Loading...
Hydrodynamic stress correlations in fluid films driven by stochastic surface forcing
Mohammadi Arzanagh, M ; Sharif University of Technology | 2018
259
Viewed
- Type of Document: Article
- DOI: 10.1103/PhysRevFluids.3.064201
- Publisher: American Physical Society , 2018
- Abstract:
- We study hydrodynamic fluctuations in a compressible and viscous fluid film confined between two rigid, no-slip, parallel plates, where one of the plates is kept fixed while the other one is driven in small-amplitude, translational displacements around its reference position. This jiggling motion is assumed to be driven by a stochastic, external, surface forcing of zero mean and finite variance. Thus, while the transverse (shear) and longitudinal (compressional) hydrodynamic stresses produced in the film vanish on average on either of the plates, these stresses exhibit fluctuations that can be quantified through their equal-time, two-point, correlation functions. For transverse stresses, we show that the correlation functions of the stresses acting on the same plate (self-correlators) as well as the correlation function of the stresses acting on different plates (cross correlators) exhibit universal, decaying, power-law behaviors as functions of the interplate separation. At small separations, the exponents are given by -1, while at large separations, the exponents are found as -2 (self-correlator on the fixed plate), -4 (excess self-correlator on the mobile plate), and -3 (cross correlator). For longitudinal stresses, we find much weaker power-law decays in the large separation regime, with exponents -3/2 (excess self-correlator on the mobile plate) and -1 (cross correlator). The self-correlator on the fixed plate increases and levels off upon increasing the interplate separation, reflecting the nondecaying nature of the longitudinal forces acting on the fixed plate. © 2018 American Physical Society
- Keywords:
- Correlators ; Hydrodynamics ; Stochastic systems ; Correlation function ; Hydrodynamic fluctuations ; Hydrodynamic stress ; Longitudinal force ; Longitudinal stress ; Power-law behavior ; Stochastic surfaces ; Translational displacements ; Separation
- Source: Physical Review Fluids ; Volume 3, Issue 6 , 29 June , 2018 ; 2469990X (ISSN)
- URL: https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.3.064201