On the modeling of sand wave migration

Abstract

[1] We describe a simple mathematical model capable of reproducing the main features of sand wave inception and growth. In particular we focus on the prediction of the migration rates that sand waves undergo because of tidal and residual currents. The model adequately predicts migration rates even for the cases of upstream-propagating sand waves, i.e., for sand waves which migrate in the direction opposite to that of the residual current. We show that upstream/downstream propagation is mainly controlled by the relative strength of the residual current with respect to the amplitude of the quarter-diurnal tide constituent and by the phase shift between the semi-diurnal and quarter-diurnal tide constituents. Therefore, to accurately predict field cases, a detailed knowledge of the direction, strength, and phase of the different tide constituents is required.

Observation and Theoretical Analysis for the Sand‐Waves Migration in the North Gulf of the South China Sea

“…It is beyond explained from an intuitive understanding. The phenomenon also has been mentioned by Lanckneus [24] and Besio [5] . They also found that the migration orientations are not always consistent with residual currents and sometimes are opposite.…”

Process Control of the Sand Wave Migration in Beibu Gulf of the South China Sea

“…Nemeth et al [4] developed a model describing the formation and the migration of sand waves in the infinite medium based on a stability analysis, with which the initial evolution and the migration of sand waves may find an explanation and where the periodic water motion (M 2 ) is taken into account in combination with the steady part (M 0 ). Besio et al [5] extended their model by including an M 4 tidal constituent and the effect of the suspended sediment transport in a linear analysis. These models are basically semi-empirical and mainly applied to the sand waves with a long wavelength, which may be called the large scale sand waves.…”

Biogeomorphology of coastal seas

“…However, if a residual current U M 0 or another tidal component (e.g. the quarter-diurnal M 4 -tidal component) is present next to the semi-diurnal tidal component M 2 , the sand waves may display migration (Németh et al, 2002;Besio et al, 2004). Typical values for the residual current U M 0 and the amplitude of the M 4 -tidal component U M 4 are 0.05 m s −1 for the North Sea (Besio et al, 2004).…”

“…the quarter-diurnal M 4 -tidal component) is present next to the semi-diurnal tidal component M 2 , the sand waves may display migration (Németh et al, 2002;Besio et al, 2004). Typical values for the residual current U M 0 and the amplitude of the M 4 -tidal component U M 4 are 0.05 m s −1 for the North Sea (Besio et al, 2004). The phase lag between the M 2 and M 4 -tidal component determines the direction of migration (Besio et al, 2004), whereas the residual current causes sand waves to migrate always in the downstream direction (Németh et al, 2002).…”

“…Moreover, Gerkema (2000) and Besio et al (2003) extended the model of Hulscher (1996) by focusing on the hydrodynamic solution method. To explain sand wave migration, Németh et al (2002) and Besio et al (2004) introduced a residual current and tidal asymmetry respectively, while keeping the simplified turbulence model. Blondeaux and Vittori (2005ab) and Besio et al (2006) extended the model proposed by Hulscher (1996) by introducing a depth dependent eddy viscosity in combination with a no-slip condition at the bed.…”