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We investigate scalar spectra in a Hele-Shaw cell, where mixing is achieved through chaotic advection. Even though the flow is almost 2D (the dependance in z is parabolic velocity profile), we recover features found numerically in 3D chaotic advection, that are also similar with what one would expect in a turbulent flow: a −1.1 power-law behavior is found at intermediate scales, while the spectrum decays exponentially at the smallest scales at which diffusion is effective. Moreover, a scaling in Pe^(−1/2) (therefore in Sc^(−1/2)) is found, which is consistent with the scaling of the Batchelor scalar dissipation scale.
Author(s):
Cyril Mauger
ENS Lyon
France
Nathanaël Machicoane
ENS Lyon
France
Mickaël Bourgoin
LEGI
France
Romain Volk
ENS lyon
France
Florence Raynal
LMFA
France