scholarly journals The transformation between the Eulerian and Lagrangian solutions for irrotational standing gravity waves

2009 ◽  
Vol 58 (6) ◽  
pp. 3637
Author(s):  
Chen Yang-Yih ◽  
Hsu Hung-Chu
Keyword(s):  
Gravity Waves ◽  
Standing Gravity Waves

STANDING GRAVITY WAVES OF FINITE AMPLITUDE

1967 ◽  
pp. 691-712 ◽  
Author(s):  
LAWRENCE R. MACK ◽  
BENNY E. JAY ◽  
DONALD F. SATTLER
Keyword(s):  
Gravity Waves ◽  
Finite Amplitude ◽  
Standing Gravity Waves

The Transformation Between the Eulerian and Lagrangian Solutions for Irrotational Standing Gravity Waves

2009 ◽  
Author(s):  
Yang-Yih Chen ◽  
Hung-Chu Hsu
Keyword(s):  
Gravity Waves ◽  
Particle Motion ◽  
Mass Conservation ◽  
Perturbation Parameter ◽  
Third Order ◽  
The Third ◽  
Asymptotic Expressions ◽  
Lagrangian Form ◽  
Standing Gravity Waves ◽  
The Given

This study reports the transformations between the third-order Eulerian and Lagrangian solutions for the standing gravity waves on the uniform depth. Regarding the motion of a marked fluid particle, the instantaneous velocity, the mass conservation and the free surface must be the same for either Eulerian or Lagrangian methods. We impose the assumption that the Lagrangian wave frequency is a function of wave steepness. Expanding the unknown function in a small perturbation parameter and using a successive expansion in a Taylor series for the water particle path and the period of a particle motion, the third order asymptotic expressions for the particle trajectories and the period of particle motion can be derived directly in Lagrangian form. It shows that the given Eulerian solutions are capable of being transformed into the completely unknown Lagrangian solutions and the reversible process is also identified.

GLIDE OF STANDING SOLITARY WAVE IN AN INCLINED LONG WATER TROUGH

1992 ◽  
Vol 06 (18) ◽  
pp. 3021-3030
Author(s):  
Y. XU ◽  
R. WEI
Keyword(s):  
Solitary Wave ◽  
Gravity Waves ◽  
Solitary Wave Solution ◽  
Type Equation ◽  
Additional Term ◽  
Water Layer ◽  
Multiple Scale ◽  
Variable Depth ◽  
Water Trough ◽  
Standing Gravity Waves

A NLS-type equation with an additional term of variable coefficient governing the modulational evolution of standing gravity waves on a water layer with slowly variable depth is obtained by using the multiple scale method to the potential-flow boundary value problem. A single solitary wave solution of this equation, that corresponds to the standing solitary wave observed by Wu et al. in a slightly inclined rectangular water trough, is given. It is found that such solitary wave moves slowly, with an acceleration, toward the shallow region.

scholarly journals Existence of Multimodal Standing Gravity Waves

2005 ◽  
Vol 7 (S3) ◽  
pp. S349-S364 ◽  
Author(s):  
Gérard Iooss ◽  
Pavel Plotnikov
Keyword(s):  
Gravity Waves ◽  
Standing Gravity Waves
Sign in / Sign up

Export Citation Format

Share Document