scholarly journals Scale-similar structures of homogeneous isotropic non-mirror-symmetric turbulence based on the Lagrangian closure theory

2021 ◽  
Vol 926 ◽  
Author(s):  
Kazuhiro Inagaki
Keyword(s):  
Response Function ◽  
Time Scale ◽  
Dissipation Rate ◽  
Power Laws ◽  
Energy Cascade ◽  
Small Scale ◽  
Cascade Process ◽  
Velocity Correlation ◽  
Similar Range ◽  
Closure Theory

We investigate the effect of helicity on the scale-similar structures of homogeneous isotropic and non-mirror-symmetric turbulence based on the Lagrangian renormalised approximation (LRA), which is a self-consistent closure theory proposed by Kaneda (J. Fluid Mech., vol. 107, 1981, pp. 131–145). In this study, we focus on the time scale representing the scale-similar range. For the LRA, the Lagrangian two-time velocity correlation and response function determine the representative time scale. The LRA predicts that both the Lagrangian two-time velocity correlation and response function equation do not explicitly depend on helicity. We assume the extended scale-similar spectra and time scale by considering the helicity dissipation rate. Considering the small-scale structures, the requirements for the energy and helicity fluxes and response function equation to be scale similar, yield the conventional inertial-range power laws and provide the energy and helicity spectra $\propto k^{-5/3}$ and the time scale $\propto \varepsilon ^{-1/3} k^{-2/3}$ , where $\varepsilon$ and $k$ denote the energy dissipation rate and wavenumber, respectively. Notably, energy flux can be scale similar only when $k^H /k \ll 1$ , where $k^H = \varepsilon ^H/\varepsilon$ and $\varepsilon ^H$ denotes the helicity dissipation rate. This condition makes the energy cascade process in the scale-similar range completely independent of helicity. We also investigate the localness of the interscale interaction in the energy and helicity cascades for the LRA. We demonstrate that the helicity cascade is slightly non-local in scales compared with the energy cascade. This study provides a foundation on the modelling of non-mirror-symmetric turbulent flows.

Small-scale energy cascade in homogeneous isotropic turbulence

2019 ◽  
Vol 4 (10) ◽  
Author(s):  
Mohamad Ibrahim Cheikh ◽  
James Chen ◽  
Mingjun Wei
Keyword(s):  
Isotropic Turbulence ◽  
Energy Cascade ◽  
Small Scale ◽  
Homogeneous Isotropic Turbulence

scholarly journals Correlation between small-scale velocity and scalar fluctuations in a turbulent channel flow

2009 ◽  
Vol 627 ◽  
pp. 1-32 ◽  
Author(s):  
HIROYUKI ABE ◽  
ROBERT ANTHONY ANTONIA ◽  
HIROSHI KAWAMURA
Keyword(s):  
Strain Rate ◽  
Channel Flow ◽  
Dissipation Rate ◽  
Compressive Strain ◽  
Outer Region ◽  
Turbulent Channel Flow ◽  
Scalar Fields ◽  
Scalar Dissipation ◽  
Small Scale ◽  
Scalar Dissipation Rate

Direct numerical simulations of a turbulent channel flow with passive scalar transport are used to examine the relationship between small-scale velocity and scalar fields. The Reynolds number based on the friction velocity and the channel half-width is equal to 180, 395 and 640, and the molecular Prandtl number is 0.71. The focus is on the interrelationship between the components of the vorticity vector and those of the scalar derivative vector. Near the wall, there is close similarity between different components of the two vectors due to the almost perfect correspondence between the momentum and thermal streaks. With increasing distance from the wall, the magnitudes of the correlations become smaller but remain non-negligible everywhere in the channel owing to the presence of internal shear and scalar layers in the inner region and the backs of the large-scale motions in the outer region. The topology of the scalar dissipation rate, which is important for small-scale scalar mixing, is shown to be associated with the organized structures. The most preferential orientation of the scalar dissipation rate is the direction of the mean strain rate near the wall and that of the fluctuating compressive strain rate in the outer region. The latter region has many characteristics in common with several turbulent flows; viz. the dominant structures are sheetlike in form and better correlated with the energy dissipation rate than the enstrophy.

scholarly journals Estimation of the Turbulent Fraction in the Free Atmosphere from MST Radar Measurements

2005 ◽  
Vol 22 (9) ◽  
pp. 1326-1339 ◽  
Author(s):  
Richard Wilson ◽  
Francis Dalaudier ◽  
Francois Bertin
Keyword(s):  
Dissipation Rate ◽  
Spectral Width ◽  
Unbiased Estimation ◽  
Small Scale ◽  
Doppler Width ◽  
Free Atmosphere ◽  
Dissipation Rates ◽  
Sampling Volume ◽  
Radar Measurements ◽  
Width Measurements

Abstract Small-scale turbulence in the free atmosphere is known to be intermittent in space and time. The turbulence fraction of the atmosphere is a key parameter in order to evaluate the transport properties of small-scale motions and to interpret clear-air radar measurements as well. Mesosphere–stratosphere–troposphere (MST)/stratosphere–troposphere (ST) radars provide two independent methods for the estimation of energetic parameters of turbulence. First, the Doppler spectral width σ2 is related to the dissipation rate of kinetic energy εk. Second, the radar reflectivity, or C2n, relates to the dissipation rate of available potential energy εp. However, these two measures yield estimates that differ with respect to an important point. The Doppler width measurements, and related εk, are reflectivity-weighted averages. On the other hand, the reflectivity estimate is a volume-averaged quantity. The values of εp depend on both the turbulence intensity and the turbulent fraction within the radar sampling volume. Now, the two dissipation rates εp and εk are related quantities as shown by various measurements within stratified fluids (atmosphere, ocean, lakes, or laboratory). Therefore, by assuming a “canonical” value for the ratio of dissipation rates, an indirect method is proposed to infer the turbulent fraction from simultaneous radar measurements of reflectivity and Doppler broadening within a sampling volume. This method is checked by using very high resolution radar measurements (30 m and 51 s), obtained by the PROUST radar during a field campaign. The method is found to provide an unbiased estimation of the turbulent fraction, within a factor of 2 or less.

scholarly journals Cloud droplet diffusional growth in homogeneous isotropic turbulence: bin microphysics versus Lagrangian superdroplet simulations

2020 ◽  
Author(s):  
Wojciech W. Grabowski ◽  
Lois Thomas
Keyword(s):  
Fluid Flow ◽  
Time Scale ◽  
Isotropic Turbulence ◽  
Spectral Width ◽  
Small Scale ◽  
Computational Domain ◽  
Homogeneous Isotropic Turbulence ◽  
Diffusional Growth ◽  
Droplet Concentration ◽  
Bin Microphysics

Abstract. Increase of the spectral width of initially monodisperse population of cloud droplets in homogeneous isotropic turbulence is investigated applying a finite-difference fluid flow model combined with either Eulerian bin microphysics or Lagrangian particle-based scheme. The turbulence is forced applying a variant of the so-called linear forcing method that maintains the mean turbulent kinetic energy (TKE) and the TKE partitioning between velocity components. The latter is important for maintaining the quasi-steady forcing of the supersaturation fluctuations that drive the increase of the spectral width. We apply a large computational domain, 643 m3, one of the domains considered in Thomas et al. (2020). The simulations apply 1 m grid length and are in the spirit of the implicit large eddy simulation (ILES), that is, with explicit small-scale dissipation provided by the model numerics. This is in contrast to the scaled-up direct numerical simulation (DNS) applied in Thomas et al. (2020). Two TKE intensities and three different droplet concentrations are considered. Analytic solutions derived in Sardina et al. (2015), valid for the case when the turbulence time scale is much larger than the droplet phase relaxation time scale, are used to guide the comparison between the two microphysics simulation techniques. The Lagrangian approach reproduces the scalings relatively well. Representing the spectral width increase in time is more challenging for the bin microphysics because appropriately high resolution in the bin space is needed. The bin width of 0.5 μm is only sufficient for the lowest droplet concentration, 26 cm−3. For the highest droplet concentration, 650 cm−3, even an order of magnitude smaller bin size is not sufficient. The scalings are not expected to be valid for the lowest droplet concentration and the high TKE case, and the two microphysics schemes represent similar departures. Finally, because the fluid flow is the same for all simulations featuring either low or high TKE, one can compare point-by-point simulation results. Such a comparison shows very close temperature and water vapor point-by-point values across the computational domain, and larger differences between simulated mean droplet radii and spectral width. The latter are explained by fundamental differences in the two simulation methodologies, numerical diffusion in the Eulerian bin approach and relatively small number of Lagrangian particles that are used in the particle-based microphysics.

Evaluation of Turbulent Kinetic Energy Dissipation Rate in a Free Jet Flow from PIV Measurements

2012 ◽  
Vol 7 (1) ◽  
pp. 53-69
Author(s):  
Vladimir Dulin ◽  
Yuriy Kozorezov ◽  
Dmitriy Markovich
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Turbulent Velocity ◽  
Small Scale ◽  
Velocity Fluctuations ◽  
Piv Measurements ◽  
Free Jet

The present paper reports PIV (Particle Image Velocimetry) measurements of turbulent velocity fluctuations statistics in development region of an axisymmetric free jet (Re = 28 000). To minimize measurement uncertainty, adaptive calibration, image processing and data post-processing algorithms were utilized. On the basis of theoretical analysis and direct measurements, the paper discusses effect of PIV spatial resolution on measured statistical characteristics of turbulent fluctuations. Underestimation of the second-order moments of velocity derivatives and of the turbulent kinetic energy dissipation rate due to a finite size of PIV interrogation area and finite thickness of laser sheet was analyzed from model spectra of turbulent velocity fluctuations. The results are in a good agreement with the measured experimental data. The paper also describes performance of possible ways to account for unresolved small-scale velocity fluctuations in PIV measurements of the dissipation rate. In particular, a turbulent viscosity model can be efficiently used to account for the unresolved pulsations in a free turbulent flow

scholarly journals Viscosity and Large-Scale Magnetic Fields from Accretion Disc Dynamos

1997 ◽  
Vol 163 ◽  
pp. 190-200
Author(s):  
Christopher A. Tout
Keyword(s):  
Magnetic Fields ◽  
Large Scale ◽  
Small Scale ◽  
Cascade Process ◽  
Jet Formation ◽  
Magnetohydrodynamic Turbulence ◽  
Discs Large ◽  
Scale Field ◽  
Large Scale Field ◽  
Nova Outbursts

AbstractWe review those processes associated with accretion discs that are probably influenced by magnetic fields, specifically, accretiondisc viscosity, energy dissipation and jet formation. We consider how magnetic instabilities in the disc can lead to a self-sustaining dynamical dynamo and how this is manifested as magnetohydrodynamic turbulence in numerical simulations. We show that currently these models do not fit with observational constraints imposed by dwarf-nova outbursts. We also show that the drop in ionisation fraction does not lead to the apparently necessary drop in viscosity in quiescent cataclysmic variable discs. Large-scale magnetic fields are required to launch and collimate jets form discs. We describe an inverse cascade process that can construct sufficient large-scale field from small-scale field generated by a dynamo.

scholarly journals Inverse Energy Cascade in Advanced MHD Turbulence (the RNG Method)

1993 ◽  
Vol 157 ◽  
pp. 255-261
Author(s):  
N. Kleeorin ◽  
I. Rogachevskii
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Magnetic Field Effect ◽  
Magnetic Reynolds Number ◽  
Energy Cascade ◽  
Small Scale ◽  
Magnetic Fluctuations ◽  
Mhd Turbulence ◽  
Inverse Energy Cascade ◽  
Large Scale Magnetic Field

The nonlinear (in terms of the large-scale magnetic field) effect of the modification of the magnetic force by an advanced small-scale magnetohydrodynamic (MHD) turbulence is considered. The phenomenon is due to the generation of magnetic fluctuations at the expense of hydrodynamic pulsations. It results in a decrease of the elasticity of the large-scale magnetic field.The renormalization group (RNG) method was employed for the investigation of the MHD turbulence at the large magnetic Reynolds number. It was found that the level of the magnetic fluctuations can exceed that obtained from the equipartition assumption due to the inverse energy cascade in advanced MHD turbulence.This effect can excite an instability of the large-scale magnetic field due to the energy transfer from the small-scale turbulent pulsations. This instability is an example of the inverse energy cascade in advanced MHD turbulence. It may act as a mechanism for the large-scale magnetic ropes formation in the solar convective zone and spiral galaxies.

Infrared Reynolds number dependency of the two-dimensional inverse energy cascade

2011 ◽  
Vol 667 ◽  
pp. 463-473 ◽  
Author(s):  
ANDREAS VALLGREN
Keyword(s):  
Reynolds Number ◽  
Cascade Range ◽  
Energy Cascade ◽  
Energy Spectra ◽  
Small Scale ◽  
Two Dimensional ◽  
Inverse Energy Cascade ◽  
Linear Friction ◽  
Non Local ◽  
Reynolds Number Dependency

High-resolution simulations of forced two-dimensional turbulence reveal that the inverse cascade range is sensitive to an infrared Reynolds number, Reα = kf/kα, where kf is the forcing wavenumber and kα is a frictional wavenumber based on linear friction. In the limit of high Reα, the classic k−5/3 scaling is lost and we obtain steeper energy spectra. The sensitivity is traced to the formation of vortices in the inverse energy cascade range. Thus, it is hypothesized that the dual limit Reα → ∞ and Reν = kd/kf → ∞, where kd is the small-scale dissipation wavenumber, will lead to a steeper energy spectrum than k−5/3 in the inverse energy cascade range. It is also found that the inverse energy cascade is maintained by non-local triad interactions.

Turbulent energy density in scale space for inhomogeneous turbulence

2018 ◽  
Vol 842 ◽  
pp. 532-553 ◽  
Author(s):  
Fujihiro Hamba
Keyword(s):  
Energy Spectrum ◽  
Energy Density ◽  
Isotropic Turbulence ◽  
Scale Space ◽  
Scale Dependence ◽  
Energy Cascade ◽  
Homogeneous Isotropic Turbulence ◽  
Velocity Correlation ◽  
Inhomogeneous Turbulence ◽  
Point Velocity

The energy spectrum is commonly used to describe the scale dependence of the turbulent fluctuations in homogeneous isotropic turbulence. In contrast, one-point statistical quantities, such as the turbulent kinetic energy, are employed for inhomogeneous turbulence modelling. To obtain a better understanding of inhomogeneous turbulence, some attempts have been made to describe its scale dependence by using the second-order structure function and the two-point velocity correlation. However, previous expressions for the energy density in the scale space do not satisfy the requirement that it should be non-negative. In this work, a new expression for the energy density in the scale space is proposed on the basis of the two-point velocity correlation; the integral with a filter function is introduced to satisfy the non-negativity of the energy density. Direct numerical simulation (DNS) data of homogeneous isotropic turbulence were first used to assess the role of the energy density by comparing it with the energy spectrum. DNS data of a turbulent channel flow were then used to investigate the energy density and its transport equation in inhomogeneous turbulence. It was shown that the new energy density is positive in the scale space of the homogeneous direction. The energy transfer was successfully examined in the scale space both in the homogeneous and inhomogeneous directions. The energy cascade from large to small scales was clearly observed. Moreover, the inverse energy cascade from large to very large scales was observed in the scale space of the spanwise direction.

scholarly journals Stochastic modelling of star-formation histories II: star-formation variability from molecular clouds and gas inflow

2020 ◽  
Vol 497 (1) ◽  
pp. 698-725 ◽  
Author(s):  
Sandro Tacchella ◽  
John C Forbes ◽  
Neven Caplar
Keyword(s):  
Life Cycle ◽  
Star Formation ◽  
Time Scales ◽  
Time Scale ◽  
Molecular Clouds ◽  
Star Formation History ◽  
Small Scale ◽  
Inflow Rate ◽  
Wide Range ◽  
The Galaxy

ABSTRACT A key uncertainty in galaxy evolution is the physics regulating star formation, ranging from small-scale processes related to the life-cycle of molecular clouds within galaxies to large-scale processes such as gas accretion on to galaxies. We study the imprint of such processes on the time-variability of star formation with an analytical approach tracking the gas mass of galaxies (‘regulator model’). Specifically, we quantify the strength of the fluctuation in the star-formation rate (SFR) on different time-scales, i.e. the power spectral density (PSD) of the star-formation history, and connect it to gas inflow and the life-cycle of molecular clouds. We show that in the general case the PSD of the SFR has three breaks, corresponding to the correlation time of the inflow rate, the equilibrium time-scale of the gas reservoir of the galaxy, and the average lifetime of individual molecular clouds. On long and intermediate time-scales (relative to the dynamical time-scale of the galaxy), the PSD is typically set by the variability of the inflow rate and the interplay between outflows and gas depletion. On short time-scales, the PSD shows an additional component related to the life-cycle of molecular clouds, which can be described by a damped random walk with a power-law slope of β ≈ 2 at high frequencies with a break near the average cloud lifetime. We discuss star-formation ‘burstiness’ in a wide range of galaxy regimes, study the evolution of galaxies about the main sequence ridgeline, and explore the applicability of our method for understanding the star-formation process on cloud-scale from galaxy-integrated measurements.

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