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 breakingAbstract
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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References
Asor V.E. , Okeke E.O. ; A quantitative evaluation of the microseismic activites in the far field. Bollettino di Geofica Teorica ed Applicata, Vol. 41(2) (2000) pp. 149-158.
Aupetit B. ; On log-subharmonicity of singular values of matrices. Studia Mathematica 122 (2) (1997) , 195-199.
Babanin A.V. ; On a wave – induced turbulence and a wave –mixed upper Ocean layer. Geophysical Research Letters, Vol. 33. L20605, doi: 10.1029/2006 GL 027308, 2006.
Deep-Water Ocean Waves Teacher’s guild, The Maury project. American Meteorological Society , Washington DC, 2018.
Huang P.A. , Burrage D.M. , Wang D.W. , and Wesson J.C. ; Ocean surface roughness spectrum in high wind condition for microwave backscatter and emission computations. Journal of atmospheric and Oceanic technology Vol. 30 (2013), 2169-2183. DOI:
1175/JTECH-D-1200239.1.
Jansen P.A. ; Quasi-linear theory of wind-wave generation applied to wave forecasting. J. Phys. Oceanography , 21 (1991) , pp. 745-
Jarosz E., Mitchell D.A., Wang D.W. and Teague W.J. ; Bottom- up determination of air-sea momentum exchange under major tropical cyclone. Science 315, pp. 1707-1709, 2007.
Kara A.B, Wallcraft A.J, Metzger E.J and Hurlburt H.E. ; Notes and correspondence. Journal Climate Vol. 20, pp. 5856-5864, 2007. DOI:10.1175/2007JCL11825.1
Lin W., Sanford L.P, Suttles S.E. ; Drag coefficients with –limited wind waves. Journal of Physical Oceanography Vol. 32 (2002), pp.
-3072.
Reichl B.G, Hara T, Ginis I. ; Sea state dependence of the wind stress over the Ocean under hurricane winds. Journal of Geophysical
Research: Oceans. 119(1) (2014), pp. 30-51.
Schoen, R and Uhlenbeck, K. ; A regularity theory for harmonic maps. J. Differential Geometry 17 (1982), pp. 307-335.
SWAN Technical documentation, Cycle III version 40.5. Delft University of Technology, Netherlands, 2006.
Uwamusi S.E. Information Criteria on Regularized Least Squares Problem. Transactions of the Nigerian Association of Mathematical
Society, Vol. 11 ( January-June) (2020), pp. 173-180.
Uwamusi S.E.; Computing Square Root of Diagonalizable Matrix With Positive Eigenvalues and Iterative Solution to Nonlinear
System of Equation: The Role of Lagrange Interpolation Formula, Transactions of the Nigerian Association of Mathematical Physics,Vol. 5 (2017) pp. 65-72.
Vitanov N.K. Chabchoub A., and Hoffman N.; Deep – water waves: On the nonlinear Schrodinger equation and its solutions.
arXiv:1301.0990V1 [nlin:SI], 2013. [7] Reichl B.G, Hara T., Ginis I. Sea state dependence of the wind stress over the Ocean under hurricane winds. Journal of Geophysical Research: Oceans. 119 (1) (2014): 30-51.
Wang Y, Navon I.M, Wang X, Cheng Y. 2D Burgers equations with large Reynolds number using POD/DEIM and Calibration.
International Journal for Numerical methods in Fluids 2016; 00: 1-32.
Winter M.W (Rear Admiral). ‘’ Before the Emerging threats and capabilities’’. Subcommittee of the House armed services committee
on the Fiscal year 2016 Budget request, March 2015, USA.
You Z.J. , A close approximation of wave dispersion relation for direct calculation of wavelength in any coastal depth. Applied Ocean
Research vol. 30(2) (2008), pp. 113-119.
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