Estimation of mean turbulent kinetic energy and temperature variance dissipation rates using a spectral chart method

2020 ◽  
Vol 32 (5) ◽  
pp. 055109
Author(s):  
Jean Lemay ◽  
Lyazid Djenidi ◽  
Robert Antonia
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Temperature Variance ◽  
Dissipation Rates

scholarly journals Resolved and subgrid dynamics of Rayleigh–Bénard convection

2019 ◽  
Vol 867 ◽  
pp. 906-933 ◽  
Author(s):  
Riccardo Togni ◽  
Andrea Cimarelli ◽  
Elisabetta De Angelis
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Theoretical Framework ◽  
Temperature Fields ◽  
Temperature Variance ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Subgrid Scales ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

In this work we present and demonstrate the reliability of a theoretical framework for the study of thermally driven turbulence. It consists of scale-by-scale budget equations for the second-order velocity and temperature structure functions and their limiting cases, represented by the turbulent kinetic energy and temperature variance budgets. This framework represents an extension of the classical Kolmogorov and Yaglom equations to inhomogeneous and anisotropic flows, and allows for a novel assessment of the turbulent processes occurring at different scales and locations in the fluid domain. Two relevant characteristic scales, $\ell _{c}^{u}$ for the velocity field and $\ell _{c}^{\unicode[STIX]{x1D703}}$ for the temperature field, are identified. These variables separate the space of scales into a quasi-homogeneous range, characterized by turbulent kinetic energy and temperature variance cascades towards dissipation, and an inhomogeneity-dominated range, where the production and the transport in physical space are important. This theoretical framework is then extended to the context of large-eddy simulation to quantify the effect of a low-pass filtering operation on both resolved and subgrid dynamics of turbulent Rayleigh–Bénard convection. It consists of single-point and scale-by-scale budget equations for the filtered velocity and temperature fields. To evaluate the effect of the filter length $\ell _{F}$ on the resolved and subgrid dynamics, the velocity and temperature fields obtained from a direct numerical simulation are split into filtered and residual components using a spectral cutoff filter. It is found that when $\ell _{F}$ is smaller than the minimum values of the cross-over scales given by $\ell _{c,min}^{\unicode[STIX]{x1D703}\ast }=\ell _{c,min}^{\unicode[STIX]{x1D703}}Nu/H=0.8$, the resolved processes correspond to the exact ones, except for a depletion of viscous and thermal dissipations, and the only role of the subgrid scales is to drain turbulent kinetic energy and temperature variance to dissipate them. On the other hand, the resolved dynamics is much poorer in the near-wall region and the effects of the subgrid scales are more complex for filter lengths of the order of $\ell _{F}\approx 3\ell _{c,min}^{\unicode[STIX]{x1D703}}$ or larger. This study suggests that classic eddy-viscosity/diffusivity models employed in large-eddy simulation may suffer from some limitations for large filter lengths, and that alternative closures should be considered to account for the inhomogeneous processes at subgrid level. Moreover, the theoretical framework based on the filtered Kolmogorov and Yaglom equations may represent a valuable tool for future assessments of the subgrid-scale models.

scholarly journals Diffusional and accretional growth of water drops in a rising adiabatic parcel: effects of the turbulent collision kernel

2009 ◽  
Vol 9 (7) ◽  
pp. 2335-2353 ◽  
Author(s):  
W. W. Grabowski ◽  
L.-P. Wang
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Collision Kernel ◽  
Small Scale ◽  
Large Set ◽  
Initiation Time ◽  
Cloud Droplets ◽  
Dissipation Rates ◽  
Speedup Factor

Abstract. A large set of rising adiabatic parcel simulations is executed to investigate the combined diffusional and accretional growth of cloud droplets in maritime and continental conditions, and to assess the impact of enhanced droplet collisions due to small-scale cloud turbulence. The microphysical model applies the droplet number density function to represent spectral evolution of cloud and rain/drizzle drops, and various numbers of bins in the numerical implementation, ranging from 40 to 320. Simulations are performed applying two traditional gravitational collection kernels and two kernels representing collisions of cloud droplets in the turbulent environment, with turbulent kinetic energy dissipation rates of 100 and 400 cm2 s−3. The overall result is that the rain initiation time significantly depends on the number of bins used, with earlier initiation of rain when the number of bins is low. This is explained as a combination of the increase of the width of activated droplet spectrum and enhanced numerical spreading of the spectrum during diffusional and collisional growth when the number of model bins is low. Simulations applying around 300 bins seem to produce rain at times which no longer depend on the number of bins, but the activation spectra are unrealistically narrow. These results call for an improved representation of droplet activation in numerical models of the type used in this study. Despite the numerical effects that impact the rain initiation time in different simulations, the turbulent speedup factor, the ratio of the rain initiation time for the turbulent collection kernel and the corresponding time for the gravitational kernel, is approximately independent of aerosol characteristics, parcel vertical velocity, and the number of bins used in the numerical model. The turbulent speedup factor is in the range 0.75–0.85 and 0.60–0.75 for the turbulent kinetic energy dissipation rates of 100 and 400 cm2 s−3, respectively.

scholarly journals Rates of Dissipation of Turbulent Kinetic Energy in a High Reynolds Number Tidal Channel

2016 ◽  
Vol 33 (4) ◽  
pp. 817-837 ◽  
Author(s):  
Justine M. McMillan ◽  
Alex E. Hay ◽  
Rolf G. Lueck ◽  
Fabian Wolk
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
High Speed ◽  
Flow Speed ◽  
Small Scale ◽  
Tidal Channel ◽  
Dissipation Rates ◽  
Channel Separation ◽  
Shear Probe

AbstractThe ability to estimate the rate of dissipation (ε) of turbulent kinetic energy at middepth in a high-speed tidal channel using broadband acoustic Doppler current profilers (ADCPs) is assessed by making comparisons to direct measurements of ε obtained using shear probes mounted on a streamlined underwater buoy. The investigation was carried out in Grand Passage, Nova Scotia, Canada, where the depth-averaged flow speed reached 2 m s−1 and the Reynolds number was 8 × 107. The speed bin–averaged dissipation rates estimated from the ADCP data agree with the shear probe data to within a factor of 2. Both the ADCP and the shear probe measurements indicate a linear dependence of ε on the cube of the flow speed during flood and much lower dissipation rates during ebb. The ebb–flood asymmetry and the small-scale intermittency in ε are also apparent in the lognormal distributions of the shear probe data. Possible sources of bias and error in the ε estimates are investigated, and the most likely causes of the discrepancy between the ADCP and shear probe estimates are the cross-channel separation of the instruments and the high degree of spatial variability that exists in the channel.

scholarly journals Diffusional and accretional growth of water drops in a rising adiabatic parcel: effects of the turbulent collision kernel

2008 ◽  
Vol 8 (4) ◽  
pp. 14717-14763 ◽  
Author(s):  
W. W. Grabowski ◽  
L.-P. Wang
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Collision Kernel ◽  
Small Scale ◽  
Large Set ◽  
Initiation Time ◽  
Cloud Droplets ◽  
Dissipation Rates ◽  
Speedup Factor

Abstract. A large set of rising adiabatic parcel simulations is executed to investigate the combined diffusional and accretional growth of cloud droplets in maritime and continental conditions, and to assess the impact of enhanced droplet collisions due to small-scale cloud turbulence. The microphysical model applies the droplet number density function to represent spectral evolution of cloud and rain/drizzle drops, and various numbers of bins in the numerical implementation, ranging from 40 to 320. Simulations are performed applying two traditional gravitational collection kernels and two kernels representing collisions of cloud droplets in the turbulent environment, with turbulent kinetic energy dissipation rates of 100 and 400 cm2 s−3. The overall result is that the rain initiation time significantly depends on the number of bins used, with earlier initiation of rain when the number of bins is low. This is explained as a combination of the increase of the width of activated droplet spectrum and enhanced numerical spreading of the spectrum during diffusional and collisional growth when the number of model bins is low. Simulations applying around 300 bins seem to produce rain at times which no longer depend on the number of bins, but the activation spectra are unrealistically narrow. These results call for an improved representation of droplet activation in numerical models of the type used in this study. Despite the numerical effects that impact the rain initiation time in different simulations, the turbulent speedup factor, the ratio of the rain initiation time for the turbulent collection kernel and the corresponding time for the gravitational kernel, is approximately independent of aerosol characteristics, parcel vertical velocity, and the number of bins used in the numerical model. The turbulent speedup factor is in the range 0.75–0.85 and 0.60–0.75 for the turbulent kinetic energy dissipation rates of 100 and 400 cm2 s−3, respectively.

A Near-Wall Eddy Conductivity Model for Fluids With Different Prandtl Numbers

1994 ◽  
Vol 116 (4) ◽  
pp. 844-854 ◽  
Author(s):  
R. M. C. So ◽  
T. P. Sommer
Keyword(s):  
Kinetic Energy ◽  
Prandtl Number ◽  
Turbulent Kinetic Energy ◽  
Dissipation Rate ◽  
Reynolds Numbers ◽  
Turbulence Statistics ◽  
Temperature Variance ◽  
Prandtl Numbers ◽  
Good Agreement ◽  
Near Wall

Near-wall turbulence models for the velocity and temperature fields based on the transport equations for the Reynolds stresses, the dissipation rate of turbulent kinetic energy, and the temperature variance and its dissipation rate are formulated for flows with widely different Prandtl numbers. Conventional high-Reynolds-number models are used to close these equations and modifications are proposed to render them asymptotically correct near a wall compared to the behavior of the corresponding exact equations. Thus formulated, two additional constants are introduced into the definition of the eddy conductivity. These constants are found to be parametric in the Prandtl number. The near-wall models are used to calculate flows with different wall thermal boundary conditions covering a wide range of Reynolds numbers and Prandtl numbers. The calculated Nusselt number variations with Prandtl number are in good agreement with established formulae at two different Reynolds numbers. Furthermore, the mean profiles, turbulence statistics, heat flux, temperature variance, and the dissipation rates of turbulent kinetic energy and temperature variance are compared with measurements and direct numerical simulation data. These comparisons show that correct near-wall asymptotic behavior is recovered for the calculated turbulence statistics and the calculations are in good agreement with measurements over the range of Prandtl numbers investigated.

Thermal-Fluid Transport Phenomena in Concentric Annulus With Inner Core Rotation Under Strong Heating

2000 ◽  
Author(s):  
Shuichi Torii ◽  
Wen-Jei Yang
Keyword(s):  
Heat Transfer ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Fluid Transport ◽  
Inner Core ◽  
Outer Cylinder ◽  
Temperature Variance ◽  
Concentric Annulus ◽  
Core Rotation ◽  
Inner Core Rotation

Abstract A numerical study is performed to investigate thermal-fluid transport phenomena in a concentric annulus, in which an axially rotating inner cylinder and stationary outer cylinder are strongly heated under the same heat flux. The anisotropic t 2 ¯ -εt heat-transfer model is employed to determine thermal eddy diffusivity. When the inner cylinder is at rest, the turbulent kinetic energy and temperature variance over the whole cross-section in the flow and thermal fields substantially diminish along the flow, resulting in laminartization, i.e., a deterioration in heat transfer performance at the inner and outer cylinder walls. By contrast, a substantial reduction in the turbulent kinetic energy and temperature variance in the laminarzing flow are suppressed in the presence of inner core rotation. In other words, an inner core rotation contributes to a suppression of laminarization of the strongly heated gas flow.

Doppler spectral width studies from polar mesospheric summer echoes

2020 ◽  
Author(s):  
Nikoloz Gudadze ◽  
Gunter Stober ◽  
Hubert Luce ◽  
Jorge Luis Chau
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Spectral Width ◽  
Target Area ◽  
Fundamental Parameter ◽  
Dissipation Rates ◽  
Summer Echoes ◽  
Width Measurements ◽  
Fossil Turbulence

<p>Investigation of turbulence in the polar mesopause is essential for a better understanding of dynamical or mixing processes in the region. Polar Mesospheric Summer Echoes (PMSEs), occurring at mesopause altitudes during the summer season, are known to be a result of turbulence-induced fluctuations in the refractive index. The presence of ice particles controls and reduce the free-electron diffusivity in D region plasma, which in turn leads to complex, strong radar echoes at very high frequencies.</p><p>Often, Doppler spectral width of radar measurements are associated with the strength of turbulence in the target area and traditionally used to estimate turbulent kinetic energy dissipation rates, a fundamental parameter of the turbulence processes. Besides the cooling of summer mesopause region induced by GW drag, the turbulence produced by GW breaking contributes to the total energy budget due to release of turbulent kinetic energy to heat. We use PMSE spectral width measurements observed by Middle Atmosphere Alomar Radar System (MAARSY) during summer of 2016 to study their summer temporal mean profiles as well as temporal evolution and connection to the atmospheric turbulence at PMSE altitudes - 80 and 90 km. The current theoretical models suggest that the radar reflectivity should correlate to the strength of the turbulence; however, such a relation is mainly observed for the weaker PMSEs. The mean summer behaviour of estimated turbulent kinetic energy dissipation rates shows an increase from lower altitudes up to 90 km. It should be noticed that spectral width measurements contain additional broadening rather than turbulence, so derived energy dissipation rates are “upper values” than expected from pure turbulence. The results are still slightly lower than those known from climatology obtained from rocket soundings, mostly at altitudes close to the maximum occurrence of PMSE, 86-87 km.</p><p>We discuss a possible consequence of spectral width measurements under strong PMSEs. In such conditions, the strength of the echo does not correlate with the turbulence intensity, and the observed spectral width is weaker. However, the uniform distribution of spectral width values throughout the echo power is expected from the present theoretical understandings. Based on previous studies, strong PMSEs can also be observed during fossil turbulence. The interpretation of connection the spectral with measurements under fossil turbulence with the turbulence energy dissipation rates and the possibility of using PMSEs for the turbulence studies will be discussed.</p>

The Budget of Turbulent Kinetic Energy during Premonsoon Season over Kharagpur as Revealed by STORM Experimental Data

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Bhishma Tyagi ◽  
A. N. V. Satyanarayana
Keyword(s):  
Experimental Data ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Atmospheric Stability ◽  
Regional Modeling ◽  
Severe Thunderstorms ◽  
Dissipation Rates ◽  
Turbulence Data ◽  
Neutral Conditions ◽  
Tropical Station

Turbulent kinetic energy (TKE) budget variations during thunderstorm days (TD) and nonthunderstorm days (NTD) of premonsoon seasons of 2007, 2009, and 2010 have been investigated at a tropical station Kharagpur (22°30′N, 87°20′E) using the surface layer turbulence data obtained during severe thunderstorms-observations and regional modeling (STORM) experiment. Significant variations in the contributions of the TKE budget parameters with respect to stability are observed on these contrasting days of weather activity. In highly unstable conditions, smaller dissipation rates are seen on TD compared to NTD, while approaching near neutral conditions, higher dissipation rates are found in TD. New relationships between TKE dissipation rates with respect to atmospheric stability are proposed at Kharagpur for TD and NTD.

Intermittency in Estuarine Turbulence: A Framework toward Limiting Bias in Microstructure Measurements

2019 ◽  
Vol 36 (10) ◽  
pp. 1917-1932 ◽  
Author(s):  
Kimberly Huguenard ◽  
Kris Bears ◽  
Brandon Lieberthal
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Time Scales ◽  
Small Scale ◽  
Field Sampling ◽  
Intermittent Turbulence ◽  
Statistical Framework ◽  
Dissipation Rates ◽  
Multiple Comparison Test ◽  
Microstructure Measurements

AbstractIntermittent turbulence behavior has a number of implications for field sampling, namely, that if undersampled, it can result in over- or underestimates of turbulent kinetic energy (TKE) dissipation rates. Sampling thresholds and common distributions have previously been defined for oceanic environments, but estuaries remain relatively underrepresented. Utilizing vertical microstructure profilers is a robust way to directly measure TKE dissipation rates; however, microstructure sensors are delicate and conducting a limited number of profiles in a burst is desirable. In this work, a statistical framework is used to characterize intermittency in a partially mixed estuary. In particular, a multiple comparison test is proposed to evaluate the number of profiles required to sufficiently represent TKE dissipation averages. The technique is tested on a microstructure dataset from the Damariscotta River in Maine, which covers seasonal and fortnightly time scales. The Damariscotta River features a variety of bathymetric and channel complexities, which provide the opportunity to examine intermittency as it relates to different processes. Small-scale intermittency is prominent during stratified conditions in shallow locations as well as near channel-shoal morphology, channel bends, and constrictions.

Sign in / Sign up

Export Citation Format

Share Document