scholarly journals Effect of Compliant Boundaries on Weakly Nonlinear Shear Waves in Channel Flow

1990 ◽  
Vol 50 (2) ◽  
pp. 361-394 ◽  
Author(s):  
James M. Rotenberry ◽  
Philip G. Saffman
Keyword(s):  
Channel Flow ◽  
Shear Waves ◽  
Weakly Nonlinear ◽  
Nonlinear Shear

Weakly nonlinear shear waves

1998 ◽  
Vol 372 ◽  
pp. 71-91 ◽  
Author(s):  
FALK FEDDERSEN
Keyword(s):  
Shear Wave ◽  
Surf Zone ◽  
Second Harmonic ◽  
Shear Waves ◽  
Finite Amplitude ◽  
Shear Instability ◽  
Weakly Nonlinear ◽  
Wide Range ◽  
Alongshore Current ◽  
Nonlinear Shear

Alongshore propagating low-frequency O(0.01 Hz) waves related to the direction and intensity of the alongshore current were first observed in the surf zone by Oltman-Shay, Howd & Birkemeier (1989). Based on a linear stability analysis, Bowen & Holman (1989) demonstrated that a shear instability of the alongshore current gives rise to alongshore propagating shear (vorticity) waves. The fully nonlinear dynamics of finite-amplitude shear waves, investigated numerically by Allen, Newberger & Holman (1996), depend on α, the non-dimensional ratio of frictional to nonlinear terms, essentially an inverse Reynolds number. A wide range of shear wave environments are reported as a function of α, from equilibrated waves at larger α to fully turbulent flow at smaller α. When α is above the critical level αc, the system is stable. In this paper, a weakly nonlinear theory, applicable to α just below αc, is developed. The amplitude of the instability is governed by a complex Ginzburg–Landau equation. For the same beach slope and base-state alongshore current used in Allen et al. (1996), an equilibrated shear wave is found analytically. The finite-amplitude behaviour of the analytic shear wave, including a forced second-harmonic correction to the mean alongshore current, and amplitude dispersion, agree well with the numerical results of Allen et al. (1996). Limitations in their numerical model prevent the development of a side-band instability. The stability of the equilibrated shear wave is demonstrated analytically. The analytical results confirm that the Allen et al. (1996) model correctly reproduces many important features of weakly nonlinear shear waves.

Cylindrically converging nonlinear shear waves

2017 ◽  
Vol 141 (5) ◽  
pp. 3551-3552
Author(s):  
John M. Cormack ◽  
Kyle S. Spratt ◽  
Mark F. Hamilton
Keyword(s):  
Shear Waves ◽  
Nonlinear Shear

Pumping or drag reduction?

2009 ◽  
Vol 635 ◽  
pp. 171-187 ◽  
Author(s):  
JÉRÔME HŒPFFNER ◽  
KOJI FUKAGATA
Keyword(s):  
Pressure Gradient ◽  
Drag Reduction ◽  
Flow Control ◽  
Channel Flow ◽  
Travelling Waves ◽  
Weakly Nonlinear ◽  
Flow Response ◽  
Flow Motion ◽  
Strongly Connected ◽  
Wall Deformation

Two types of wall actuation in channel flow are considered: travelling waves of wall deformation (peristalsis) and travelling waves of blowing and suction. The flow response and its mechanisms are analysed using nonlinear and weakly nonlinear computations. We show that both actuations induce a flux in the channel in the absence of an imposed pressure gradient and can thus be characterized as pumping. In the context of flow control, pumping and drag reduction are strongly connected, and we seek to define them properly based on these two actuation examples. Movies showing the flow motion for the two types of actuation are available with the online version of this paper (journals.cambridge.org/FLM).

Modeling of nonlinear shear waves in soft solids

2004 ◽  
Vol 116 (5) ◽  
pp. 2807-2813 ◽  
Author(s):  
Evgenia A. Zabolotskaya ◽  
Mark F. Hamilton ◽  
Yurii A. Ilinskii ◽  
G. Douglas Meegan
Keyword(s):  
Shear Waves ◽  
Soft Solids ◽  
Nonlinear Shear
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