Wave-Follower Field Measurements of the Wind-Input Spectral Function. Part II: Parameterization of the Wind Input

Abstract

Nearly all of the momentum transferred from wind to waves comes about through wave-induced pressure acting on the slopes of waves: known as form drag. Direct field measurements of the wave-induced pressure in airflow over water waves are difficult and consequently rare. Those that have been reported are for deep water conditions and conditions in which the level of forcing, measured by the ratio of wind speed to the speed of the dominant (spectral peak) waves, is quite weak, U10/cp < 3. The data reported here were obtained over a large shallow lake during the Australian Shallow Water Experiment (AUSWEX). The propagation speeds of the dominant waves were limited by depth and the waves were correspondingly steep. This wider range of forcing and concomitant wave steepness revealed some new aspects of the rate of wave amplification by wind, the so-called wind input source function, in the energy balance equation for wind-driven water waves. It was found that the exponential growth rate parameter (fractional energy increase per radian) depended on the slope of the waves, ak, vanishing as ak → 0. For very strong forcing a condition of “full separation” occurs, where the airflow detaches from the crests and reattaches on the windward face leaving a separation zone over the leeward face and the troughs. In a sense, the outer flow does not “see” the troughs and the resulting wave-induced pressure perturbation is much reduced, leading to a reduction in the wind input source function relative to that obtained by extrapolation from more benign conditions. The source function parameterized on wave steepness and degree of separation is shown to be in agreement with previous field and laboratory data obtained in conditions of much weaker forcing and wave steepness. The strongly forced steady-state conditions of AUSWEX have enabled the authors to define a generalized wind input source function that is suitable for a wide range of conditions.

Evidence of Energy and Momentum Flux from Swell to Wind

“…These data were interpreted as evidence for a wave-coherent component of the velocity field (also Davidson and Frank 1973). More recent field observations showing an effect of swell on the air-sea momentum flux include those of Geernaert et al (1988), Rieder (1997), Donelan et al (1997), Drennan et al (1999), Smedman et al (1999Smedman et al ( , 2009, and Grachev and Fairall (2001). The consensus of data shows that swell in the presence of light to moderate winds can dramatically change the air-sea momentum flux over pure wind sea values, increasing it when the swell runs against the wind and reducing it, sometimes to zero or even to an opposite direction, when the swell travels with the wind.…”

Source term balance in a severe storm in the Southern North Sea

“…Donelan et al (2005Donelan et al ( , 2006, Rogers et al (2012), Babanin et al (2010) and Zieger et al (2015) developed an observation-based whitecapping dissipation and wind input term. The whitecapping part is composed of two components, as formulated in action density N(k, θ)…”

Integrated Model for a Wave Boundary Layer

“…Reasonability of extraction of wave stress w τ , associated with the energy transfer from the wind to waves, from total stress tot τ is due to the fact that the value of w τ can be measured to a certain extent, and even can be theoretically described in terms of the wave-dynamics equations within certain limits (see references in [13,16,17] In a higher and broader frequency domain, which includes the capillary waves ranging up to 100 rad/s (where the most significant part of the wave momentum flux is accumulated), the contact measurement of ( )…”

“…Function β  drops to zero both at the low frequencies corresponding to condition W/ c ω <1 (i.e. when the waves overtake the wind) and at high frequencies corresponding to the region of the phase-velocity 5 There are more detailed representation of β  , using dependences on wave age А and wave component steepness ( ) k ε [16]. But they are not discussed here.…”

“…additional to the known) about the physics of the interface dynamics. Moreover, parameterizations of (...) β  via W are widely spread [16]. and (1) t c = 0.8, are found in the verification process.…”