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Macroscopic effects of the spectral structure in turbulent flows
 Nature Physics
"... There is a missing link between the macroscopic properties of turbulent flows1–4, such as the frictional drag5 of a wallbounded flow, and the turbulent spectrum1,6,7. The turbulent spectrum is a power law of exponentα (the ‘spectral exponent’) that gives the characteristic velocity of a turbulent f ..."
Abstract

Cited by 4 (1 self)
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There is a missing link between the macroscopic properties of turbulent flows1–4, such as the frictional drag5 of a wallbounded flow, and the turbulent spectrum1,6,7. The turbulent spectrum is a power law of exponentα (the ‘spectral exponent’) that gives the characteristic velocity of a turbulent fluctuation (or ‘eddy’) of size s as a function of s (ref. 1). Here we seek the missing link by comparing the frictional drag in soapfilm flows8, where α = 3 (refs 9,10), and in pipe flows5, where α = 5/3 (refs 11,12). For moderate values of the Reynolds number Re, we find experimentally that in soapfilm flows the frictional drag scales as Re−1/2, whereas in pipe flows the frictional drag scales13 as Re−1/4. Each of these scalings may be predicted from the attendant value of α by using a new theory14–16, in which the frictional drag is explicitly linked to the turbulent spectrum.
EXPERIMENTS IN TURBULENT SOAPFILM FLOWS: MARANGONI SHOCKS, FRICTIONAL DRAG, AND ENERGY SPECTRA BY
"... We carry out unprecedented experimental measurements of the frictional drag in turbulent soapfilm flows over smooth walls. These flows are effectively twodimensional, and we are able to create soapfilm flows with the two types of turbulent spectrum that are theoretically possible in two dimension ..."
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We carry out unprecedented experimental measurements of the frictional drag in turbulent soapfilm flows over smooth walls. These flows are effectively twodimensional, and we are able to create soapfilm flows with the two types of turbulent spectrum that are theoretically possible in two dimensions: the “enstrophy cascade, ” for which the spectral exponent α = 3, and the “inverse energy cascade, ” for which the spectral exponent α = 5/3. We find that the functional relation between the frictional drag f and the Reynolds number Re depends on the spectral exponent: where α = 3, f ∝ Re−1/2; where α = 5/3, f ∝ Re−1/4. These findings cannot be reconciled with the classic theory of the frictional drag. The classic theory provides no means of distinguishing between one type of turbulent spectrum and another, and cannot account for the existence of a “spectral link ” between the frictional drag and the turbulent spectrum. In view of our experimental results, we conclude that the classic theory must be considered incomplete. In contrast, our findings are consistent with a recently proposed spectral theory of the frictional drag. In this theory the frictional drag of turbulent flows on smooth walls is pre
EXPERIMENTS IN TURBULENT SOAPFILM FLOWS: MARANGONI SHOCKS, FRICTIONAL DRAG, AND ENERGY SPECTRA
, 2011
"... We carry out unprecedented experimental measurements of the frictional drag in turbulent soapfilm flows over smooth walls. These flows are effectively twodimensional, and we are able to create soapfilm flows with the two types of turbulent spectrum that are theoretically possible in two dimension ..."
Abstract
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We carry out unprecedented experimental measurements of the frictional drag in turbulent soapfilm flows over smooth walls. These flows are effectively twodimensional, and we are able to create soapfilm flows with the two types of turbulent spectrum that are theoretically possible in two dimensions: the “enstrophy cascade, ” for which the spectral exponent α = 3, and the “inverse energy cascade, ” for which the spectral exponent α = 5/3. We find that the functional relation between the frictional drag f and the Reynolds number Re depends on the spectral exponent: where α = 3, f ∝ Re −1/2; where α = 5/3, f ∝ Re −1/4. These findings cannot be reconciled with the classic theory of the frictional drag. The classic theory provides no means of distinguishing between one type of turbulent spectrum and another, and cannot account for the existence of a “spectral link” between the frictional drag and the turbulent spectrum. In view of our experimental results, we conclude that the classic theory must be considered incomplete. In contrast, our findings are consistent with a recently proposed spectral theory of the frictional drag. In this theory the frictional drag of turbulent flows on smooth walls is predicted to be f ∝ Re (1−α)/(1+α) , where α is the spectral exponent. This prediction is in exact
Experiments in . . . : MARANGONI SHOCKS, FRICTIONAL DRAG, AND ENERGY SPECTRA
, 2011
"... We carry out unprecedented experimental measurements of the frictional drag in turbulent soapfilm flows over smooth walls. These flows are effectively twodimensional, and we are able to create soapfilm flows with the two types of turbulent spectrum that are theoretically possible in two dimension ..."
Abstract
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We carry out unprecedented experimental measurements of the frictional drag in turbulent soapfilm flows over smooth walls. These flows are effectively twodimensional, and we are able to create soapfilm flows with the two types of turbulent spectrum that are theoretically possible in two dimensions: the “enstrophy cascade, ” for which the spectral exponent α = 3, and the “inverse energy cascade, ” for which the spectral exponent α = 5/3. We find that the functional relation between the frictional drag f and the Reynolds number Re depends on the spectral exponent: where α = 3, f ∝ Re −1/2; where α = 5/3, f ∝ Re −1/4. These findings cannot be reconciled with the classic theory of the frictional drag. The classic theory provides no means of distinguishing between one type of turbulent spectrum and another, and cannot account for the existence of a “spectral link ” between the frictional drag and the turbulent spectrum. In view of our experimental results, we conclude that the classic theory must be considered incomplete. In contrast, our findings are consistent with a recently proposed spectral theory of the frictional drag. In this theory the frictional drag of turbulent flows on smooth walls is predicted to be f ∝ Re (1−α)/(1+α) , where α is the spectral exponent. This prediction is in exact
2 Design and Process/Measurement for Immersed Element Control in a Reconfigurable Vertically Falling Soap Film
, 2007
"... Summary: Reinforcement learning has proven successful at harnessing the passive dynamics of underactuated systems to achieve least energy solutions. However, coupled fluidstructural models are too computationally intensive for intheloop control in viscous flow regimes. My vertically falling soap ..."
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Summary: Reinforcement learning has proven successful at harnessing the passive dynamics of underactuated systems to achieve least energy solutions. However, coupled fluidstructural models are too computationally intensive for intheloop control in viscous flow regimes. My vertically falling soap film will provide a reconfigurable experimental environment for machine learning controllers. The realtime position and velocity data will be collected with a High Speed Video system, illuminated by a Low Pressure Sodium Lamp. Approximating lines of interference within the soap film to known pressure variations, controllers will shape downstream flow to desired conditions.
turbulence. Part I: Direct methods
"... The widely accepted theory of twodimensional turbulence predicts a direct enstrophy cascade with an energy spectrum which behaves in terms of the frequency range k as k3 and an inverse energy cascade with a k5=3 decay. However the graphic representation of the energy spectrum (even its shape) is cl ..."
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The widely accepted theory of twodimensional turbulence predicts a direct enstrophy cascade with an energy spectrum which behaves in terms of the frequency range k as k3 and an inverse energy cascade with a k5=3 decay. However the graphic representation of the energy spectrum (even its shape) is closely related to the tool which is used to perform the numerical computation. With the same initial
ow, eventually treated thanks to dierent tools such as wavelet decompositions or POD representations, the energy spectra are computed using direct various methods: FFT, autocovariance function, auto regressive model, wavelet transform. Numerical results are compared to each other and confronted with theoretical predictions. In a forthcoming part II some adaptative methods combined with the above direct ones will be developed. Key words and phrases: timeseries analysis, power spectra, auto correlation, wavelets decomposition, auto regressive methods, proper orthogonal decomposition, wavelet and cosine packets. 2000 AMS Mathematics Subject Classication  94A12, 62M10 1