scholarly journals Number of degrees of freedom and energy spectrum of surface quasi-geostrophic turbulence

2011 ◽  
Vol 684 ◽  
pp. 427-440 ◽  
Author(s):  
Chuong V. Tran ◽  
Luke A. K. Blackbourn ◽  
Richard K. Scott
Keyword(s):  
Dissipation Rate ◽  
Degrees Of Freedom ◽  
Energy Dissipation Rate ◽  
Inertial Range ◽  
Energy Spectra ◽  
Phenomenological Method ◽  
Integral Scale ◽  
General Power ◽  
Geostrophic Turbulence ◽  
Molecular Viscosity

AbstractWe study both theoretically and numerically surface quasi-geostrophic turbulence regularized by the usual molecular viscosity, with an emphasis on a number of classical predictions. It is found that the system’s number of degrees of freedom $N$, which is defined in terms of local Lyapunov exponents, scales as ${\mathit{Re}}^{3/ 2} $, where $\mathit{Re}$ is the Reynolds number expressible in terms of the viscosity, energy dissipation rate and system’s integral scale. For general power-law energy spectra ${k}^{\ensuremath{-} \ensuremath{\alpha} } $, a comparison of $N$ with the number of dynamically active Fourier modes, i.e. the modes within the energy inertial range, yields $\ensuremath{\alpha} = 5/ 3$. This comparison further renders the scaling ${\mathit{Re}}^{1/ 2} $ for the exponential dissipation rate at the dissipation wavenumber. These results have been predicted on the basis of Kolmogorov’s theory. Our approach thus recovers these classical predictions and is an analytic alternative to the traditional phenomenological method. The implications of the present findings are discussed in conjunction with related results in the literature. Support for the analytic results is provided through a series of direct numerical simulations.

Local energy flux and subgrid-scale statistics in three-dimensional turbulence

1998 ◽  
Vol 366 ◽  
pp. 1-31 ◽  
Author(s):  
VADIM BORUE ◽  
STEVEN A. ORSZAG
Keyword(s):  
Energy Transfer ◽  
Energy Dissipation ◽  
Energy Flux ◽  
Dissipation Rate ◽  
Three Dimensional ◽  
Energy Dissipation Rate ◽  
Inertial Range ◽  
Local Energy ◽  
Subgrid Scale ◽  
Velocity Gradients

Statistical properties of the subgrid-scale stress tensor, the local energy flux and filtered velocity gradients are analysed in numerical simulations of forced three-dimensional homogeneous turbulence. High Reynolds numbers are achieved by using hyperviscous dissipation. It is found that in the inertial range the subgrid-scale stress tensor and the local energy flux allow simple parametrization based on a tensor eddy viscosity. This parametrization underlines the role that negative skewness of filtered velocity gradients plays in the local energy transfer. It is found that the local energy flux only weakly correlates with the locally averaged energy dissipation rate. This fact reflects basic difficulties of large-eddy simulations of turbulence, namely the possibility of predicting the locally averaged energy dissipation rate through inertial-range quantities such as the local energy flux is limited. Statistical properties of subgrid-scale velocity gradients are systematically studied in an attempt to reveal the mechanism of local energy transfer.

scholarly journals Point-source scalar turbulence

2007 ◽  
Vol 583 ◽  
pp. 189-198 ◽  
Author(s):  
ANTONIO CELANI ◽  
MARCO MARTINS AFONSO ◽  
ANDREA MAZZINO
Keyword(s):  
Point Source ◽  
First Principles ◽  
Dissipation Rate ◽  
Passive Scalar ◽  
Inertial Range ◽  
Main Question ◽  
Homogeneous Case ◽  
Integral Scale ◽  
Statistical Indicator ◽  
Injection Mechanism

The statistics of a passive scalar randomly emitted from a point source is investigated analytically for the Kraichnan ensemble. Attention is focused on the two-point equal-time scalar correlation function, a statistical indicator widely used both in experiments and in numerical simulations. The only source of inhomogeneity/anisotropy is the injection mechanism, the advecting velocity being here statistically homogeneous and isotropic. The main question we address is on the possible existence of an inertial range of scales and a consequent scaling behaviour. The question arises from the observation that for a point source the injection scale is formally zero and the standard cascade mechanism cannot thus be taken for granted. We find from first principles that an intrinsic integral scale, whose value depends on the distance from the source, emerges as a result of sweeping effects. For separations smaller than this integral scale a standard forward cascade occurs. This is characterized by a Kolmogorov–Obukhov power-law behaviour as in the homogeneous case, except that the dissipation rate is also dependent on the distance from the source. Finally, we also find that the combined effect of a finite inertial-range extent and of inhomogeneities causes the emergence of subleading anisotropic corrections to the leading isotropic term, that are here quantified and discussed.

scholarly journals Using an ADCP to Estimate Turbulent Kinetic Energy Dissipation Rate in Sheltered Coastal Waters

2015 ◽  
Vol 32 (2) ◽  
pp. 318-333 ◽  
Author(s):  
A. D. Greene ◽  
P. J. Hendricks ◽  
M. C. Gregg
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Cell Size ◽  
Dissipation Rate ◽  
Puget Sound ◽  
Acoustic Doppler Current Profiler ◽  
Energy Dissipation Rate ◽  
Integral Scale ◽  
Thorpe Scale

AbstractTurbulent microstructure and acoustic Doppler current profiler (ADCP) data were collected near Tacoma Narrows in Puget Sound, Washington. Over 100 coincident microstructure profiles have been compared to ADCP estimates of turbulent kinetic energy dissipation rate (ϵ). ADCP dissipation rates were calculated using the large-eddy method with theoretically determined corrections for sensor noise on rms velocity and integral-scale calculations. This work is an extension of Ann Gargett’s approach, which used a narrowband ADCP in regions with intense turbulence and strong vertical velocities. Here, a broadband ADCP is used to measure weaker turbulence and achieve greater horizontal and vertical resolution relative to the narrowband ADCP. Estimates of ϵ from the Modular Microstructure Profiler (MMP) and broadband ADCP show good quantitative agreement over nearly three decades of dissipation rate, 3 × 10−8–10−5 m2 s−3. This technique is most readily applied when the turbulent velocity is greater than the ADCP velocity uncertainty (σ) and the ADCP cell size is within a factor of 2 of the Thorpe scale. The 600-kHz broadband ADCP used in this experiment yielded a noise floor of 3 mm s−1 for 3-m vertical bins and 2-m along-track average (≈four pings), which resulted in turbulence levels measureable with the ADCP as weak as 3 × 10−8 m2 s−3. The value and trade-off of changing the ADCP cell size, which reduces noise but also changes the ratio of the Thorpe scale to the cell size, are discussed as well.

scholarly journals Lagrangian cascade in three-dimensional homogeneous and isotropic turbulence

2014 ◽  
Vol 741 ◽  
Author(s):  
Yongxiang Huang ◽  
François G. Schmitt
Keyword(s):  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Three Dimensional ◽  
Energy Dissipation Rate ◽  
Inertial Range ◽  
Order Moment ◽  
Scaling Exponent ◽  
Tracer Particles ◽  
Homogeneous And Isotropic Turbulence ◽  
Multiplicative Cascade

AbstractIn this work, the scaling statistics of the dissipation along Lagrangian trajectories are investigated by using fluid tracer particles obtained from a high-resolution direct numerical simulation with $\mathit{Re}_{\lambda }=400$. Both the energy dissipation rate $\epsilon $ and the local time-averaged $\epsilon _{\tau }$ agree rather well with the lognormal distribution hypothesis. Several statistics are then examined. It is found that the autocorrelation function $\rho (\tau )$ of $\ln (\epsilon (t))$ and variance $\sigma ^2(\tau )$ of $\ln (\epsilon _{\tau }(t))$ obey a log-law with scaling exponent $\beta '=\beta =0.30$ compatible with the intermittency parameter $\mu =0.30$. The $q{\rm th}$-order moment of $\epsilon _{\tau }$ has a clear power law on the inertial range $10<\tau /\tau _{\eta }<100$. The measured scaling exponent $K_L(q)$ agrees remarkably with $q-\zeta _L(2q)$ where $\zeta _L(2q)$ is the scaling exponent estimated using the Hilbert methodology. All of these results suggest that the dissipation along Lagrangian trajectories could be modelled by a multiplicative cascade.

scholarly journals Turbulent characteristics of a semiarid atmospheric surface layer from cup anemometers – effects of soil tillage treatment (Northern Spain)

2003 ◽  
Vol 21 (10) ◽  
pp. 2119-2131 ◽  
Author(s):  
S. Yahaya ◽  
J. P. Frangi ◽  
D. C. Richard
Keyword(s):  
Surface Roughness ◽  
Surface Layer ◽  
Dissipation Rate ◽  
Atmospheric Surface Layer ◽  
Friction Velocity ◽  
Roughness Length ◽  
Energy Dissipation Rate ◽  
Horizontal Wind ◽  
Length Scale ◽  
Integral Scale

Abstract. This paper deals with the characteristics of turbulent flow over two agricultural plots with various tillage treatments in a fallow, semiarid area (Central Aragon, Spain). The main dynamic characteristics of the Atmospheric Surface Layer (ASL) measured over the experimental site (friction velocity, roughness length, etc.), and energy budget, have been presented previously (Frangi and Richard, 2000). The current study is based on experimental measurements performed with cup anemometers located in the vicinity of the ground at 5 different levels (from 0.25 to 4 m) and sampled at 1 Hz. It reveals that the horizontal wind variance, the Eulerian integral scales, the frequency range of turbulence and the turbulent kinetic energy dissipation rate are affected by the surface roughness. In the vicinity of the ground surface, the horizontal wind variance logarithmically increases with height, directly in relation to the friction velocity and the roughness length scale. It was found that the time integral scale (and subsequently the length integral scale) increased with the surface roughness and decreased with the anemometer height. These variations imply some shifts in the meteorological spectral gap and some variations of the spectral peak length scale. The turbulent energy dissipation rate, affected by the soil roughness, shows a z-less stratification behaviour under stable conditions. In addition to the characterization of the studied ASL, this paper intends to show which turbulence characteristics, and under what conditions, are accessible through the cup anemometer.Key words. Meteorology and atmospheric dynamics (climatology, turbulence, instruments and techniques)

Non-dimensional energy dissipation rate near the turbulent/non-turbulent interfacial layer in free shear flows and shear free turbulence

2019 ◽  
Vol 875 ◽  
pp. 321-344 ◽  
Author(s):  
Tomoaki Watanabe ◽  
Carlos B. da Silva ◽  
Koji Nagata
Keyword(s):  
Energy Dissipation ◽  
Turbulent Flows ◽  
Dissipation Rate ◽  
Mixing Layer ◽  
Energy Dissipation Rate ◽  
Integral Scale ◽  
Jet Mixing ◽  
Planar Jet ◽  
Turbulent Reynolds Number ◽  
Original Procedure

The non-dimensional dissipation rate $C_{\unicode[STIX]{x1D700}}=\unicode[STIX]{x1D700}L/u^{\prime 3}$, where $\unicode[STIX]{x1D700}$, $L$ and $u^{\prime }$ are the viscous energy dissipation rate, integral length scale of turbulence and root-mean-square of the velocity fluctuations, respectively, is computed and analysed within the turbulent/non-turbulent interfacial (TNTI) layer using direct numerical simulations of a planar jet, mixing layer and shear free turbulence. The TNTI layer that separates the turbulent and non-turbulent regions exists at the edge of free shear turbulent flows and turbulent boundary layers, and comprises both the viscous superlayer and turbulent sublayer regions. The computation of $C_{\unicode[STIX]{x1D700}}$ is made possible by the introduction of an original procedure, based on local volume averages within spheres of radius $r$, combined with conditional sampling as a function of the location with respect to the TNTI layer. The new procedure allows for a detailed investigation of the scale dependence of several turbulent quantities near the TNTI layer. An important achievement of this procedure consists in permitting the computation of the turbulent integral scale within the TNTI layer, which is shown to be approximately constant. Both the non-dimensional dissipation rate and turbulent Reynolds number $Re_{\unicode[STIX]{x1D706}}$ vary in space within the TNTI layer, where two relations are observed: $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-1}$ and $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-2}$. Specifically, whereas the viscous superlayer and part of the turbulent sublayer display $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-2}$, the remaining of the turbulent sublayer exhibits $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-1}$, which is consistent with non-equilibrium turbulence (Vassilicos, Annu. Rev. Fluid Mech. vol. 47, 2015, pp. 95–114).

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