# THE EFFECTS OF WAVE BREAKING IN FAR FIELD OCEAN WATER FLOW AND THEIR GROUP VELOCITY

## Keywords:

Secondary: 34A55,11K70, 26A15, Primary: 76B15, 74J15, 76D05, 76D06, 2010 AMS subject classifications, eigenvalue problem, Navier –Stokes equations, spectral density functions, turbulence, wave breaking## Abstract

The paper presents the effects of wave breaking in the far field ocean water by wind generated from a given source with irregular heights and periods where the depth of water is considered deep and gravitational force important. We take into consideration Cariolis force and the Reynolds number from Laminar to turbulence typical of Rogue wave of the surface wind impact on Upper Ocean dynamic energy fluxes across boundary layers simultaneously interacting. Dissipation of energy waves lost in the forms of white capping, depth induced wave breaking, bottom friction and, wave-wave interactions are analyzed. Associated equations for the wind growths for both linear and exponential forms are given. It is established that wave variance densities for both potential and kinetic energies with their wave energy modulations are dependent on the wave height and water depth. The cross correlation function for the stationary ergodic real valued process for the spectral density functions and their auto correlation spectral density functions for the wave horizontal velocities inform of Fourier transform for the wave velocity and acceleration transfer functions are discussed. The regularity theory of energy minimizing harmonic maps into Riemannian manifolds in the sense of Schoelen and Uhlenbeck is introduced. The 2 D Burgers equation for the Stokes waves is stated under special conditions. The eigenvalue bounds and backward stability for the flow of waves mechanism formed the peak of discussion for the pressure matrix based on pre-conditioned iterative solvers for the incompressible flow of the Navier –Stokes equation.

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*17*, 167–178. https://nampjournals.org.ng/index.php/tnamp/article/view/192