Modeling film flows down inclined planes. Ruyer-Quil, C. and Manneville, P. Eur. Phys. J. B, 1998.
Modeling film flows down inclined planes [pdf]Paper  abstract   bibtex   
A new model of film flow down an inclined plane is derived by a method combining results of the classical long wavelength expansion to a weighted-residuals technique. It can be expressed as a set of three coupled evolution equations for three slowly varying fields, the thickness h, the flow-rate q, and a new variable τ that measures the departure of the wall shear from the shear predicted by a parabolic velocity profile. Results of a preliminary study are in good agreement with theoretical asymptotic properties close to the instability threshold, laboratory experiments beyond threshold and numerical simulations of the full Navier–Stokes equations.
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 title = {Modeling film flows down inclined planes},
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 abstract = {A new model of film flow down an inclined plane is derived by a method combining results of the classical long wavelength expansion to a weighted-residuals technique. It can be expressed as a set of three coupled evolution equations for three slowly varying fields, the thickness h, the flow-rate q, and a new variable τ that measures the departure of the wall shear from the shear predicted by a parabolic velocity profile. Results of a preliminary study are in good agreement with theoretical asymptotic properties close to the instability threshold, laboratory experiments beyond threshold and numerical simulations of the full Navier–Stokes equations.},
 bibtype = {article},
 author = {Ruyer-Quil, C and Manneville, P},
 journal = {Eur. Phys. J. B}
}
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