Velocity inertial subrange model - Revision history

CynthiaBluteau: /* Inertial subrange collapse and anisotropy */

2022-07-05T18:54:57Z

Inertial subrange collapse and anisotropy

← Older revision		Revision as of 18:54, 5 July 2022
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	}}</ref>.		}}</ref>.

	[[Velocity inertial subrange model#anisotropy\|Anisotropic velocity spectra]] are exhibited when the largest turbulence scales are less than {{FontColor\|fg=white\|bg=red\|text=XX}} times the Kolmogorov length scale, may inhibit using the vertical velocity component to derive <math>\varepsilon</math>. In these situations, it may be possible to use the longitudinal velocity component (see Bluteau et al (2011)<ref name="Bluteau.etal2011"/>), which requires the user to [[Rotation of the velocity measurements\|rotate the velocity]] in the direction of the mean flow.		[[Velocity inertial subrange model#anisotropy\|Anisotropic velocity spectra]] are exhibited when the largest turbulence scales are less than {{FontColor\|fg=white\|bg=red\|text=XX}} times the Kolmogorov length scale, may inhibit using the vertical velocity component to derive <math>\varepsilon</math>. In these situations, it may be possible to use the longitudinal velocity component (see Bluteau et al. 2011<ref name="Bluteau.etal2011"/>), which requires the user to [[Rotation of the velocity measurements\|rotate the velocity]] in the direction of the mean flow.

	[[File:Anisotropy.png\|center\|thumbnail\|600px\|Example of how [[Velocity inertial subrange model#anisotropy\| turbulence anisotropy]] influences the velocity spectral shapes. This instrument was located very close to the bed (0.15 m) in a shallow waterway less than 2 m deep, which results in the vertical velocity's inertial subrange being reduced by the flattening of the spectra at wavenumbers of 10 cpm (0.1m scales). Strong stratification (or shear) is another mechanism that shortens the inertial subrange at the lower wavenumbers<ref name="Bluteau.etal2011"/>. The wavenumber at which its impact is felt is approximately <math>L_o/3</math> where <math>L_o</math> is the Ozmidov length scale.]]		[[File:Anisotropy.png\|center\|thumbnail\|600px\|Example of how [[Velocity inertial subrange model#anisotropy\| turbulence anisotropy]] influences the velocity spectral shapes. This instrument was located very close to the bed (0.15 m) in a shallow waterway less than 2 m deep, which results in the vertical velocity's inertial subrange being reduced by the flattening of the spectra at wavenumbers of 10 cpm (0.1m scales). Strong stratification (or shear) is another mechanism that shortens the inertial subrange at the lower wavenumbers<ref name="Bluteau.etal2011"/>. The wavenumber at which its impact is felt is approximately <math>L_o/3</math> where <math>L_o</math> is the Ozmidov length scale.]]

	== Notes ==		== Notes ==

CynthiaBluteau: /* Inertial subrange collapse and anisotropy */

2022-07-05T18:53:44Z

Inertial subrange collapse and anisotropy

← Older revision		Revision as of 18:53, 5 July 2022
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	\|doi=10:4319/lom.2011.9.302		\|doi=10:4319/lom.2011.9.302
	}}</ref>.		}}</ref>.

			[[Velocity inertial subrange model#anisotropy\|Anisotropic velocity spectra]] are exhibited when the largest turbulence scales are less than {{FontColor\|fg=white\|bg=red\|text=XX}} times the Kolmogorov length scale, may inhibit using the vertical velocity component to derive <math>\varepsilon</math>. In these situations, it may be possible to use the longitudinal velocity component (see Bluteau et al (2011)<ref name="Bluteau.etal2011"/>), which requires the user to [[Rotation of the velocity measurements\|rotate the velocity]] in the direction of the mean flow.

	[[File:Anisotropy.png\|center\|thumbnail\|600px\|Example of how [[Velocity inertial subrange model#anisotropy\| turbulence anisotropy]] influences the velocity spectral shapes. This instrument was located very close to the bed (0.15 m) in a shallow waterway less than 2 m deep, which results in the vertical velocity's inertial subrange being reduced by the flattening of the spectra at wavenumbers of 10 cpm (0.1m scales). Strong stratification (or shear) is another mechanism that shortens the inertial subrange at the lower wavenumbers<ref name="Bluteau.etal2011"/>. The wavenumber at which its impact is felt is approximately <math>L_o/3</math> where <math>L_o</math> is the Ozmidov length scale.]]		[[File:Anisotropy.png\|center\|thumbnail\|600px\|Example of how [[Velocity inertial subrange model#anisotropy\| turbulence anisotropy]] influences the velocity spectral shapes. This instrument was located very close to the bed (0.15 m) in a shallow waterway less than 2 m deep, which results in the vertical velocity's inertial subrange being reduced by the flattening of the spectra at wavenumbers of 10 cpm (0.1m scales). Strong stratification (or shear) is another mechanism that shortens the inertial subrange at the lower wavenumbers<ref name="Bluteau.etal2011"/>. The wavenumber at which its impact is felt is approximately <math>L_o/3</math> where <math>L_o</math> is the Ozmidov length scale.]]

	== Notes ==		== Notes ==

CynthiaBluteau: /* Inertial subrange collapse and anisotropy */

2022-07-05T18:32:53Z

Inertial subrange collapse and anisotropy

← Older revision		Revision as of 18:32, 5 July 2022
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	== Inertial subrange collapse and <span id="anisotropy">anisotropy</span> ==		== Inertial subrange collapse and <span id="anisotropy">anisotropy</span> ==
	Near boundaries or low energy environments~~, are~~ defined as flows with a small separation between the large turbulent overturns <math>L</math> and the smallest (Kolmogorov).		Near boundaries or low energy environments--defined as flows with a small separation between the large turbulent overturns <math>L</math> and the smallest (Kolmogorov)-- tends to adversely impact our ability to estimate <math>\varepsilon</math> from the lower wavenumbers. In certain cases, the velocity spectra may not have a sufficiently developed inertial subrange to estimate <math>\varepsilon</math> <ref name="Gargett.etal1984">{{Cite journal
			\|authors= A. E. Gargett, T. R. Osborn, and P.W. Nasmyth
	~~[[File:Anisotropy.png\|center\|thumbnail\|600px\|Example of how~~ ~~[[Velocity~~ inertial subrange ~~model#anisotropy~~\| ~~turbulence anisotropy]] influences the velocity spectral shapes~~. ~~This instrument was located very close to the bed (0~~.~~15 m) in a shallow waterway less than 2 m deep~~, ~~which results in the vertical velocity's inertial subrange being reduced by~~ the ~~flattening of the spectra at wavenumbers~~ of 10 ~~cpm (0~~.~~1m scales). Strong stratification (or shear) is another mechanism that shortens the inertial subrange at the lower wavenumbers~~<ref name="Bluteau.etal2011">{{Cite journal		\|journal_or_publisher= J. Fluid. Mech.
			\|paper_or_booktitle= Local isotropy and the decay of turbulence in a stratified fluid
			\|year= 1984
			\|doi=10.1017/S0022112084001592
			}}</ref><ref name="Bluteau.etal2011">{{Cite journal
	\|authors= C.E. Bluteau, N.L. Jones, and G. Ivey		\|authors= C.E. Bluteau, N.L. Jones, and G. Ivey
	\|journal_or_publisher= Limnol. Oceanogr.: Methods		\|journal_or_publisher= Limnol. Oceanogr.: Methods
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	\|year= 2011		\|year= 2011
	\|doi=10:4319/lom.2011.9.302		\|doi=10:4319/lom.2011.9.302
	}}</ref>. The wavenumber at which its impact is felt is approximately <math>L_o/3</math> where <math>L_o</math> is the Ozmidov length scale.]]		}}</ref>.

			[[File:Anisotropy.png\|center\|thumbnail\|600px\|Example of how [[Velocity inertial subrange model#anisotropy\| turbulence anisotropy]] influences the velocity spectral shapes. This instrument was located very close to the bed (0.15 m) in a shallow waterway less than 2 m deep, which results in the vertical velocity's inertial subrange being reduced by the flattening of the spectra at wavenumbers of 10 cpm (0.1m scales). Strong stratification (or shear) is another mechanism that shortens the inertial subrange at the lower wavenumbers<ref name="Bluteau.etal2011"/>. The wavenumber at which its impact is felt is approximately <math>L_o/3</math> where <math>L_o</math> is the Ozmidov length scale.]]

	== Notes ==		== Notes ==

CynthiaBluteau: /* Inertial subrange collapse and anisotropy */

2022-07-05T18:26:17Z

Inertial subrange collapse and anisotropy

← Older revision		Revision as of 18:26, 5 July 2022
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	Near boundaries or low energy environments, are defined as flows with a small separation between the large turbulent overturns <math>L</math> and the smallest (Kolmogorov).		Near boundaries or low energy environments, are defined as flows with a small separation between the large turbulent overturns <math>L</math> and the smallest (Kolmogorov).

	[[File:Anisotropy.png\|center\|thumbnail\|600px\|Example of how [[Velocity inertial subrange model#anisotropy\| turbulence anisotropy]] influences the velocity spectral shapes. This instrument was located very close to the bed (0.15 m) in a shallow waterway less than 2 m deep, which results in the vertical velocity's inertial subrange being reduced by the flattening of the spectra at wavenumbers of 10 cpm (0.1m scales). Strong stratification (or shear) is another mechanism that shortens the inertial subrange at the lower wavenumbers ~~</ref>~~<ref name="Bluteau.etal2011">{{Cite journal		[[File:Anisotropy.png\|center\|thumbnail\|600px\|Example of how [[Velocity inertial subrange model#anisotropy\| turbulence anisotropy]] influences the velocity spectral shapes. This instrument was located very close to the bed (0.15 m) in a shallow waterway less than 2 m deep, which results in the vertical velocity's inertial subrange being reduced by the flattening of the spectra at wavenumbers of 10 cpm (0.1m scales). Strong stratification (or shear) is another mechanism that shortens the inertial subrange at the lower wavenumbers<ref name="Bluteau.etal2011">{{Cite journal
	\|authors= C.E. Bluteau, N.L. Jones, and G. Ivey		\|authors= C.E. Bluteau, N.L. Jones, and G. Ivey
	\|journal_or_publisher= Limnol. Oceanogr.: Methods		\|journal_or_publisher= Limnol. Oceanogr.: Methods

CynthiaBluteau: /* Inertial subrange collapse and anisotropy */

2022-07-05T18:25:55Z

Inertial subrange collapse and anisotropy

← Older revision		Revision as of 18:25, 5 July 2022
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	Near boundaries or low energy environments, are defined as flows with a small separation between the large turbulent overturns <math>L</math> and the smallest (Kolmogorov).		Near boundaries or low energy environments, are defined as flows with a small separation between the large turbulent overturns <math>L</math> and the smallest (Kolmogorov).

	[[File:Anisotropy.png\|center\|thumbnail\|Example of how [[Velocity inertial subrange model#anisotropy\| turbulence anisotropy]] influences the velocity spectral shapes. This instrument was located very close to the bed (0.15 m) in a shallow waterway less than 2 m deep, which results in the vertical velocity's inertial subrange being reduced by the flattening of the spectra at wavenumbers of 10 cpm (0.1m scales). Strong stratification (or shear) is another mechanism that shortens the inertial subrange at the lower wavenumbers. The wavenumber at which its impact is felt is approximately <math>L_o/3</math> where <math>L_o</math> is the Ozmidov length scale.]]		[[File:Anisotropy.png\|center\|thumbnail\|600px\|Example of how [[Velocity inertial subrange model#anisotropy\| turbulence anisotropy]] influences the velocity spectral shapes. This instrument was located very close to the bed (0.15 m) in a shallow waterway less than 2 m deep, which results in the vertical velocity's inertial subrange being reduced by the flattening of the spectra at wavenumbers of 10 cpm (0.1m scales). Strong stratification (or shear) is another mechanism that shortens the inertial subrange at the lower wavenumbers </ref><ref name="Bluteau.etal2011">{{Cite journal
			\|authors= C.E. Bluteau, N.L. Jones, and G. Ivey
			\|journal_or_publisher= Limnol. Oceanogr.: Methods
			\|paper_or_booktitle= Estimating turbulent kinetic energy dissipation using the inertial subrange method in environmental flows
			\|year= 2011
			\|doi=10:4319/lom.2011.9.302
			}}</ref>. The wavenumber at which its impact is felt is approximately <math>L_o/3</math> where <math>L_o</math> is the Ozmidov length scale.]]

	== Notes ==		== Notes ==

CynthiaBluteau at 18:24, 5 July 2022

2022-07-05T18:24:34Z

← Older revision		Revision as of 18:24, 5 July 2022
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	Near boundaries or low energy environments, are defined as flows with a small separation between the large turbulent overturns <math>L</math> and the smallest (Kolmogorov).		Near boundaries or low energy environments, are defined as flows with a small separation between the large turbulent overturns <math>L</math> and the smallest (Kolmogorov).

	~~{{FontColor~~\|~~fg=white~~\|~~bg=red~~\|~~text=Add example spectra, and link~~ to ~~Kolmogorv~~, ~~Maybe refer to SV94}}~~		[[File:Anisotropy.png\|center\|thumbnail\|Example of how [[Velocity inertial subrange model#anisotropy\| turbulence anisotropy]] influences the velocity spectral shapes. This instrument was located very close to the bed (0.15 m) in a shallow waterway less than 2 m deep, which results in the vertical velocity's inertial subrange being reduced by the flattening of the spectra at wavenumbers of 10 cpm (0.1m scales). Strong stratification (or shear) is another mechanism that shortens the inertial subrange at the lower wavenumbers. The wavenumber at which its impact is felt is approximately <math>L_o/3</math> where <math>L_o</math> is the Ozmidov length scale.]]



	== Notes ==		== Notes ==

CynthiaBluteau at 14:04, 5 July 2022

2022-07-05T14:04:40Z

← Older revision		Revision as of 14:04, 5 July 2022
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	<math>\Psi_{Vj}(\hat{k})=a_jC_k\varepsilon^{2/3}\hat{k}^{-5/3}</math>		<math>\Psi_{Vj}(\hat{k})=a_jC_k\varepsilon^{2/3}\hat{k}^{-5/3}</math>

	[[File:InertialSubrangeSchematic.png\|thumb\|Sketch of velocity power density spectrum in log-log space. The inertial subrange's -5/3 slope is highlighted. The vertical axis represents <math>\Psi_{Vj}(\hat{k})</math>. Large scale [[~~Anisotropic turbulence~~\|turbulence anisotropy]] in low energy flow may alter the expected spectral shape]]		[[File:InertialSubrangeSchematic.png\|thumb\|Sketch of velocity power density spectrum in log-log space. The inertial subrange's -5/3 slope is highlighted. The vertical axis represents <math>\Psi_{Vj}(\hat{k})</math>. Large scale [[#anisotropy\|turbulence anisotropy]] in low energy flow may alter the expected spectral shape]]

	Here <math>\hat{k}</math> is expressed in rad/m and <math>Vj</math> represents the velocities <math>V</math> in direction <math>j</math>. <math>C_k</math> is the empirical Kolmogorov universal constant of C		Here <math>\hat{k}</math> is expressed in rad/m and <math>Vj</math> represents the velocities <math>V</math> in direction <math>j</math>. <math>C_k</math> is the empirical Kolmogorov universal constant of C
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	{{FontColor\|fg=white\|bg=red\|text=Add example spectra, and link to Kolmogorv, Maybe refer to SV94}}		{{FontColor\|fg=white\|bg=red\|text=Add example spectra, and link to Kolmogorv, Maybe refer to SV94}}

	~~Testing my new anchor [[#anisotropy\|anisotropy]]~~

	== Notes ==		== Notes ==

CynthiaBluteau: /* Inertial subrange collapse and anisotropy */

2022-07-05T14:03:17Z

Inertial subrange collapse and anisotropy

← Older revision		Revision as of 14:03, 5 July 2022
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	</ref>		</ref>

	== Inertial subrange collapse and anisotropy ==		== Inertial subrange collapse and <span id="anisotropy">anisotropy</span> ==
	Near boundaries or low energy environments, are defined as flows with a small separation between the large turbulent overturns <math>L</math> and the smallest (Kolmogorov).		Near boundaries or low energy environments, are defined as flows with a small separation between the large turbulent overturns <math>L</math> and the smallest (Kolmogorov).

	{{FontColor\|fg=white\|bg=red\|text=Add example spectra, and link to Kolmogorv, Maybe refer to SV94}}		{{FontColor\|fg=white\|bg=red\|text=Add example spectra, and link to Kolmogorv, Maybe refer to SV94}}

			Testing my new anchor [[#anisotropy\|anisotropy]]

	== Notes ==		== Notes ==

CynthiaBluteau: /* Inertial subrange for flows influenced by surface waves */

2022-07-05T13:54:39Z

Inertial subrange for flows influenced by surface waves

← Older revision		Revision as of 13:54, 5 July 2022
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	* In the other directions <math>a_2=a_3=\frac{4}{3}a_1</math>		* In the other directions <math>a_2=a_3=\frac{4}{3}a_1</math>

	== ~~Inertial subrange for flows~~ influenced by surface waves ==		== Models influenced by surface waves ==
	{{FontColor\|fg=white\|bg=red\|text=Need to add equations and figures from Lumley & Terray}}<ref name="Lumley_Terray">		{{FontColor\|fg=white\|bg=red\|text=Need to add equations and figures from Lumley & Terray}}<ref name="Lumley_Terray">
	{{Cite journal		{{Cite journal

CynthiaBluteau: /* Inertial subrange for steady-flows */

2022-07-05T13:53:31Z

Inertial subrange for steady-flows

← Older revision		Revision as of 13:53, 5 July 2022
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	\|instrument_type=Velocity point-measurements, Velocity profilers		\|instrument_type=Velocity point-measurements, Velocity profilers
	}}		}}
	== ~~Inertial subrange~~ for steady-flows ==		== Model for steady-flows ==
	This theoretical model predicts the spectral shape of velocities in wavenumber space.		This theoretical model predicts the spectral shape of velocities in wavenumber space.