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Wave Models in Marine Science: Understanding Wave Generation and Energy Transfer

This study explores the generation of waves and the transfer of energy from wind to waves in marine science, focusing on wave height, dominant period, average period, and frequency. Various wave models are examined, including numerical wave prediction models and first, second, and third-generation wave models, such as WAM and SWAN, to understand wave growth and development. Emphasis is placed on the differences between these models and the factors that influence wave simulations, such as wind input, dissipation, and wave-wave interactions. Hindcast studies on storms and wave spectra are also discussed in detail.

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Wave Models in Marine Science: Understanding Wave Generation and Energy Transfer

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  1. MODELS IN MARINE SCIENCEMARN 391 ERICK RAFAEL RIVERA LEMUS

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

  3. 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

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

  5. 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.

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

  7. 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

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

  9. THANK YOUTO BE CONTINUED…

  10. 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

  11. 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)

  12. 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

  13. 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

  14. 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

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

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