Nonlinear interaction of wind-driven oblique surface waves and parametric growth of lower frequency modes

2012 ◽  
Vol 707 ◽  
pp. 150-190
Author(s):  
Sang Soo Lee
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Nonlinear Interaction ◽  
Critical Layer ◽  
Mode Interaction ◽  
Secondary Wave ◽  
Primary Wave ◽  
Nonlinear Growth ◽  
Free Surface Waves ◽  
Difference Mode

AbstractNonlinear interactions between free-surface waves of the same wave speed and wind are studied by extending the linear resonant theory of Miles (J. Fluid Mech., vol. 3, 1957, pp. 185–204). A nonlinear interaction can occur when the steepness of a primary three-dimensional wave, which propagates obliquely to the wind direction, becomes of the order of the cube of the density ratio of air to water. If a secondary wave of smaller amplitude is also an oblique wave, the nonlinear critical-layer interaction between the primary and secondary fluctuations in air generates a difference mode whose wavenumbers are equal to the differences between the primary and secondary values. In addition, the nonlinear interaction in the critical layer between the primary and difference modes induces a parametric-growth effect on the secondary surface wave, if the frequency of the primary wave is higher than that of the secondary wave. The primary wave remains linear during this ‘$2+ 1$ mode critical-layer interaction’ stage between two free-surface waves and a nonlinearly generated mode. The evolution of the secondary-wave amplitude is governed by an integro-differential equation and that of the difference mode is determined by an integral equation. Both inviscid and viscous numerical results show that the nonlinear growth rates become much larger than the linear growth rates. Effect of viscosity is shown to delay the onset of the nonlinear growth. The growth of the secondary and difference modes is more effectively enhanced when the signs of propagation angles of the primary and secondary waves are opposite than when they are equal. The $2+ 1$ mode interaction can occur when wave steepnesses are very small. The nonlinear interaction is entirely confined to a thin critical layer, and the perturbations outside the critical layer are governed by linear equations. It is shown that the initial nonlinear growth of a free-surface wave could be governed by a mode–mode interaction in air.

Study on vibration of dragon wash basin and free surface waves inside

2018 ◽  
Vol 35 (1) ◽  
pp. 15-23
Author(s):  
Zi-Yu Guo ◽  
Xiao-Peng Chen ◽  
Lai-Bing Jia ◽  
Bin Xu
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Wash Basin ◽  
Free Surface Waves

Pseudo-three-timescale approximation of exponentially modulated free-surface waves

2009 ◽  
Vol 625 ◽  
pp. 435-443 ◽  
Author(s):  
MARK A. KELMANSON
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Test Problem ◽  
Evolution Equations ◽  
Film Coating ◽  
Rotating Cylinder ◽  
New Method ◽  
Free Surface Waves ◽  
Numerical Integrations ◽  
Order Of Magnitude

A novel pseudo-three-timescale asymptotic procedure is developed and implemented for obtaining accurate approximations to solutions of an evolution equation arising in thin-film free-surface viscous flow. The new procedure, which employs strained fast and slow timescales, requires considerably fewer calculations than its standard three-timescale counterpart employing fast, slow and slower timescales and may readily be applied to other evolution equations of fluid mechanics possessing wave-like solutions exhibiting exponential decay in amplitude and variations in phase over disparate timescales. The new method is validated on the evolution of free-surface waves on a thin, viscous film coating the exterior of a horizontal rotating cylinder and is shown to yield accurate solutions up to non-dimensional times exceeding by an order of magnitude those of previous related studies. Results of the new method applied to this test problem are demonstrated to be in excellent agreement, over large timescales, with those of corroborative spectrally accurate numerical integrations.

Large amplitude progressive interfacial waves

1979 ◽  
Vol 93 (3) ◽  
pp. 433-448 ◽  
Author(s):  
Judith Y. Holyer
Keyword(s):  
Free Surface ◽  
Surface Wave ◽  
Surface Waves ◽  
Large Amplitude ◽  
Phase Speed ◽  
Maximum Height ◽  
Interfacial Waves ◽  
Free Surface Waves ◽  
Lower Fluid ◽  
Over The Top

This paper contains a study of large amplitude, progressive interfacial waves moving between two infinite fluids of different densities. The highest wave has been calculated using the criterion that it has zero horizontal fluid velocity at the interface in a frame moving at the phase speed of the waves. For free surface waves this criterion is identical to the criterion due to Stokes, namely that there is a stagnation point at the crest of each wave. I t is found that as the density of the upper fluid increases relative to the density of the lower fluid the maximum height of the wave, for fixed wavelength, increases. The maximum height of a Boussinesq wave, which has the density almost the same above and below the interface, is 2·5 times the maximum height of a surface wave of the same wavelength. A wave with air over the top of it can be about 2% higher than the highest free surface wave. The point at which the limiting criterion is first satisfied moves from the crest for free surface waves to the point half-way between the crest and the trough for Boussinesq waves. The phase speed, momentum, energy and other wave properties are calculated for waves up to the highest using Padé approximants. For free surface waves and waves with air above the interface the maximum value of these properties occurs for waves which are lower than the highest. For Boussinesq waves and waves with the density of the upper fluid onetenth of the density of the lower fluid these properties each increase monotonically with the wave height.

scholarly journals Heat transfer in the seabed boundary layer

2021 ◽  
Vol 928 ◽  
Author(s):  
S. Michele ◽  
R. Stuhlmeier ◽  
A.G.L. Borthwick
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Free Surface ◽  
Surface Waves ◽  
Multiple Scales ◽  
Perturbation Expansion ◽  
Phase Speed ◽  
Maximum Heat ◽  
Practical Applications ◽  
Free Surface Waves

We present a theoretical model of the temperature distribution in the boundary layer region close to the seabed. Using a perturbation expansion, multiple scales and similarity variables, we show how free-surface waves enhance heat transfer between seawater and a seabed with a solid, horizontal, smooth surface. Maximum heat exchange occurs at a fixed frequency depending on ocean depth, and does not increase monotonically with the length and phase speed of propagating free-surface waves. Close agreement is found between predictions by the analytical model and a finite-difference scheme. It is found that free-surface waves can substantially affect the spatial evolution of temperature in the seabed boundary layer. This suggests a need to extend existing models that neglect the effects of a wave field, especially in view of practical applications in engineering and oceanography.

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