Kinematics and depth-integrated terms in surf zone waves from laboratory measurement

Abstract

Kinematics of nominally periodic surf zone waves have been measured in the laboratory using LDA (laser Doppler anemometry), above trough level as well as below, for weakly plunging breakers transforming into bores in shallower water. The aim was to determine, through phase- or ensemble-averaging, periodic flow structures in a two-dimensional vertical plane, from large-scale down to small-scale vortical structures. Coherent multiple vortical structures were evident at the initiation of breaking, becoming elongated along the surface during bore propagation. The initial region is likely to become more extensive as waves become more strongly plunging and could explain the difference in turbulence characteristics between plunging and spilling breakers observed elsewhere. Comparison of vorticity magnitudes with hydraulic-jump measurements showed some similarities during the initial stages of breaking, but these quickly grew less as breaking progressed into shallower water. Period-averaged kinematics and vorticity were also obtained showing shoreward mass transport above trough level and undertow below, with a thick layer of vorticity at trough level and a thin layer of vorticity of opposite rotation at the bed. There were also concentrated regions of mean vorticity near the end of the plunging region. Residual turbulence of relatively high frequency was presented as Reynolds stresses, showing marked anisotrophy. Dynamic pressure (pressure minus its hydrostatic component) was determined from the kinematics. The magnitudes of different effects were evaluated through the depth-integrated Reynolds-averaged Navier–Stokes (RANS) equations, which may be reduced to nine terms (the standard inviscid terms of the shallow-water equations conserving mass and momentum with hydrostatic pressure, and six additional terms), assuming that the complex, often aerated, free surface is treated as a simple interface. All terms were evaluated, assuming that a space/time transformation was justified with a slowly varying phase speed, and the net balance was always small in relation to the maxima of the larger terms. Terms due to dynamic pressure and vertical dispersion (due to the vertical variation of velocity) were as significant as the three terms in the inviscid shallow-water equations; terms involving residual turbulence were insignificant. The r.m.s. (root mean square) variation of each along the slope is highly irregular, with the inertia term due to (Eulerian) acceleration always greatest. This is consistent with complex, though repetitive, coherent structures. Modelling the flow with the shallow-water equations, using the surface elevation variation at the break point as input, nevertheless gave a good prediction of the wave height variation up the slope.

Observations of Turbulence within a Natural Surf Zone

“…The (Fig. 8c); Stansby and Feng (2005) and Kimmoun and Branger (2007) observed similar shear stress values under laboratory surf-zone bores. Intriguingly, hu9w9i 1(3) can also attain positive values for H s $ 0.48 (Fig.…”

“…The change in sign of hu9w9i as the seabed is approached has not been observed in the aforementioned laboratory studies, however, and generally the intensity of bed-generated turbulence is assumed to be an order of magnitude smaller than the breaker-generated turbulence (Svendsen 1987). Beneath periodic plunging breakers, ODEs have also been observed beneath the initial breakpoint (e.g., Zhang and Sunamura 1990;Stansby and Feng 2005); farther onshore, vortices with a more two-dimensional horizontal structure develop where the splash-up that occurs immediately after plunging again hits the water surface (e.g., Zhang and Sunamura 1990;Kimmoun and Branger 2007). As for spilling waves, hu9w9i is negative, with maximum values at the first splash-up position (Stansby and Feng 2005;Kimmoun and Branger 2007).…”

“…Near the bed, where most of the ODEs no longer exist, hu9w9i reduces to 0. In the inner surf zone hu9w9i is smaller than near the initial breakpoint but is also more depth uniform (Stansby and Feng 2005;Kimmoun and Branger 2007). Ting (2001) argued that, if near-bed flow is dominated by bottomgenerated turbulence, hu9w9i should be positive: u and its vertical gradient are both negative, and positive hu9w9i is thus consistent with typical boundary layer flow.…”

“…Beneath periodic plunging breakers, ODEs have also been observed beneath the initial breakpoint (e.g., Zhang and Sunamura 1990;Stansby and Feng 2005); farther onshore, vortices with a more two-dimensional horizontal structure develop where the splash-up that occurs immediately after plunging again hits the water surface (e.g., Zhang and Sunamura 1990;Kimmoun and Branger 2007). As for spilling waves, hu9w9i is negative, with maximum values at the first splash-up position (Stansby and Feng 2005;Kimmoun and Branger 2007). Collapsing breakers do not result in any coherent vortex motion (Zhang and Sunamura 1990).…”

Measurements of Surface Kinematics and Temperature in the Surf and Swash Zones Using Infrared Image Velocimetry

“…LDV has been used to measure the flow structure, undertow, turbulence intensity, turbulent transport terms, and Reynolds stresses in small laboratory surf zones under spilling and plunging breakers (e.g., Stive, 1980;Nadaoka and Kondoh, 1982;Ting and Kirby, 1994;Ting and Kirby, 1995;Ting and Kirby, 1996;Stansby and Feng, 2005;De Serio and Mossa, 2006;Shin and Cox, 2006). However, measurements using LDV are usually restricted below wave trough level due to the failure of this technique (signal drop-out) in the aerated region of breaking waves.…”