title: Extension of the momentum transfer model to time-dependent pipe turbulence.
abstract: We analyze a possible extension of Gioia and Chakraborty's momentum transfer model of friction in steady turbulent pipe flows [Phys. Rev. Lett. 96, 044502 (2006)] to the case of time- and/or space-dependent turbulent flows. The end result is an expression for the stress at the wall as the sum of a steady and a dynamic component. The steady part is obtained by using the instantaneous velocity in the expression for the stress at the wall of a stationary flow. The unsteady part is a weighted average over the history of the flow acceleration, with a weighting function similar to that proposed by Vardy and Brown [J. Sound Vibr. 259, 1011 (2003); J. Sound Vibr. 270, 233 (2004)], but naturally including the effect of spatial derivatives of the mean flow, as in the Brunone model [Brunone et al., J. Water Res. Plan. Manage. 126, 236 (2000)].
authors.affiliation: Departamento de Física, FCEN, Universidad de Buenos Aires, and IFIBA-CONICET, Pabellón I, 1428, Buenos Aires, Argentina. calzetta@df.uba.ar
authors.forename: Esteban
authors.initials: E
authors.lastname: Calzetta