Nonlinear interaction of internal and surface gravity waves in a two-layer fluid with free surface

2010 ◽  
Vol 168 (4) ◽  
pp. 590-602 ◽  
Author(s):  
I. T. Selezov ◽  
O. V. Avramenko ◽  
Yu. V. Gurtovyi ◽  
V. V. Naradovyi
Keyword(s):  
Free Surface ◽  
Gravity Waves ◽  
Nonlinear Interaction ◽  
Surface Gravity ◽  
Surface Gravity Waves

Steady gravity waves due to a submerged source

2013 ◽  
Vol 732 ◽  
pp. 660-686 ◽  
Author(s):  
Christopher J. Lustri ◽  
S. Jonathan Chapman
Keyword(s):  
Free Surface ◽  
Gravity Waves ◽  
Asymptotic Methods ◽  
Asymptotic Series ◽  
Surface Gravity ◽  
Transverse Waves ◽  
Surface Gravity Waves ◽  
Flow Past ◽  
Stokes Lines ◽  
Low Froude Number

AbstractIn the low-Froude-number limit, free-surface gravity waves caused by flow past a submerged obstacle have amplitude that is exponentially small. Consequently, these cannot be represented using an asymptotic series expansion. Steady linearized flow past a submerged source is considered, and exponential asymptotic methods are applied to determine the behaviour of the free-surface gravity waves. The free surface is found to contain longitudinal and transverse waves that switch on rapidly across curves known as Stokes lines on the free surface. The longitudinal waves are present everywhere downstream of the singularity, while the transverse waves are restricted to two downstream wedges. As the depth of the source approaches the surface, the familiar Kelvin-wedge wave behaviour is recovered.

Unsteady flow over a submerged source with low Froude number

2014 ◽  
Vol 25 (5) ◽  
pp. 655-680 ◽  
Author(s):  
CHRISTOPHER J. LUSTRI ◽  
S. JONATHAN CHAPMAN
Keyword(s):  
Free Surface ◽  
Unsteady Flow ◽  
Froude Number ◽  
Gravity Waves ◽  
Surface Gravity ◽  
Infinite Depth ◽  
Surface Gravity Waves ◽  
Flow Past ◽  
Low Froude Number ◽  
Exponential Asymptotics

In the low-Froude number limit, free-surface gravity waves caused by flow past a submerged obstacle have amplitude that is exponentially small. Consequently, these cannot be represented using an asymptotic series expansion. Previous studies have considered linearized steady flow past a submerged source in infinite-depth fluids, in which exponential asymptotics were used to determine the behaviour of downstream longitudinal and transverse free-surface gravity waves. Here, unsteady flow past a submerged source in an infinite-depth fluid is investigated, with the free surface taken to be initially waveless. The source is taken to be weak, and the flow is linearized about the undisturbed solution. Exponential asymptotics are applied to determine the wave behaviour on the free surface in terms of the two-dimensional plan-view, in order to show how the free surface waves evolve over time and eventually tend to the steady solution.

Experimental investigation of capillarity effects on surface gravity waves: non-wetting boundary conditions

1993 ◽  
Vol 246 ◽  
pp. 43-66 ◽  
Author(s):  
Bruno Cocciaro ◽  
Sandro Faetti ◽  
Crescenzo Festa
Keyword(s):  
Contact Angle ◽  
Experimental Investigation ◽  
Free Surface ◽  
Boundary Conditions ◽  
Gravity Waves ◽  
Contact Line ◽  
Surface Gravity ◽  
Surface Gravity Waves ◽  
Damping Rate ◽  
Vertical Walls

Damping and eigenfrequencies of surface capillary—gravity waves greatly depend on the boundary conditions. To the best of our knowledge, so far no direct measurement has been made of the dynamic behaviour of the contact angle at the three-phase interface (fluid—vapour—solid walls) in the presence of surface oscillation. Therefore, theoretical models of surface gravity–capillary waves involve ad hoc phenomenological assumptions as far as the behavior of the contact angle is concerned. In this paper we report a systematic experimental investigation of the static and dynamic properties of surface waves in a cylindrical container where the free surface makes a static contact angle $\theta_{\rm c} = 62^{\circ}$ with the vertical walls. The actual boundary condition relating the contact angle to the velocity of the contact line is obtained using a new stroboscopic optical method. The experimental results are compared with the theoretical expressions to be found in the literature. Two different regimes are observed: (i) a low-amplitude regime, where the contact line always remains at rest and the contact angle oscillates during the oscillation of the free surface; (ii) a higher-amplitude regime, where the contact line slides on the vertical walls. The profile, the eigenfrequency and the damping rate of the first non-axisymmetric mode of the surface gravity waves are investigated. The eigenfrequency and damping rate in regime (i) are in satisfactory agreement with the predictions of the Graham-Eagle theory (1983) of pinned-end edge conditions. The eigenfrequency and damping rate in regime (ii) show a strongly nonlinear dependence on the oscillation amplitude of the free surface. All the experimental results concerning regime (ii) can be explained in terms of the Hocking (1987 a) and Miles (1967, 1991) models of capillary damping by introducing an ‘effective’ capillary coefficient $\lambda_{\rm eft}$. This coefficient is directly obtained for the first time in our experiment from dynamic measurements on the contact line. A satisfactory agreement is found to exist between theory and experiment.

Sign in / Sign up

Export Citation Format

Share Document