Surface ripples due to steady breaking waves

Abstract

Breaking waves generated by a two-dimensional hydrofoil moving near a free surface at constant speed (U∞), angle of attack and depth of submergence were studied experimentally. The measurements included the mean and fluctuating shape of the breaking wave, the surface ripples downstream of the breaker and the vertical distribution of vertical and horizontal velocity fluctuations at a single station behind the breaking waves. The spectrum of the ripples is highly peaked and shows little variation in both its peak frequency and its shape over the first three wavelengths of the wavetrain following the breaker. For a given speed, as the breaker strength is increased, the high-frequency ends of the spectra are nearly identical but the spectral peaks move to lower frequencies. A numerical instability model, in conjunction with the experimental data, shows that the ripples are generated by the shear flow developed at the breaking region. The spectrum of the vertical velocity fluctuations was also found to be highly peaked with the same peak frequency as the ripples, while the corresponding spectrum of the horizontal velocity fluctuations was found not to be highly peaked. The root-mean-square (r.m.s.) amplitude of the ripples (νrms) increases with increasing speed and with decreasing depth of submergence of the hydrofoil, and decreases as x-1/2 with increasing distance x behind the breaker. The quantity (gνrms)/(U∞Vrms) (where Vrms is the maximum r.m.s. vertical velocity fluctuation and g is the gravitational acceleration) was found to be nearly constant for all of the measurements.

Instabilities of a horizontal shear flow with a free surface

“…The previous classification of unstable normal modes into 'Branch I' and 'Branch II' has been confirmed, but with the restriction that over some ranges of Froude number and depth ratio the two branches are found to merge. A reasonable agreement has been found with the calculations in Duncan & Dimas (1996), and also with the observations by Coakley & Duncan (1997).…”

“…The dispersion relation, which is similar to figure 4 above, shows there is one maximum growth rate at a dimensionless wavenumber κ 1 = 0.338 and a very small bubble of instability at κ 2 = 18.3. These correspond to dimensional wavelengths 2π/k 1 = 72.5 cm and 2π/k 2 = 1.34 cm compared with the two wavelengths of 36 cm and 1.4 cm calculated by Duncan and Dimas (1996) †. The present calculations indicate that the rate of growth of the second instability was exceedingly small.…”

Energy dissipation mechanisms in wave breaking processes: Spilling and highly aerated plunging breaking events

“…In order to get a better comprehension of the mechanisms behind the enhanced dissipation related to the occurrence of breaking, the flow within the breaking region is analyzed in more detail. For spilling breaking events, existing experimental and numerical studies are mainly focused on quasi‐steady wave breaking flows [ Duncan and Dimas , 1996; Duncan , 2001; Iafrati and Campana , 2005] or on unsteady breaking events induced by the dispersive focusing technique [ Qiao and Duncan , 2001; Tian et al , 2008]. In both cases, it is seen that a shear layer develops at the toe of the breaker due to the interaction between the flow inside the bulge of the breaker and the upslope flow underneath.…”

Large-wave simulation of microscale breaking waves induced by a free-surface drift layer

“…This last result is in accordance to the conclusion in [3,4] that, for microscale breaking waves, the free-surface shear stress of the associated drift layer flow is small, and the applied wind stress is balanced mainly by the wave form drag and secondary by the tangential surface stress. Also, similarly to spilling breakers [5], it has been identified [2,4], through PIV and IR measurements, the presence of vorticity in the wake of wind-generated microscale breakers. Furthermore, the effect of surface tension on the free-surface profile evolution in spilling breakers, generated mechanically by a dispersive focusing technique, has been studied experimentally [6], while the free-surface profile evolution and the propagation of ripples in microscale breakers, generated by a submerged hydrofoil, has been studied numerically [7].…”