Turbulent flow structure in a gravel-bed river: Markov chain analysis of the fluctuating velocity profile

Three electromagnetic current meter probes were deployed in a Canadian gravel-bed river to obtain simultaneous records at 10 Hz of streamwise (u) and vertical (v) velocity components at three heights above the bed. By looking at the positive and negative signs of the instantaneous fluctuations from the time-average values of each velocity component at each height, the fluctuating velocity profile of u or v can be treated as a Markov chain with eight states and its statistical properties can be tested against null hypotheses based on the absence of spatial structure. We report results of this novel approach. The most common states of the u profile were those with either higher-than-average or lower-than-average velocities at all heights; these 'high speed' and 'low speed' states persisted for up to 3 s. The most common v profiles were all-upwards or all-downwards, but these persisted for shorter times than the high speed and low speed u profiles. Analysis of transition probabilities shows statistically significant tendencies for acceleration from the low speed u profile, and change from all-upwards to all-downwards v profile, to take place progressively from the uppermost probe downwards, in a sweep-like way. Deceleration from the high speed to low speed u profile and change from all-downwards to all-upwards v profile (burst-like behaviour) do not show such clear patterns. The results are interpreted in terms of the advection of inverted wedges of relatively high-momentum fluid, followed by more chaotic structures. A separate set of flow visualization experiments over a mixed gravel bed in a flume supports the presence of advected wedge structures, the decelerating part of the sequence corresponding to irregular ejections of near-bed fluid.