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Anisotropy and scaling corrections in turbulence
chao-dyn · Submitted 29 Jul 1994
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our observations emphasize the need for more experimental information on crossovers between different subranges.
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The abstract, sentence by sentence
Two parametrizations for second order velocity moments, the Batchelor parametrization for the r-space structure function and a common parametrization for the energy spectrum, $E(p)\propto p^{-5/3}\exp(-p/p_d)$, are examined and compared. In particular, we investigate corrections to the local scaling exponents induced by finite size effects. The behavior of local r-- and p--space exponents differs dramatically. The Batchelor type parametrization leads to energy pileups in p-space at the ends of the ISR. These bottleneck effects result in an extended r-space scaling range, comparable to experimental ones for the same Taylor-Reynolds number $\rel$. Shear effects are discussed in terms of (global) apparent scaling correction $\delta\zeta^{app}$ to classical scaling. The scaling properties of $\delta\zeta^{app}(\rel )$ differ not only among the parametrizations considered, but also among r-- and p--space for a {\it given} parametrization. The difference can be traced back to the subtleties of the crossovers in the velocity moments. Our observations emphasize the need for more experimental information on crossovers between different subranges.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Two parametrizations for second order velocity moments, the Batchelor parametrization for the r-space structure function and a common parametrization for the energy spectrum, $E(p)\propto p^{-5/3}\exp(-p/p_d)$, are examined and compared. | contribution 0.71 | 0.67 | 0.05 | asserted 0.88 |
| s1 | In particular, we investigate corrections to the local scaling exponents induced by finite size effects. | contribution 0.99 | 0.82 | 0.06 | asserted 0.65 |
| s2 | The behavior of local r-- and p--space exponents differs dramatically. | result 1.00 | 0.70 | 0.21 | asserted 1.00 |
| s3 | The Batchelor type parametrization leads to energy pileups in p-space at the ends of the ISR. | result 1.00 | 0.74 | 0.14 | asserted 1.00 |
| s4 | These bottleneck effects result in an extended r-space scaling range, comparable to experimental ones for the same Taylor-Reynolds number $\rel$. | result 0.96 | 0.79 | 0.23 | asserted 1.00 |
| s5 | Shear effects are discussed in terms of (global) apparent scaling correction $\delta\zeta^{app}$ to classical scaling. | contribution 0.62 | 0.49 | 0.08 | asserted 0.91 |
| s6 | The scaling properties of $\delta\zeta^{app}(\rel )$ differ not only among the parametrizations considered, but also among r-- and p--space for a {\it given} parametrization. | result 0.99 | 0.78 | 0.23 | asserted 1.00 |
| s7 | The difference can be traced back to the subtleties of the crossovers in the velocity moments. | interpretation 0.98 | 0.68 | 0.13 | asserted 0.97 |
| s8 | Our observations emphasize the need for more experimental information on crossovers between different subranges. | future work 0.96 | 0.48 | 0.39 | asserted 0.71 |
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The paper
Original abstract
Two parametrizations for second order velocity moments, the Batchelor parametrization for the r-space structure function and a common parametrization for the energy spectrum, $E(p)\propto p^{-5/3}\exp(-p/p_d)$, are examined and compared. In particular, we investigate corrections to the local scaling exponents induced by finite size effects. The behavior of local r-- and p--space exponents differs dramatically. The Batchelor type parametrization leads to energy pileups in p-space at the ends of the ISR. These bottleneck effects result in an extended r-space scaling range, comparable to experimental ones for the same Taylor-Reynolds number $\rel$. Shear effects are discussed in terms of (global) apparent scaling correction $\delta\zeta^{app}$ to classical scaling. The scaling properties of $\delta\zeta^{app}(\rel )$ differ not only among the parametrizations considered, but also among r-- and p--space for a {\it given} parametrization. The difference can be traced back to the subtleties of the crossovers in the velocity moments. Our observations emphasize the need for more experimental information on crossovers between different subranges.
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