5.2 Secondary circulations and curvature-induced helical flows
According to classic flow fields observed in sinuous channels, secondary (i.e., cross-sectional) circulations are observed in our study bend, both during high-amplitude (HAT) and low-amplitude (LAT ) tidal cycles (Figures 8,9,10,11). These secondary circulations are more pronounced during overbank stages, their intensity increasing as the water depth increases within the studied channel. Indeed, secondary circulations tend to be stronger for HAT than LAT cycles (Figures 8,9,10,11). They also appear to be mostly related to flood flows, which is in agreement with the generally flood-dominated character of tidal flows observed in the studied bend (Figure 5e,f,g). In some cases, the orientation of secondary circulations is reversed compared to classic flow models such as, for example, at the seaward bend inflection as well as at the meander apex (Figure 8 and Figure 10), where secondary circulations are directed toward the inner and outer bank at the top and bottom of the water column, respectively. Secondary currents can trigger cross-sectional sediment transport processes such that fine-grained deposits are transported up to the point bar from the channel bed, giving rise to fining upward trends due to the progressive upbar weakening of secondary currents (Bathurst et al., 1977; Blanckaert, 2011; Dietrich, 1987; Termini & Piraino, 2011). This is supported by the fining upward trends that are consistently observed from sediment cores collected at different sites along the studied bend (Figure 3).
Interestingly, secondary circulations are more pronounced at the meander inflections than at the apex, where they should be stronger owing to higher channel curvature. This could however depend on the surveying strategy we used, since we only monitored the velocity profile in correspondence to the channel axis rather than across the entire cross-section. Previous studies have demonstrated that secondary circulation cells do not necessarily occupy the whole channel cross-section (e.g., Blanckaert, 2009, 2011; Finotello, Ghinassi, et al., 2020). Particularly, hydrodynamic nonlinearities can arise in sharp bends characterized by radius-to-width ratios\(R/\overset{\overline{}}{W}\ \)lower than 2-3, and flow separation may occur either at the inner or outer bank, respectively, immediately upstream or downstream of the bend apex (Blanckaert et al., 2013; Finotello, Ghinassi, et al., 2020; Hickin, 1978; Hickin & Nanson, 1975; Hooke, 2013; Parsons et al., 2004; Rozovskiĭ, 1957). Flow separation, which is common in tidal meanders owing to the high curvature values that they typically display (Ferguson et al., 2003; Finotello, D’Alpaos, et al., 2019), can effectively reduce the portion of the channel that is hydrodynamically active and confine curvature-induced secondary circulations to the nonrecirculating portion of the primary flow (Finotello, Ghinassi, et al., 2020; Leeder & Bridges, 1975; Parsons et al., 2004). Our studied meander bend is characterized by a\(R/\overset{\overline{}}{W}\)=2.2, and the formation of flow sepeartion is therefore highly likely. Direct measurement of tidal flows across the entire channel cross section would be necessary to settle the dispute, but such data are hard to collect because channel banks at our studied site are flooded by more than 3 m of water at high tides, thus making field measuring campaigns complicated. Nevertheless, we can still estimate the chance for flow separation at the apex of our studied channel by comparing our data with the results obtained by Leeder and Bridges (1975) for intertidal meanders in the vegetated Solway Firth (Scotland). According to Leeder and Bridges (1975), the chances for flow separation in tidal meander bends can be expressed as a function of bend tightness (\(\frac{R}{W}\)) and Froude number (Fr). Although extending the results of Leeder and Bridges (1975) to unvegetated mudflats might not be entirely appropriate, results would still offer useful insights on the possible occurrence of flow separation, especially for below-bankfull stages when tidal flows are confined within the channel. Since our measurements include several consecutive tidal cycles, we were able to calculate how the \(\frac{R}{W}\) changes according to varying water depths. Specifically, we assumed that \(R\)does not vary significantly with changing water elevation, and we computed the channel width \(W_{Y}\) corresponding to different water depths (\(Y\)) based on topographic data of the meander-apex cross-section (Figure 4b). Plotting of \(\frac{R}{W_{Y}}\) againstFr shows that flow separations at the bend apex site are likely to occur at near-bankfull stages (Figure 12). This is clearly related to the morphology of the studied bend, which is characterized by a relatively low width-to-depth ratio (\(\beta\)), whereby \(W_{Y}\)increases rapidly as \(Y\) increases, thus producing progressively lower\(\frac{R}{W_{Y}}\) in the range from 8 to 2. In addition, flow velocities at the below-bankfull stage generate a modest Frvalue of 0.2~0.3, which can possibly induce flow separations (Leeder & Bridges, 1975). In contrast to our observations, Figure 12 suggests that flow separation will be suppressed at overbank stages, likely because of the observed flow velocity reduction at\(Y\)>\(Y_{B}\). Care should be however given when extending the results proposed by Leeder and Bridges (1975) to situations where tidal flows do not remain confined within channel banks. Regardless, our analyses support the idea that reduce secondary circulations observed at the meander apex could be ascribed to flow separation, which makes secondary circulations hard to identify through localized flow measurements.
Regardless of flow separation, it is worthwhile noting that secondary circulations are stronger during overbank stages, when flow confinement within channel banks is significantly reduced and, as a result, primary velocities (\(V_{P}\)) are small. Thus, there seems to be a phase shift between peaks of primary (\(V_{P}\)) and secondary velocity (\(V_{S}\)), such that \(V_{P}\) is maximum when \(V_{S}\) is low, and vice versa. Such a shift would effectively limit the advection of cross‐stream circulations operated by the primary flow, thus hampering the formation of characteristic curvature‐induced helical flows (e.g., Blanckaert, 2011; Blanckaert & de Vriend, 2003; Dinehart & Burau, 2005; Ferguson et al., 2003; Frothingham & Rhoads, 2003). Moreover, we notice that primary velocities at overbank stages are sometimes characterized by reverse direction relative to below-bankfull stages, that is, \(V_{P}\)are directed seaward (landward) during flood (ebb) tides (see for example Figure 8c). This would further limit the transfer of secondary circulation by primary velocity along the meander bend, thus hampering the formation of helical flows even further. Such behavior has not been observed in tidal channels flanked by vegetated intertidal plain, wherein \(V_{P}\) and \(V_{S}\) maxima are approximately in phase and correspond roughly to near-bankfull water stages (e.g., Fagherazzi et al., 2008; Finotello, Ghinassi, et al., 2020; Kearney et al., 2017). Additionally, secondary circulations also appear poorly developed at the confluence site. It is well known that complex circulation patterns can arise at channel confluences (e.g., Lane et al., 2000; Leite Ribeiro et al., 2012; Rhoads & Kenworthy, 1995; Schindfessel et al., 2015), which are likely to suppress curvature-induced secondary flows. Nonetheless, one should appreciate that channel confluences in intertidal mudflat channel networks are somehow less frequent than in networks carving vegetated intertidal plains, owing to the lower drainage density that characterizes bare intertidal areas (e.g., Kearney & Fagherazzi, 2016). Therefore, flow disturbances and helical flow disruption due to channel confluences and bifurcations are not likely to have a significant limiting effect on meander morphodynamics in intertidal mudflats.
Overall, the results we illustrated so far suggest poor development of curvature-induced secondary flows in intertidal mudflat meander bends. The implications of this hydrodynamic peculiarity, as well as those highlighted in Section 5.1, for the morphodynamics of intertidal mudflat meanders, will be discussed in the next section.