Sand banks of finite amplitude

Abstract

[1] The process which leads to the appearance of sand banks in shallow seas is investigated by studying the growth of small-amplitude perturbations of the sea bottom, forced by oscillatory tidal currents. Since the analysis of field data carried out by Dyer and Huntley (1999) suggests that sand banks are likely to occur where the tidal ellipse is circular or characterized by a low ellipticity, attention is focused on small values of, where e is the ratio between minor and major axes of the tidal ellipse. The linear analysis, which considers perturbations of small (strictly infinitesimal) amplitude, shows the existence of a critical value r C of the Keulegan-Carpenter number r of the tide (r = U 0 */ (h 0 *w*), U 0 * and w* being the amplitude and angular frequency of the velocity oscillations induced by the tide propagation and h 0 * being the averaged water depth) such that for r smaller than r C the flat bottom configuration is stable, while for r larger than r C the sand banks start to appear. Close to the critical condition, the wavelength of the most unstable mode turns out to be finite. Then a weakly nonlinear analysis is developed which allows the evaluation of the equilibrium amplitude of the bottom forms when the parameter r is close to its critical value. The configuration of the sea bottom, when the bottom forms attain their equilibrium, is characterized by the presence of long ridges, almost parallel to the main axis of the tidal ellipse, with crest-to-crest distances similar to those observed during field surveys. The crests of the bottom forms turn out to be flat, and the extensive shallow waters at the crests are compensated by deep troughs between the ridges.

Modeling the finite-height behavior of offshore tidal sand ridges, a sensitivity study

“…It was also found that the modeled ridge height overestimated the observed ridge height of the Dutch Banks in the southern North Sea. Tambroni and Blondeaux (2008) carried out a weakly nonlinear stability analysis to investigate the behavior of finite-height ridges. Their method is fast, but it is only applicable for tidal currents with large ellipticity ϵ (the ratio between the minor axis and the major axis of the tidal current ellipse).…”

“…Many tidal sand ridges are actually observed at locations where tidal currents are close to rectilinear (ϵ ∼ 0), for instance, in the southern North Sea (Collins et al, 1995). Furthermore, the effect of the critical bed shear stress for sand erosion on the evolution of finite-height ridges has not been considered in the above studies, except in Tambroni and Blondeaux (2008). In Yuan et al (2016), it was shown that including the critical bed shear stress for sand erosion significantly affects the characteristics of tidal sand ridges during their initial formation.…”

Dynamics of offshore tidal sand ridges, a review

“…In Besio et al [5], as well as in later studies by Tambroni and Blondeaux [72], Blondeaux et al [8] and Yuan et al [91] , two additional effects are accounted for that are not present in formulation (1). The first is that transport includes a critical velocity for erosion and the second is that transport due to longitudinal and lateral bed slopes differ.…”

“…The ridges with asymmetrical profiles migrate in the flood direction (positive x-direction). Tambroni and Blondeaux [72] carried out a weakly nonlinear stability analysis to investigate the behaviour of finite-height ridges in a 2DH (depth-averaged) model. Their method is fast and yields insight into the mechanism that causes saturation of the height of the ridges, but it is only applicable for tidal currents with large ellipticity .…”

Effect of sea level rise and tidal current variation on the long-term evolution of offshore tidal sand ridges

“…Linear stability analysis yields a preferred bedform of which the spacing and orientation are in fair agreement with those of the observed tidal sand ridges. For ridges with a finite height, nonlinear (or weakly nonlinear) models (Huthnance, 1982b;Roos et al, 2004;Tambroni and Blondeaux, 2008;Yuan et al, 2017, and references therein) were employed to investigate the behavior of these ridges. In these models, the sea level and the tidal current were kept constant in time.…”