scholarly journals Discontinuous Galerkin Method for Linear Free-Surface Gravity Waves

2005 ◽  
Vol 22-23 (1-3) ◽  
pp. 531-567 ◽  
Author(s):  
J.J.W. van der Vegt ◽  
S.K. Tomar
Keyword(s):  
Free Surface ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Gravity Waves ◽  
Surface Gravity ◽  
Surface Gravity Waves

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.

Sign in / Sign up

Export Citation Format

Share Document