Energy considerations for nonlinear equatorial water waves
American Institute of Mathematical Sciences (AIMS)
In this article we consider the excess kinetic and potential energies for exact nonlinear equatorial water waves. An investigation of linear waves establishes that the excess kinetic energy density is always negative, whereas the excess potential energy density is always positive, for periodic travelling irrotational water waves in the steady reference frame. For negative wavespeeds, we prove that similar inequalities must also hold for nonlinear wave solutions. Characterisations of the various excess energy densities as integrals along the wave surface profile are also derived.
Nonlinear water waves , Wave energy , Equatorial , Exact solutions
Henry, D. (2022) 'Energy considerations for nonlinear equatorial water waves', Communications on Pure and Applied Analysis, 21(7), pp. 2337-2356. doi: 10.3934/cpaa.2022057
© 2022, American Institute of Mathematical Sciences. This is the version of the article before peer review or editing, as submitted by an author to Communications on Pure and Applied Analysis. AIMS is not responsible for any errors or omissions in this version of the manuscript, or any version derived from it. The version of record is available online: https://dx.doi.org/10.3934/cpaa.2022057