Conditions for tidal bore formation in convergent alluvial estuaries

Consideration of the Mechanisms for Tidal Bore Formation in an Idealized Planform Geometry

“…Using the results of these simulations, they could draw isocontour lines of S max in the ( ϕ 0 , ε 0 ) plane. Interestingly, the shape of these isocontour lines, when S max is in the range 0.0005–0.001, is very similar to the curve Bonneton et al () drew by eye, separating a region in which conditions are such that tidal bores occur from a region where they do not occur. However, as previously observed (see Figure ), the use of a threshold value for S max does not allow establishing if a bore has actually formed or not.…”

“…Based on a scaling analysis of the one‐dimensional shallow water equations, Bonneton et al () showed that the global tidal dynamics is governed by three dimensionless parameters, namely, (i) the dimensionless tidal amplitude with A 0 = T R /2 the tide amplitude at the estuary mouth, T R being the tidal range, and D 0 some characteristic water depth; (ii) the friction parameter with C f 0 a characteristic and constant friction coefficient, and the frictionless tidal wave length scale (e.g., Friedrichs, ; Lanzoni & Seminara, ; Savenije, ), ω 0 being the tidal angular frequency; (iii) the convergence ratio where L b 0 , which is referred to as the convergence length, is given by L b 0 =− B /(d B /d x ), with B the channel width. Bonneton et al () observed that bore formation is weakly affected by the convergence ratio δ 0 ; they speculate that this is possibly because most of real estuaries all have approximately the same δ 0 . When plotting the available data in the ( ϕ 0 , ε 0 ) plane, Bonneton et al () found that a curve can be drawn that definitely separates a region in which conditions are such that tidal bores occur from a region where they do not occur.…”

“…Among the many mechanisms and conditions that affect the process of tidal bore formation, the more relevant are (i) the rate of tidal level rise (e.g., Bonneton et al, 2016;Chanson, 2011b), (ii) the characteristics of the incoming flow, typically flow depth and velocity (e.g., Cai et al, 2014;Filippini et al, 2018), (iii) the funneling shape of the estuary that deforms the tidal wave by steepening the rising limb, hence enhancing the rate of level rise (e.g., Friedrichs & Aubrey, 1994;Lanzoni & Seminara, 1998;Savenije, 2012;Toffolon et al, 2006), (iv) the channel bed profile that also affects the characteristics of the propagating tidal wave (e.g., Cai et al, 2012;Savenije et al, 2008;Shi et al, 2014), and (v) the irregular shape of cross sections, which may introduce additional dissipative processes, alter the wave celerity, and produce reflections and/or distortions of the bore front (e.g., Bonneton et al, 2011;Pan et al, 2007;Shi et al, 2014;Treske, 1994).…”

High Frequency Field Measurements of an Undular Bore Using a 2D LiDAR Scanner

“…Prior to the bore passage, the river water surface is glassy and steady with no significant roughness or surface bubbles to scatter the incident laser from the LiDAR. Although tidal bores generally generate and propagate in quite turbid environments [1], there may not always be sufficient particle density at the surface to reflect the infra-red laser. Hence, the laser will often penetrate the water column and be scattered by particles floating at some unknown depth below the surface that can vary with location (Tyndall effect, e.g., [10]).…”

“…A commonly used approach is to deploy underwater pressure transducers on the seabed and reconstruct the surface elevation using the hydrostatic assumption. However, with the intensification of nonlinear interactions as the wave propagates into shallow water, the wave shape becomes more asymmetrical and the front steepens, potentially leading to the formation of dispersive shocks, also called undular bores (e.g., [1][2][3][4]). The hydrostatic assumption is no longer valid for these highly nonlinear processes ( [5,6]).…”