Measurements of the turbulent energy dissipation rate

Pearson, B. R.; Krogstad, Per‐Åge; Water, van de W Willem

doi:10.1063/1.1445422

Cited by 138 publications

(132 citation statements)

References 11 publications

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“…Such a breakdown of classical conservation laws of the fluid equations under turbulent conditions is not unprecedented. For example, it is well-known that energy is not conserved in the limit of small viscosity for hydrodynamic turbulence, as observed both in laboratory experiments [14,15,16,17] and high-resolution numerical simulations [18,19]. A fundamental explanation for this phenomenon was proposed in 1949 by Lars Onsager [20], who showed that solutions of the ideal incompressible Euler equations do not need to conserve energy if they are sufficiently singular.…”

Section: H Alfvén (1942)mentioning

confidence: 99%

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The breakdown of Alfvén’s theorem in ideal plasma flows: Necessary conditions and physical conjectures

Eyink

Aluie

2006

Physica D: Nonlinear Phenomena

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This paper presents both rigorous results and physical theory on the breakdown of magnetic flux conservation for ideal plasmas, by nonlinear effects. Our analysis is based upon an effective equation for magnetohydrodynamic (MHD) modes at length-scales > ℓ, with smaller scales eliminated, as in renormalization-group methodology. We prove that flux-conservation can be violated for an arbitrarily small length-scale ℓ, and in the absence of any non-ideality, but only if singular current sheets and vortex sheets both exist and intersect in sets of large enough dimension. This result gives analytical support to and rigorous constraints on theories of fast turbulent reconnection. Mathematically, our theorem is analogous to

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Section: H Alfvén (1942)mentioning

confidence: 99%

“…Because of the additional normal velocity component (17), the field lines now slip through the plasma and Alfvén's "frozen-in" property is violated at length-scale ℓ.…”

Section: The Filtering Approach and Large-scale Flux Balancementioning

confidence: 99%

The breakdown of Alfvén’s theorem in ideal plasma flows: Necessary conditions and physical conjectures

Eyink

Aluie

2006

Physica D: Nonlinear Phenomena

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“…[5] and references therein) and experimental (see Refs. [6,7,8] for recent results) efforts to determine the value of C ε and its dependence on the Reynolds number. Perhaps the most convincing of these are the numerical attempts since there is no re-course to one-dimensional surrogacy as there is for experiments.…”

Section: Introductionmentioning

confidence: 99%

Delayed correlation between turbulent energy injection and dissipation

et al. 2004

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The dimensionless kinetic energy dissipation rate Cε is estimated from numerical simulations of statistically stationary isotropic box turbulence that is slightly compressible. The Taylor microscale Reynolds number (Re λ ) range is 20Re λ 220 and the statistical stationarity is achieved with a random phase forcing method. The strong Re λ dependence of Cε abates when Re λ ≈ 100 after which Cε slowly approaches ≈ 0.5, a value slightly different to previously reported simulations but in good agreement with experimental results. If Cε is estimated at a specific time step from the time series of the quantities involved it is necessary to account for the time lag between energy injection and energy dissipation. Also, the resulting value can differ from the ensemble averaged value by up to ±30%. This may explain the spread in results from previously published estimates of Cε.

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“…It has been found that the normalized energy dissipation rate C ε is a constant of approximately 0.5 for a wide range of Reynolds numbers, including both laboratory flows and flows in the atmosphere (Burattini et al, 2005;Pearson et al, 2002;Sreenivasan, 1998). This observation has also been called the "zeroth law of turbulence", as Kolmogorov's hypotheses assume that the mean energy dissipation rate is independent of the viscosity at high Reynolds numbers (Frisch, 1995;Pearson et al, 2004).…”

Section: Large-scale Turbulencementioning

confidence: 98%

Schneefernerhaus as a mountain research station for clouds and turbulence

Risius

Lorenzo

et al. 2015

Atmos. Meas. Tech.

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Abstract. Cloud measurements are usually carried out with airborne campaigns, which are expensive and are limited by temporal duration and weather conditions. Ground-based measurements at high-altitude research stations therefore play a complementary role in cloud study. Using the meteorological data (wind speed, direction, temperature, humidity, visibility, etc.) collected by the German Weather Service (DWD) from 2000 to 2012 and turbulence measurements recorded by multiple ultrasonic sensors (sampled at 10 Hz) in 2010, we show that the Umweltforschungsstation Schneefernerhaus (UFS) located just below the peak of Zugspitze in the German Alps, at a height of 2650 m, is a well-suited station for cloud-turbulence research. The wind at UFS is dominantly in the east-west direction and nearly horizontal. During the summertime (July and August) the UFS is immersed in warm clouds about 25 % of the time. The clouds are either from convection originating in the valley in the east, or associated with synoptic-scale weather systems typically advected from the west. Air turbulence, as measured from the second-and third-order velocity structure functions that exhibit well-developed inertial ranges, possesses Taylor microscale Reynolds numbers up to 10 4 , with the most probable value at ∼ 3000. In spite of the complex topography, the turbulence appears to be nearly as isotropic as many laboratory flows when evaluated on the "Lumley triangle".

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Measurements of the turbulent energy dissipation rate

Cited by 138 publications

References 11 publications

The breakdown of Alfvén’s theorem in ideal plasma flows: Necessary conditions and physical conjectures

The breakdown of Alfvén’s theorem in ideal plasma flows: Necessary conditions and physical conjectures

Delayed correlation between turbulent energy injection and dissipation

Schneefernerhaus as a mountain research station for clouds and turbulence

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