scholarly journals Nonlinear Shear Waves in the Surf Zone

2000 ◽  
Author(s):  
John S. Allen
Keyword(s):  
Surf Zone ◽  
Shear Waves ◽  
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

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

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

scholarly journals Refraction of Surface Gravity Waves by Shear Waves

2006 ◽  
Vol 36 (4) ◽  
pp. 629-635 ◽  
Author(s):  
Stephen M. Henderson ◽  
R. T. Guza ◽  
Steve Elgar ◽  
T. H. C. Herbers
Keyword(s):  
Gravity Waves ◽  
Surf Zone ◽  
Shear Waves ◽  
Surface Gravity ◽  
Field Observations ◽  
New Model ◽  
Surface Gravity Waves ◽  
Snell’S Law ◽  
The Cross ◽  
Snell's Law

Abstract Previous field observations indicate that the directional spread of swell-frequency (nominally 0.1 Hz) surface gravity waves increases during shoreward propagation across the surf zone. This directional broadening contrasts with the narrowing observed seaward of the surf zone and predicted by Snell’s law for bathymetric refraction. Field-observed broadening was predicted by a new model for refraction of swell by lower-frequency (nominally 0.01 Hz) current and elevation fluctuations. The observations and the model suggest that refraction by the cross-shore currents of energetic shear waves contributed substantially to the observed broadening.

Overturning of nonlinear shear waves in media with power-law attenuation

2016 ◽  
Vol 140 (4) ◽  
pp. 3327-3327
Author(s):  
John M. Cormack ◽  
Mark F. Hamilton
Keyword(s):  
Power Law ◽  
Shear Waves ◽  
Nonlinear Shear

Plane nonlinear shear waves in relaxing media

2015 ◽  
Vol 137 (4) ◽  
pp. 2364-2365
Author(s):  
John Cormack ◽  
Mark F. Hamilton
Keyword(s):  
Shear Waves ◽  
Nonlinear Shear
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