On the migration of tidal free bars

We derive and employ a depth-averaged model for the formation of free bars in infinitely long tidal channels in order to investigate the mechanism whereby tidal bars may experience a net migration over a tidal cycle. The flux of the suspended sediment is modeled by means of an analytical relationship derived by Bolla Pittaluga and Seminara [ M. Bolla Pittaluga and G. Seminara, Water Resour. Res. 39, 5 (2003) ] for slowly varying flows. The model is validated by performing a linear stability analysis of flow and bed topography in a rectangular channel with an erodible bed, subject to the propagation of a symmetric tidal wave of small amplitude. The results of the present depth averaged model show a fairly satisfactory agreement with previous results based on a three-dimensional model [ G. Seminara and M. Tubino, J. Fluid Mech. 440, 49 (2001) ]. We then investigate the role of overtides, showing that a flood or ebb asymmetry of the basic flow gives rise to a net migration of bars. The mechanism is due to the nonlinearity of the dependence of sediment flux on bottom stress. This phenomenon is somewhat similar to processes occurring in various fields of fluid mechanics, such as steady streaming in an oscillatory boundary layer [ N. Riley, Annu. Rev. Fluid Mech. 33, 43 (2001) ] or acoustic streaming. The present investigation also bears some relevance to the problem of nonlinear development of tidal bars, as it suggests that a depth averaged approach may be adequate to its treatment, while definitely requiring a computational effort much smaller than treatments based on 3D formulations.