We thank Sylvester et al. (2013) for the opportunity to further consider the nature of, and controls on, sinuosity variation in submarine channels. However, in stating that we propose a Coriolis force (Fc) control on the correlation between peak sinuosity and latitude, and discounted slope and sediment supply, Sylvester et al. misquote us. We concluded “The most probable causative controls on [the] global distribution [of peak sinuosity with latitude] are the Coriolis force… and latitudinal variations in both the nature of flows and sediment type” (Peakall et al., 2012, p. 14). Slope was shown to be a very weak control on global channel sinuosity variation, though it is important in controlling sinuosity in individual channels (Peakall et al., 2012, our figures 1 and 2A).
Peak Sinuosity: Sylvester et al. argue that the use of peak sinuosity is unjustified, citing (1) the need to include all bends, and (2) the reliability in identifying it. We address these in turn.
(1) Sylvester et al. add all bends for several channels into their analysis, demonstrating that slope influences sinuosity. This replicates Clark et al.’s (1992) result that slope is an important control on downstream sinuosity in individual channels. However, Sylvester et al.’s approach conflates this universally recognized intra-channel relationship, with global changes in sinuosity between submarine channels. It was for this very reason that Clark et al. (1992) introduced the peak sinuosity concept, to enable comparison between channels.
(2) Peak sinuosity varies with the measurement length-scale (e.g., average over 3, 5, 10, etc., km/bends), and due to factors influencing individual bends (e.g., faults; sea-floor topography). Yet channels do reach their highest sinuosities in the mid-fan region, and show very marked variations, from highly sinuous to approaching straight. So while the exact values may have appreciable error bars, there is no ambiguity in the ability of peak sinuosity to differentiate overall variations in channel sinuosity.
Additional examples: Both the Danube Fan and Knight Inlet studies mentioned in Sylvester et al. exhibit high sinuosity at latitudes of ∼44°N and 51°N. These are within or close to the cut-off for high-sinuosity systems of ∼50° suggested by us. While adding examples (of both high and low sinuosity) will alter the precise strength of the relationship, this does not change the result that latitude accounts for the majority of the variation in peak sinuosity.
Coriolis Force: Sylvester et al. suggest that for typical channels, Fc is unlikely to affect those flow aspects that drive sinuosity development. This is based on an implicit assumption that to have an effect, Fc ≥ Fcf, where Fcf is the centrifugal force, as given by a Rossby number, RoR = U/fR = 1 (U is downstream velocity, f is the Coriolis parameter, and R is the radius of curvature). A “typical” channel was given as R = 2000 m and U = 2 m/s, giving RoR of 7.1 at a latitude of 75°. Two points are pertinent. First, channelized flows are influenced when Fc < Fcf (Cossu and Wells, 2010). Using a width (W)–based definition of the Rossby number, RoW = U/fW, Cossu et al. (2010) estimated that Fc significantly influenced flows for RoW <10, and Cossu and Wells (2013, their figure 1C) showed that low peak sinuosity correlates well with RoW <10. Data for R are rarely given for higher-latitude channels as sinuosities approach 1. Given this, a first-order approach to calculating RoR is to use the relationship R = 2.7W1.44 (Pirmez and Imran, 2003), to calculate RoR (equal to W/R RoW); rearranging gives W/R = 0.37 W−0.44, and therefore for a W of 10 km, W/R = 0.135, and for 1 km, W/R = 0.847. This suggests that Fc becomes important when RoR <∼1.4–8.5. Secondly, a key implication from our paper is that there is no “typical” submarine channel planform; this varies in large part as a function of latitude. Sylvester et al.’s values are perhaps typical of low-latitude sinuous channels, but as bend sinuosity decreases with latitude, radius of curvature increases. Given these two factors, then for a U of 1–2 m/s in the Northwest Atlantic Mid-Ocean Channel, an R of 14–63 km, and at 55–60°N (Klaucke et al., 1997), RoR values are ∼0.1–1.1.
These results suggest that channels at high latitude that initiate with relatively straight planforms will be heavily influenced by Fc. A mechanistic model for this maintenance of low sinuosity has been proposed based on physical modeling, where properties other than “latitude” were kept constant (Cossu and Wells, 2013). The sense of Fc-driven secondary circulation is constant downchannel, forcing the downstream velocity core to one side, restricting bend growth. This led Cossu and Wells (2013) to propose that Fc promotes low-sinuosity channels at high latitudes.
In conclusion, we counter the assertion that peak sinuosity cannot be used; to do otherwise is to confuse intra- and inter-channel variations of sinuosity. The changes in peak sinuosity with latitude are robust, and evidence has been presented that Coriolis forces may indeed play a major role in controlling this relationship. Nonetheless, as we argued, this is likely a multifactorial process, and flow type and sediment supply almost certainly play a role.