TY - JOUR

T1 - Flow induced by a randomly vibrating boundary

AU - Volfson, Dmitri

AU - Viñals, Jorge

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2001/4/10

Y1 - 2001/4/10

N2 - We study the flow induced by random vibration of a solid boundary in an otherwise quiescent fluid. The analysis is motivated by experiments conducted under the low level and random effective acceleration field that is typical of a microgravity environment. When the boundary is planar and is being vibrated along its own plane, the variance of the velocity field decays as a power law of distance away from the boundary. If a low-frequency cut-off is introduced in the power spectrum of the boundary velocity, the variance decays exponentially for distances larger than a Stokes layer thickness based on the cut-off frequency. Vibration of a gently curved boundary results in steady streaming in the ensemble average of the tangential velocity. Its amplitude diverges logarithmically with distance away from the boundary, but asymptotes to a constant value instead if a low-frequency cut-off is considered. This steady component of the velocity is shown to depend logarithmically on the cut-off frequency. Finally, we consider the case of a periodically modulated solid boundary that is being randomly vibrated. We find steady streaming in the ensemble average of the first-order velocity, with flow extending up to a characteristic distance of the order of the boundary wavelength. The structure of the flow in the vicinity of the boundary depends strongly on the correlation time of the boundary velocity.

AB - We study the flow induced by random vibration of a solid boundary in an otherwise quiescent fluid. The analysis is motivated by experiments conducted under the low level and random effective acceleration field that is typical of a microgravity environment. When the boundary is planar and is being vibrated along its own plane, the variance of the velocity field decays as a power law of distance away from the boundary. If a low-frequency cut-off is introduced in the power spectrum of the boundary velocity, the variance decays exponentially for distances larger than a Stokes layer thickness based on the cut-off frequency. Vibration of a gently curved boundary results in steady streaming in the ensemble average of the tangential velocity. Its amplitude diverges logarithmically with distance away from the boundary, but asymptotes to a constant value instead if a low-frequency cut-off is considered. This steady component of the velocity is shown to depend logarithmically on the cut-off frequency. Finally, we consider the case of a periodically modulated solid boundary that is being randomly vibrated. We find steady streaming in the ensemble average of the first-order velocity, with flow extending up to a characteristic distance of the order of the boundary wavelength. The structure of the flow in the vicinity of the boundary depends strongly on the correlation time of the boundary velocity.

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U2 - 10.1017/s0022112001003585

DO - 10.1017/s0022112001003585

M3 - Article

AN - SCOPUS:0035836754

VL - 432

SP - 387

EP - 408

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -