Laboratory study of wave bottom interaction in the bar formation on an erodible sloping bed

Abstract

Abstract.The interaction between partially standing or almost progressive surface gravity waves and erodible beds is investigated in a small wave tank under nonbreaking wave conditions. The bed is initially fiat and gently sloping, and the incident weakly nonlinear wave is either a regular wave (similar to a Stokes wave), or a regular wave superimposed on a free wave generated by the wave maker (bichromatic or birnodal wave). Accurate measurements of both the bed profile and the wave envelope are performed, showing a permanent coupled evolution of the wave field and of the bed shape. Sandbar formation is observed in the ultimate bed profile which reproduces the spatial modulations of the envelope of the first harmonic of the wave (e.g., the fundamental component). In the case of a pure regular w•ve, the interb•r sp•cing is equ•l to h•lf the local surface w•velength which corresponds to a first-order Bragg resonance with the local wavenumber of the first harmonic satisfying the dispersion relation for small waves. In the case of a birnodal wave the preceding case is perturbed by a free wave of the same frequency and similar amplitude as the second harmonic of the regular wave. Then, nonlinear interactions between the first harmonic and the free wave occur, leading to sum and difference frequencies. The difference interaction modifies the amplitude and spatial modulation of the first harmonic. The Bragg resonance mechanism based on the first harmonic in the bar formation is then modified. However, in this case, the bed profile is also the replica of the envelope of the first harmonic of the wave: the perturbation induced in the first harmonic is also present in the bed shape. For partially standing birnodal waves, the Fourier analysis of the bed profile shows a second spatial modulation with the local wavenumber of the free wave. For almost progressive birnodal waves, a third modulation is found with the local wavenumber of the observed beating between the free wave and the second harmonic component of the wave.These modulations of the envelope of the first harmonic are recovered analytically through a partially standing birnodal wave modeling. This study confirms that the bar formation under nonbreaking wave conditions is controlled by the envelope of the first harmonic of the wave even if perturbed by a free wave.

Bragg scattering of random surface gravity waves by irregular seabed topography

“…Other related developments include nonlinear effects in a long-wave approximation (Benjamin, Boczar-Karakiewicz & Pritchard 1987), higher-order Bragg scattering (Mitra & Greenberg 1984;Belzons, Rey & Guazzelli 1991;Liu & Yue 1998;Agnon & Sheremet 2000), extended mild slope equations for steep topography (Athanassoulis & Belibakis 1999), and investigations of Anderson localization of waves on a random bottom (Devillard, Dunlop & Souillard 1988;Belzons, Guazzelli & Parodi 1988). Implications for sediment transport and the formation of multiple sand bar systems just outside the surf zone were discussed by Heathershaw (1982), Mei (1985) and Dulou, Belzons & Rey (2000). Whereas Hasselmann's (1966) stochastic theory gives an energy balance equation that is an efficient tool for predicting the spectral evolution of random waves, it is restricted to homogeneous wave and bottom topography properties, and has not been verified experimentally.…”

Sandbar formation under surface waves: Theory and experiments

“…So far only Dulou et al [2000] have measured sandbars on a gently sloping bed. Their short tank of length 4.7 m, width 39 cm, and depth 15 cm housed a bed of sand grains of diameter 0.08 mm.…”

“…Jan and Lin [1998] observed the formation of sandbars and ripples under oblique standing waves in front of a seawall in a laboratory tank with a horizontal bed. Dulou et al [2000] studied sandbar formation under partially standing waves on a gently sloping bed in a small wave tank. Scaling effects limit the similarity of these small scale sandbars to those observed in the field [Yu and Mei, 2000a].…”

Experimental Study on Changes of Sloping Sandy Bed Profile under Breaking Waves

“…Dulou etc. [2] used the wave flume experiments to study the formation process under breaking waves over the sand bar and bed. Li [3] used two bottom material particles with similar properties but can be distinguished easily to identify the sand interface between turbulence and non-turbulence, and then computed the sediment runoff in bed with the knowledge of actual scour depth under waves action.…”