Volume 98, Number 1, April 2012
|Number of page(s)||6|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||05 April 2012|
Variable enstrophy flux and energy spectrum in two-dimensional turbulence with Ekman friction
Department of Physics, Indian Institute of Technology - Kanpur, 208016 India
Accepted: 6 March 2012
Experiments and numerical simulations reveal that in the forward cascade regime, the energy spectrum of two-dimensional turbulence with Ekman friction deviates from Kraichnan's prediction of k− 3 power spectrum. In this letter we explain this observation using an analytic model based on variable enstrophy flux arising due to Ekman friction. We derive an expression for the enstrophy flux which exhibits a logarithmic dependence in the inertial range for the Ekman-friction–dominated flows. The energy spectrum obtained using this enstrophy flux shows a power law scaling for large Reynolds number and small Ekman friction, but has an exponential behaviour for large Ekman friction and relatively small Reynolds number.
PACS: 47.27.E- – Turbulence simulation and modeling / 47.27.Gs – Isotropic turbulence; homogeneous turbulence / 47.27.eb – Statistical theories and models
© EPLA, 2012
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