On tidal bore formation in dissipative estuaries.

Luca Arpaia, Andrea Gilberto Filippini, Philippe Bonneton, Mario Ricchiuto

Thursday 2 july 2015

14:35 - 14:55h at Antarctica (level 0)

Themes: IAHR/COPRI Symposium on Long Waves and Relevant Extremes

Parallel session: 12D. COPRI Symposium: Long waves and relevant extremes

We study the physical conditions leading to the formation of tidal bores in convergent estuaries. The analysis of tidal waves has received considerable attention (e.g. Lanzoni and Seminara [J.Geophys.Res., 1998], Toffolon et al. [J.Geophys.Res., 2006]). The main elements influencing this process are the tidal forcing at the estuary mouth, and the properties of the channel. An actual quantitative analysis of this physical process with a precise determination of the conditions under which bores form is missing. The formation of tidal bores not only depends on the incoming tide amplitude, but on tidal wave transformation up the estuary. This transformation is itself controlled by a competition between friction, channel convergence and discharge (see e.g. Friedrichs [Contemporary Issues in Estuarine Phys., 2010], Savenije [Delft Univ. Press, 2012]). An accurate yet simple model for nonlinear wave transformation is given by the Saint-Venant or shallow water system of equations. This system has been successfully used to simulate the propagation of breaking bores in rivers in e.g. Madsen et al. [Coast.Eng., 2005], and Pan and Lu [Coast.Eng.Proc., 2011]. Following the scaling analysis made in Bonneton et al. [J.Geophys.Res., submitted], we can show that in the case of strongly convergent estuaries (such as in the Seine of Garonne rivers), the occurrence of tidal bores can be characterised by three dimensionless parameters: wave nonlinearity e=a/D (a being the reference tidal amplitude and D the reference depth); the Froude (L/T)/(gD)^{1/2} (L being the convergence length, T the period); the dissipation Di = fe/G, with G=D/L, and f the friction coefficient. Large values of Di, are associated to strongly dissipative estuaries in which the conditions are favorable to tidal bore formation. In this work we use the numerical simulations to explore the space (e,G), and to determine quantitatively the dividing line delimiting the region where bore formation is observed,. To do this, we use the shallow water solver discussed and validated by Ricchiuto [J.Comput.Phys., 2014], and based on a fully second order, monotonicity, and positivity preserving, well-balanced discretisation. We will show the existence of a critical curve in the (e,G) space separating the tidal bore regime from a smooth one.