Zakharov Equation for Surface Gravity Waves

 


Modified Zakharov Equation     2.18, 2.23, 3.2, 4.2

·  M. Stiassnie and L. Shemer, On modifications of the Zakharov equations for surface
gravity waves, J. of Fluid Mech., 143, 1984, 47-67.

·  M. Stiassnie and L. Shemer, Energy computation for  evolution of class I and II instabilities of Stokes waves, 1987, J. of Fluid Mech , 174, 299-312.

·  L.Shemer and M. Stiassnie,  Initial instability and long-time evolution of Stokes waves, in “The Ocean Surface: wave breaking turbulent mixing and  radio probing”, edited by  Y. Toba & H. Mitsuyasu, 1985, 51-57.

·  L. Shemer and M. Stiassnie, 1991. The Zakharov and Modified Zakharov
equation and their applications, in Nonlinear Topics in Ocean Physics,
Proceedings of the International School of Physics Enrico Fermi, 1988, A.R.
Osborn, Ed., 581-620.

Discretized Zakharov Equation  2.39, 2.51, 2.56, 2.66

·  J. Rasmussen and M. Stiassnie, Discretization of Zakharov’s equation, 1999, European J. of Mechanics – B/Fluids, 18, 353-364.

·  O. Gramstad, Y. Agnon and M. Stiassnie, The localized Zakharov equation:
Derivation and Validation, 2011, European J. of Mech. B./Fluids, 30, 137-146.

·  Dali Xu, Zhiliang Lin, Shijun Liao and Michael Stiassnie, On the steady-state fully resonant progressive waves in water of finite depth, 2012, J. of Fluid
Mech. 710, 379-418.

·  Shijun Liao, Dali Xu and Michael Stiassnie, On the steady-state nearly resonant waves, 2016, J. of Fluid Mech., 794, 175-199.

Finite Water Depth  2.49

·  M. Stiassnie and O. Gramstad, On Zakharov’s kernel and the interaction of non-collinear wavetrans in finite water degth, 2009, J. of Fluid Mech., 639, 433-442.

Focus on Fluids  4.4

·  M. Stiassnie, On the strength of the weakly nonlinear theory for surface gravity
waves, 2017, J. Fluid Mech., 810, 1-4.