Investigation of 37,106 ocean surface wave spectra from the Pacific, Atlantic Ocean, and Gulf of Mexico demonstrate that swell modulates the energy level of the high frequency tail of the wind-sea wave spectrum, altering sea surface roughness. With a mixture of sea and swell, the wind-sea part of spectra follows the well-known f-4 (equilibrium range) and f-5 (saturation range) power laws. Swell modulates the energy levels but does not change the power-law structure. For swell with minimal winds, the spectra follow the −4, −5 power-law paradigm, but energy correlates to swell steepness not wind speed. Swell shifts the transition between the two sub-ranges towards lower frequencies. For sea-swell mixtures, a modulation factor λ is proposed that depends on wind speed and swell steepness which allows parameterization of the spectral tail. Comparison of large swell with little wind to wind-sea spectra of same height and period, indicates that there is little difference in spectral shape and suggests that the Hasselmann Snl source term is likely the mechanism by which energy is transferred into the wind-sea tail causing the modulation. Analysis of 33,000+ directional spectra at Ocean Station Papa shows that the mean direction for the wind-sea high frequency tail is strongly correlated to wind direction, no matter the swell direction or steepness or level of swell dominance. An equation for the friction velocity of a sea state with swell (u*s) is developed, u∗s=λ1/2u∗o where u∗o is the friction velocity in the absence of swell, by neglect of the direct swell impact. Noting that this is only a partial estimate of the total measured stress, the prediction is evaluated for 3,000+ observed spectra yielding a correlation of 0.91 suggesting that it may be of consequence. Observations of u∗/u∗o suggest a dependence with swell steepness that is similar to that predicted by λ1/2. At low winds, λ1/2 overestimates the stress, but noting that it was derived absent the components from the swell frequencies. In the tail, the momentum transport is downward, while in the swell the transport is predominantly upward, suggests a possible correction for λ1/2. The case of a swell generated wind is discussed.
ASJC Scopus subject areas
- Aquatic Science