Inertial subrange: Difference between revisions

Latest revision as of 09:56, 30 March 2024

An intermediate range of turbulent scales or wavelengths that is smaller than the energy-containing eddies but larger than viscous eddies.

In the inertial subrange, the net energy coming from the energy-containing eddies is in equilibrium with the net energy cascading to smaller eddies where it is dissipated. Thus the slope of the energy spectrum in this range remains constant. Kolmogorov showed that the slope is -5/ 3 based on dimensional arguments, namely, S ∝ ε^2/3k^-5/3, for ε representing viscous dissipation rate of turbulence kinetic energy, k is wavenumber (inversely proportional to the wavelength), and S is spectral energy in a Fourier decomposition of a turbulent signal.
Compare energy spectrum, spectral gap;
see also Kolmogorov's similarity hypotheses.

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+|Display title=inertial subrange
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+|Meaning=An intermediate range of turbulent scales or wavelengths that is smaller than the  [[energy-containing eddies]] but larger than viscous [[eddies]].
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+|Explanation=In the inertial subrange, the net [[energy]] coming from the energy-containing eddies is in [[equilibrium]]  with the net energy cascading to smaller eddies where it is dissipated. Thus the slope of  the [[energy spectrum]] in this range remains constant. Kolmogorov showed that the slope is -5/  3 based on dimensional arguments, namely, ''S'' &prop; &#x003b5;<sup>2/3</sup>''k''<sup>-5/3</sup>, for &#x003b5; representing [[viscous dissipation]]  rate of [[turbulence kinetic energy]], ''k'' is [[wavenumber]] (inversely proportional to the [[wavelength]]),  and ''S'' is spectral energy in a Fourier decomposition of a turbulent [[signal]]. <br/>''Compare'' [[energy spectrum]],  [[spectral gap]]; <br/>''see also'' [[Kolmogorov's similarity hypotheses]].
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-== inertial subrange ==
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-<div class="definition"><div class="short_definition">An intermediate range of turbulent scales or wavelengths that is smaller than the  [[energy-containing eddies]] but larger than viscous [[eddies]].</div><br/> <div class="paragraph">In the inertial subrange, the net [[energy]] coming from the energy-containing eddies is in [[equilibrium]]  with the net energy cascading to smaller eddies where it is dissipated. Thus the slope of  the [[energy spectrum]] in this range remains constant. Kolmogorov showed that the slope is &minus;5/  3 based on dimensional arguments, namely, ''S'' &prop; &#x003b5;<sup>2/3</sup>''k''<sup>&minus;5/3</sup>, for &#x003b5; representing [[viscous dissipation]]  rate of [[turbulence kinetic energy]], ''k'' is [[wavenumber]] (inversely proportional to the [[wavelength]]),  and ''S'' is spectral energy in a Fourier decomposition of a turbulent [[signal]]. <br/>''Compare'' [[energy spectrum]],  [[spectral gap]]; <br/>''see also'' [[Kolmogorov's similarity hypotheses]].</div><br/> </div>
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