and the levels of small-scale turbulence; the promotion of smaller-scale turbulence, resulting from the disturbances generated upstream of separation, which provides quicker transition and shorter separation bubbles; the elimination of the separation bubble with transition occurring in an attached boundary layer; and physical disturbance, downstream of separation, of the growing instability waves to manipulate the vortical structures and cause quicker reattachment.

scholarly journals Dissipation of Turbulent Kinetic Energy in the Oscillating Bottom Boundary Layer of a Large Shallow Lake

2020 ◽  
Vol 37 (3) ◽  
pp. 517-531 ◽  
Author(s):  
Aidin Jabbari ◽  
Leon Boegman ◽  
Reza Valipour ◽  
Danielle Wain ◽  
Damien Bouffard
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Bottom Boundary Layer ◽  
Inertial Subrange ◽  
Order Structure ◽  
Inertial Method ◽  
Bottom Boundary ◽  
Law Of The Wall ◽  
Order Of Magnitude

AbstractMixing rates and biogeochemical fluxes are commonly estimated from the rate of dissipation of turbulent kinetic energy ε as measured with a single instrument and processing method. However, differences in measurements of ε between instruments/methods often vary by one order of magnitude. In an effort to identify error in computing ε, we have applied four common methods to data from the bottom boundary layer of Lake Erie. We applied the second-order structure function method (SFM) to velocity measurements from an acoustic Doppler current profiler, using both canonical and anisotropy-adjusted Kolmogorov constants, and compared the results with those computed from the law of the wall, Batchelor fitting to temperature gradient microstructure, and inertial subrange fitting to acoustic Doppler velocimeter data. The ε from anisotropy-adjusted constants in SFM increased by a factor of 6 or more at 0.2 m above the bed and showed a better agreement with microstructure and inertial method estimations. The maximum difference between SFM ε, computed using adjusted and canonical constants, and microstructure values was 25% and 50%, respectively. This difference was 30% and 55%, respectively, for those from inertial subrange fitting at times of high-intensity turbulence (Reynolds number at 1 m above the bed of more than 2 × 104). Comparison of the SFM ε to those from law of the wall was often poor, with errors as large as one order of magnitude. From the considerable improvement in ε estimates near the bed, anisotropy-adjusted Kolmogorov constants should be applied to compute dissipation in geophysical boundary layers.

scholarly journals Atmospheric Boundary Layer Structure and Turbulence during Sea Fog on the Southern China Coast

2015 ◽  
Vol 143 (5) ◽  
pp. 1907-1923 ◽  
Author(s):  
Huijun Huang ◽  
Hongnian Liu ◽  
Jian Huang ◽  
Weikang Mao ◽  
Xueyan Bi
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Latent Heat ◽  
Layer Structure ◽  
Southern China ◽  
Small Scale ◽  
Warm Advection ◽  
Thermal Turbulence ◽  
Scale Turbulence ◽  
Advection Fog

Abstract Small-scale turbulence has an essential role in sea-fog formation and evolution, but is not completely understood. This study analyzes measurements of the small-scale turbulence, together with the boundary layer structure and the synoptic and mesoscale conditions over the life cycle of a cold advection fog event and a warm advection fog event, both off the coast of southern China. The measurement data come from two sites: one on the coast and one at sea. These findings include the following: 1) For cold advection fog, the top can extend above the inversion base, but formation of an overlaying cloud causes the fog to dissipate. 2) For warm advection fog, two layers of low cloud can merge to form deep fog, with the depth exceeding 1000 m, when strong advection of warm moist air produces active thermal-turbulence mixing above the thermal-turbulence interface. 3) Turbulence near the sea surface is mainly thermally driven for cold advection fog, but mechanically driven for warm advection fog. 4) The momentum fluxes of both fog cases are below 0.04 kg m−1 s−2. However, the sensible and latent heat flux differ between the cases: in the cold advection fog case, the sensible and latent heat fluxes are roughly upward, averaging 2.58 and 26.75 W m−2, respectively; however, in the warm advection fog case, the sensible and latent heat flux are mostly downward, averaging −6.98 and −6.22 W m−2, respectively. 5) Low-level vertical advection is important for both fogs, but has a larger influence on fog development in the warm advection fog case.

Sign in / Sign up

Export Citation Format

Share Document