Research ArticleEARTH SCIENCES

Experimental river delta size set by multiple floods and backwater hydrodynamics

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Science Advances  20 May 2016:
Vol. 2, no. 5, e1501768
DOI: 10.1126/sciadv.1501768
  • Fig. 1 Compilation of avulsion lengths on river deltas scales with the computed backwater length.

    (A to D) Satellite imagery showing measured avulsion length (LA) for four deltaic systems. (E) Correlation between measured avulsion length and the computed backwater length (Lb) suggests that avulsions on deltas occur within the upstream portion of the backwater zone (the shaded region is bounded by 1:2 and 2:1 lines), which determines the length scale over which the alluvial river feels the downstream boundary condition of sea level (14, 15, 18). Data compilation of avulsion length and backwater length is from previously published work (14, 15, 18, 19); see those works for methods. Because avulsion is fundamentally a stochastic process (31), the scaling relationship between backwater length and the avulsion length can be viewed to represent an average over multiple avulsion cycles (14). (F) Because backwater hydrodynamics arise as a result of the downstream boundary condition of sea level, backwater-controlled avulsion nodes should translate seaward in step with shoreline progradation such that avulsion length on deltas reaches a constant value in time. This is in contrast with topographically controlled avulsions, which are common to alluvial fans and fan deltas (15), where avulsions may occur at a change in confinement (for example, canyon-fan transition) and the avulsion length can grow in time without impedance.

  • Fig. 2 Experimental arrangement at Caltech Earth Surface Dynamics Laboratory.

    Schematic of the experimental arrangement along with a perspective photograph showing the alluvial river section, ocean basin, and the instrument cart, which was used to collect water surface and bed elevation data during both experiments.

  • Fig. 3 Overhead image of an avulsion during the variable discharge experiment.

    The image shows the location of river avulsion, old and new channels, river mouth, and crevasse splays, which were active only during the high-flow events. The avulsion length was measured along the channel thalweg and normalized by the backwater length of the low flow (Table 1). The two silver horizontal bars are instrument rails that sit above the experiment. The gray and white dashed lines indicate the channel banks and the shoreline, respectively.

  • Fig. 4 Comparison of avulsion sites for constant discharge delta versus the variable discharge delta.

    (A and B) Avulsion sites through time for (A) experiment A and (B) experiment B overlain on the photographs of the deltas at the end of their experimental runs. The colors of the avulsion sites are graded from white to black in time, and the shorelines are indicated as dashed white lines. The white scale bars indicate a length of 0.5Lb, which are 0.75 and 1.45 m for experiments A and B (Table 1), respectively.

  • Fig. 5 Avulsion sites translate seaward in step with shoreline progradation, thus maintaining a constant delta lobe size parameterized here as the ratio of the avulsion length (LA) to the backwater length (Lb).

    Plot showing the evolution of the ratio of the avulsion length to the backwater length as a function of dimensionless time, where the experimental run time was normalized by the time it takes to build a radially symmetric, semicircular delta of size 0.5Lb (Materials and Methods). In experiment B, the avulsion sites translate seaward in step with shoreline progradation, maintaining an avulsion length of approximately 0.5Lb. Detailed measurements of water and bed surface elevation profiles, flow velocities, and in-channel sedimentation are shown for the avulsion indicated by the green marker in Fig. 6.

  • Fig. 6 Competition between low-flow deposition and high-flow erosion results in an in-channel sedimentation peak at the avulsion site, which scales with the backwater length.

    (A) Instantaneous water and bed surface elevation (black curve) profiles during low flow (blue curve) and high flow (red curve) as a function of streamwise distance from the shoreline, normalized by Lb at the beginning of the avulsion cycle (Materials and Methods). (B) During low flow, the flow decelerates in the backwater reach; however, during high flow, the water surface slope steepens, and flow accelerates through the lowermost portion of the backwater zone. (C) In-channel sedimentation (Δη) normalized by the normal-flow depth of low flow (hc) measured during each flow event of the avulsion cycle (red and blue lines indicate high- and low-flow events, respectively, and the shaded region is the SE from averaging over multiple flow events). Over multiple flow events during this avulsion cycle (six low-flow and five high-flow events), the competition between low-flow deposition and high-flow erosion results in an in-channel sedimentation peak within the backwater reach (~0.40 Lb), near where the eventual avulsion occurred (~0.45 Lb for avulsion location). The upstream distance was measured from the final shoreline when the avulsion occurred, and in-channel sedimentation data are not plotted for abscissae < 0.2 because this is a zone of progradation during the avulsion cycle, which precludes measurements of vertical aggradation. The upstream extent of these plots corresponds to the location where the river exits the narrow section in our experimental facility.

  • Table 1 The measured and given parameters of both the constant discharge and variable discharge deltas.
    Constant discharge experiment
    (experiment A)
    Variable discharge experiment
    (experiment B)
    Low flow (M1 event)High flow (M2 event)
    Water discharge, Qw (liters/min)8.38.312.0
    Sediment feed, Qs (g/min)693660
    Run time65 hours40 min*15 min*
    Normal-flow depth, hn (mm)8.59.513
    Normal-flow Froude number, Fr (−)0.810.670.63
    Channel bed slope, S (−)5.5 × 10−33.3 × 10−33.3 × 10−3
    Backwater length, Lb (m)1.52.9
    Rouse number (−)3.64.53.8
    Number of avulsions80932

    *The low- and high-flow events in experiment B were repeated 160 times, resulting in a total experimental run time of ~150 hours.

    †The normal-flow depth, normal-flow Froude number, and channel bed slope were averaged over the first 3 m of the experimental river, which was within the normal-flow zone in both experiments. See figs. S2 and S3 for additional details.

    ‡Although we can compute the backwater length scale in experiment A as a scale parameter, we note that this does not imply that nonuniform flow persisted over these length scales in our experiment (see figs. S2 and S6).

    Supplementary Materials

    • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/5/e1501768/DC1

      Supplementary Materials and Methods

      fig. S1. Idealized schematic of backwater and drawdown hydrodynamics.

      fig. S2. Instantaneous measurements of water and bed surface profiles along with the measured flow depth, depth-averaged flow velocity, and Froude number for experiment A.

      fig. S3. Instantaneous measurements of water and bed surface profiles along with the measured flow depth, depth-averaged flow velocity, and Froude number for both flows in experiment B.

      fig. S4. Photo sequence of the process of avulsion in experiment B.

      fig. S5. Temporal evolution of avulsion length in constant discharge delta.

      fig. S6. Water surface velocity across the backwater reach in constant discharge delta.

      table S1. Field data compilation of avulsion length and backwater length.

      movie S1. Experimental evolution of constant discharge delta.

      movie S2. Experimental evolution of variable discharge delta.

      movie S3. Overhead dye video of the constant discharge delta.

      References (53, 54)

    • Supplementary Materials

      This PDF file includes:

      • Supplementary Materials and Methods
      • fig. S1. Idealized schematic of backwater and drawdown hydrodynamics.
      • fig. S2. Instantaneous measurements of water and bed surface profiles along with
        the measured flow depth, depth-averaged flow velocity, and Froude number for
        experiment A.
      • fig. S3. Instantaneous measurements of water and bed surface profiles along with
        the measured flow depth, depth-averaged flow velocity, and Froude number for
        both flows in experiment B.
      • fig. S4. Photo sequence of the process of avulsion in experiment B.
      • fig. S5. Temporal evolution of avulsion length in constant discharge delta.
      • fig. S6. Water surface velocity across the backwater reach in constant discharge
        delta.
      • table S1. Field data compilation of avulsion length and backwater length.
      • Legends for movies S1 to S3
      • References (53, 54)

      Download PDF

      Other Supplementary Material for this manuscript includes the following:

      • movie S1 (.mp4 format). Experimental evolution of constant discharge delta.
      • movie S2 (.mp4 format). Experimental evolution of variable discharge delta.
      • movie S3 (.mov format). Overhead dye video of the constant discharge delta.

      Files in this Data Supplement:

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