Horizontal particle velocities in long waves

1981 ◽  
Vol 86 (C5) ◽  
pp. 4138 ◽  
Author(s):  
I. A. Svendsen ◽  
C. Staub
2016 ◽  
Vol 801 ◽  
pp. 260-288 ◽  
Author(s):  
F. Fedele ◽  
C. Chandre ◽  
M. Farazmand

We derive the John–Sclavounos equations, describing the motion of a fluid particle on the sea surface, from first principles using Lagrangian and Hamiltonian formalisms applied to the motion of a frictionless particle constrained on an unsteady surface. This framework leads to a number of new insights into the particle kinematics. The main result is that vorticity generated on a stress-free surface vanishes at a wave crest when the horizontal particle velocity equals the crest propagation speed, which is the kinematic criterion for wave breaking. If this holds for the largest crest, then the symplectic two-form associated with the Hamiltonian dynamics reduces instantaneously to that associated with the motion of a particle in free flight, as if the surface did not exist. Further, exploiting the conservation of the Hamiltonian function for steady surfaces and travelling waves, we show that particle velocities remain bounded at all times, ruling out the possibility of the finite-time blowup of solutions.


1997 ◽  
Vol 32 (2-3) ◽  
pp. 163-180 ◽  
Author(s):  
J. Bosboom ◽  
G. Klopman ◽  
J.A. Roelvink ◽  
J.A. Battjes

2003 ◽  
Vol 34 (4) ◽  
pp. 343-360 ◽  
Author(s):  
B. S. Mazumder ◽  
D. C. Dalal

A theoretical model has been developed to determine the maximum saltation layer thickness of sediment particles in water associated with the migration velocity of particle in the bed layer. This is consistent with Owen's (1964) hypothesis for saltation of uniform grain in air. The equation for mean particle velocity at the bed is derived by balancing the horizontal forces acting on the particle in the bed. The modified expression for mean particle velocity includes the effects of drag and lift coefficients, bed shear stress, coefficient of dynamic friction, settling velocity and pivoting angle. The saltation layer model presented here extends a reasonable physical assumption by converting the average horizontal particle velocity to a vertical component of velocity due to collisions with particles resting on the bed. This explicitly shows a functional dependence of saltation height on mean particle velocity and take-off angle. The proposed model has been tested using available experimental data and the agreement with particle velocities and saltation heights is excellent. An interesting outcome is that a quadratic relationship is suggested between the higher transport stage (upper plane bed) and the take-off angle of particle. This shows that the take-off angle decreases with increase in transport stage.


2014 ◽  
Vol 31 (4) ◽  
pp. 999-1011 ◽  
Author(s):  
N. Stark ◽  
A. E. Hay ◽  
R. Cheel ◽  
L. Zedel ◽  
D. Barclay

Abstract A prototype wideband coherent Doppler profiler (MFDop) was tested for measuring bedload velocity of different gravel and coarse-sand-sized fractions (d = 1–32 mm) in the laboratory. The sediment was spread out on a smooth-surface tray, and motion was initiated by tilting the tray at angles of α = 20°–39° from the horizontal. Particle velocities downslope (u), cross slope (υ), and vertical to the tray (w) were determined for different MFDop parameter settings, such as monostatic/bistatic configuration, acoustic beam angle, and pulse length. Video observations of bed particle velocity were made for comparison to the acoustic measurements. Velocities estimated using the MFDop equal to, on average, 71%–74% of the velocities determined using the video observations. Standard deviations ranged from 21% to 35%, including observed irregular motion. Three stages of sediment motion were observed: (i) single particles moving with u ≤ 5 cm s−1, (ii) varying motion of particles and particle groups with predominantly 5 cm s−1 ≤ u ≤ 20 cm s−1, and (iii) fast sheetlike motion with u ≥ 20 cm s−1. The cross-slope velocity υ and the vertical velocity w were significantly smaller than u, hinting at slipping as the major particle motion rather than rolling or saltation. Comparisons between MFDop and video-determined velocities showed good agreement. Standard deviations for the MFDop velocity estimates ranged from 22% to 35%. The trials with different gravelly sediments and coarse sand revealed a significant influence of grain size, as well as grain shape impacting the initiation of sediment transport and transport velocities.


2010 ◽  
pp. 78-92 ◽  
Author(s):  
V. Klinov

Rates and factors of modern world economic growth and the consequences of rapid expansion of the economies of China and India are analyzed in the article. Modification of business cycles and long waves of economic development are evaluated. The need of reforming business taxation is demonstrated.


1995 ◽  
Vol 165 (12) ◽  
pp. 1403 ◽  
Author(s):  
R.Kh. Zeytounian
Keyword(s):  

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