MODELS IN MARINE SCIENCE MARN 391

1. MODELS IN MARINE SCIENCEMARN 391 ERICK RAFAEL RIVERA LEMUS

3. WAVE DATA • WAVE HEIGHT (Hs) -> meters • DOMINANT PERIOD (s) • AVERAGE PERIOD (s) • FREQUENCY (1/s) • HISTOGRAMS

6. Generation of waves involves the transfer of energy from wind to waves • Higher frequency (shorter periods) Energy content is at a maximum. Equilibrium range • Lower frequency (longest periods) Energy content is at a minimum. Growth range

7. WIND AND WAVE DATA • Wind Speed • Rose Wind • Frequency of Winds • Histograms

10. Numerical wave prediction models • They have been formulated in terms of the basic transport equation for the two dimensional wave spectrum (Gelci et al. 1957) • S = Sin (Wind) + Snl (Non-linearity) + Sds (Dissipation) • None of the wave models developed have actually computed the wave spectrum from first principles. Ad hoc assumptions have always been introduced to force the spectrum.

11. Fetch-limited wave growth Fetch limited growth case had been extended to finite depth

12. Fetch limited Growth • Comparison of various results from second generation models • Different second generation models exhibit rather different Fetch/Energy • Differences between second generation models are fairly large with WAM curve lying somewhere in the middle

13. Things to consider • Calculations should be checked: • DURATION LIMITED • FETCH LIMITED • UA (Winds over water) • Delineating a Fetch • Waves for shallow water

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15. First Generation Wave Models • Avoided to explicitly modeled the Energy balance. Not specifying how the spectrum attained equilibrium • Physical processes not represented properly • Dissipation is assumed with an universal upper limit of the spectral densities (Phillip’s frequency) • Exhibit basic quantitative shortcomings: they overestimated wind input and underestimated strength of the non-linearity

16. Second Generation Wave model • Wave growth experiments (wind and wave measurements) • Parameterization of the wind and dissipation source function • Restrictions resulted from simplifying the nonlinear transfer parameterization required the spectral shape to be for frequencies higher than peak frequency • Unable to properly simulate complex windseas (hurricanes, fronts, storms) • These models do not compute all relevant physical processes (wave breaking, wave-wave interaction)

17. WAM –Third generation models- • SWAMP study proposed techniques to apply for Third generation models • Eulerian approach. Wave evolution is formulated on a grid • Wave spectrum computed alone by integration of the basic transport equation, without any restriction of the spectral shape • Parameterization of the exact nonlinear transfer source function containing the same number of degrees of freedom of the spectrum • Energy balance had to be closed by specifying the unknown dissipation source function • Once the source functions have been determined for Fetch and uniform wind case. Model is complete and should be applicable for arbitrary wind fields

18. Simulating Waves Nearshore –SWAN- • Waves are described with the two dimensional wave action density spectrum • Density spectrum is considered rather than the energy density spectrum • Action density is conserved, Energy is not

19. Simulating Waves Nearshore –SWAN- • Action Balance equation • Wind Input • Depends on wave frequency and direction and wave speed and direction • Dissipation • Sum of three contributions: Whitecapping, bottom friction and depth induced breaking • Nonlinear Wave-Wave interactions • They transfer wave energy from the spectral peak to lower frequencies and to higher frequencies

23. Hindcast studies WHIST storms Sequence of two-dimensional wave spectra at Station Statfjord for Storm 1