the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Spatiotemporal Bedload Transport Patterns Over TwoDimensional Bedforms
Leah Tevis
Mark Schmeeckle
Abstract. Despite a rich history of studies investigating transport over bedforms and dunes in rivers, the spatiotemporal patterns of subbedform bedload transport remain poorly understood. Previous experiments assessing the effects of flow separation on downstream fluid turbulent structures and bedload transport suggest that localized, intermittent, highmagnitude transport events (i.e., permeable splat events) play an important role in both downstream and crossstream bedload transport near flow reattachment. Here, we report results from flume experiments that assess the combined effects of flow separation/reattachment and flow reacceleration over fixed, twodimensional bedforms (1.7 cm high; 30 cm long). A highspeed camera observed bedload transport along the entirety of the bedform at 250 f/sec. Grain trajectories, grain velocities, and grain transport direction were acquired from bedload images using semiautomated particle tracking techniques. Downstream and vertical fluid velocity was measured 3 mm above the bed using Laser Doppler Velocimetry (LDV) at 15 distances along the bedform profile. Mean downstream fluid velocity increases nonlinearly with increasing distance along the bedform. However, observed bedload transport increases linearly with increasing distance along the bedform, except at the crest of the bedform, where both mean downstream fluid velocity and bedload transport decrease substantially. Bedload transport time series and manual particle tracking data show a zone of highmagnitude, crossstream transport near flow reattachment, suggesting that permeable splat events play an essential role in the region downstream of flowreattachment.
Kate C. P. Leary et al.
Status: open (until 09 Apr 2023)

RC1: 'Comment on esurf20233', Anonymous Referee #1, 16 Mar 2023
reply
Summary:
This study examines hydrodynamics and sediment transport over a sequence of laboratory bedforms. The key message is that the specific flow patterns driving sediment transport vary across bedforms. On the stoss side of bedforms, Reynolds stresses decrease as sediment transport increases. Maximum transport is reached just before bedform crests, a transport pattern which would act to maintain downstream migrating bedforms. At bedform crests, the flow detaches before it eventually reattaches on the lee side. Reattachment zone flow involves a higher relative frequency of Q2 and Q4 events, diagnostic of the "splat events" identified in the authors' earlier publications on the flow behind a step. Sediment transport in the reattachment zone is multidirectional and intermittent, consistent with the hypothesis that splat events dominate sediment transport there. These results summarize the linkages between turbulent hydrodynamics and sediment transport over bedforms and serve as a useful contribution, so the paper is therefore in my opinion appropriate for ESurf after some revisions aimed at clarifying its presentation and improving its readability.
Main comments:The literature review could engage more directly with the studies it cites near L24 which relate turbulent hydrodynamics and sediment transport. This would better place the present study in context. In particular, statements of what each study (or sets of studies) did and didn't do could better indicate the knowledge gap the authors examine. The text would ideally give careful attention to the findings of studies which have jointly measured hydrodynamics and transport, e.g. Nelson et al (1995) and related studies extending to the present day. In addition, the literature review and discussion do not engage much with the numerical simulation literature, which has been an extremely successful method to study the interaction between turbulence and sediment transport. It may be useful to incorporate the wider numerical literature on the interaction of turbulent hydrodynamics and sediment transport over bedforms into the discussion (e.g., other studies relatex to Schmeeckle 2015 and surely more recent work).
The paper might benefit from a graphic summarizing the key relationships observed by the authors between sediment transport and hydrodynamics over bedforms. Currently there is a repurposed diagram (with a copypasted caption) from the authors' earlier JGR paper indicating what a splat event is. In my opinion ,the key findings of the paper would be easier to understand with a summary diagram, tailored to the paper, showing (a) the stoss zone of increasing sediment transport and decreasing Reynolds stresses, with a shift in behavior just before the crest; (b) the detachment zone and its associated fluid dynamics; and (c) the reattachment zone and associated prevalence of splat events. Maybe the earlier JGR figure could feature as an inset to show the reader what a splat event is. The present work deserves an original figure tailored to its main message.
A highlighted point in the conclusion of the paper is that "Continuity, velocity, and direction of bedload transport vary significantly with increased distance along the stoss side of the bedform." The presented analyses make a convincing point that the direction and velocity vary significantly, but the paper could be more convincing about the point on "continuity" (which I would rather call "intermittency" in deference to standard terminology in the literature). To make the point about intermittency, the authors might plot the variance of the interarrival time of particles to the reference surface used to evaluate $q_s$ as a function along the bedform, or possibly the timeseries of particle arrivals (rather than the flux)  one should see additional burstiness in the splatdominated transport zone.
Finally, I believe the discussion around the Exner equation near Eq. 2 needs attention. To start with, the statement of the Exner equation is incorrect (missing minus sign), and the assertion that "a linear increase in transport is necessary for bedforms to retain a twodimensional geometry while translating downstream" seems inconsistent with successful nonlinear formulations of bedform dynamics based on the Exner equation (Jerolmack and Mohrig, 2005). A rewrite of this section fixing the conceptual errors and linking more carefully to the extensive literature relating bedform dynamics to turbulent hydrodynamics would benefit the paper.
Minor comments: L7  transport directions (plural)
 L9  downstream and vertical fluid velocities
 18  It may be useful to define the "subbedform" scale more carefully
 19  "our understanding of how bedforms evolve in three dimensions" would be more concrete
 29  This seems not exactly correct. Ashley et al did this, and if I recall, Nelson et al (1995) have as well. Heyman et al (2016) JGR:ES also did this, in a way. It would be more correct to say "With few exceptions (e.g., Ashley et al 202X, Nelson et al 199X), previous work has not accounted for the amount of sediment being ...
 I believe all citations of the type "Bennett and Best 1995 showed that" will need parentheses around the year.
 35  Notably, they observed that quadrant 4 events near flow reattachment contribute significantly to . . .
 Figure 1: This figure could be improved. The caption (which is copypasted from the JGR paper) also has a typo (which is also in the JGR paper)  characterize..d
 75 Exponents in units should be rendered as superscripts. Also D50 should be rendered (in my opinion) as $D_{50}$.
 89 Suggest "removed" instead of "pulled" for clarity
 105: $u'$ is rendered incorrectly as u'
 107: The reynolds stress is defined as $\rho \overline{u_x'u_y'}$, not $\rho \overline{u_x'}\overline{u_y'}$. I assume this is just a typo? If not, the calculations require attention as these are distinctly different quantities.
 Table 2: change in notation from $u_x'$ to $U_x'$. Also see L159.
 Section 2.2  How long did you average through time to compute the mean sediment transport rate, and how did this affect your results? See Singh et al (2009), Ancey & Pascal (2020): it is now well established that mean transport rates depend on the averaging time, precisely because transport is intermittent. Additionally you should mention how long your sediment transport analyses lasted. It seems the answer is 8 sec which is exceedingly short  a limitation that deserves mention.
 119: I assume you actually mean if the absolute value of exuberance is equal to 1, not what you wrote. Suggest "If exuberance is near $\pm 1$, ..."
 129: Just style  but consider switching "fluid velocities are following observations" to "fluid velocities follow observations"; similarly at 131, "transport is in contrast" becomes "transport contrasts" and many other locations in the paper  concise and active
 Fig 3: subscript not rendered properly in $q_s$ y axis label
 Fig 4 needs units
 Eq. 2: $\delta$ is traditionally reserved for variational derivatives or finite increments. The Exner equation requires $\partial$. Also, both spatial derivatives should have the same sign. Finally, $\partial z/\partial t$ is only an erosion rate if $\nabla q > 0$. Otherwise, it is a deposition rate.
 Fig 6: "diverge" suggests an explosion toward infinity. suggest "depart". Also a typo  "estiamtes"  suggest to spell check the entire document.
 Fig 7: "characterized particles" (typo)
 L171: As I mentioned before, intermittency implies the mean transport rate depends on observation time, so there is a need to describe the definition of mean rate used in Figs 3 and 7 with citation to the relevant papers on the topic.
 Fig 8: I am not exactly sure what the first sentence in the caption means. Do you mean step heights away from the beginning of the dune? This could be clarified perhaps.
 195: I suppose you want to say $q_s$ is the bedload transport rate (rather than sediment), since you mentioned Exner in the absence of suspended sediment exchange.
 203: Maybe this conundrum is a bit overstated. Nonlinearities in the relationship between the bed slope and the sediment transport rate produce dynamic bedforms with statistically stable characteristics. The linear stability has been analyzed (Patterns of Dirt, Neils Balmforth 2002), and initial instabilities have been attributed to noise in the sediment transport rate (Bohorquez et al near 2015)
 214: " A linear increase in transport is necessary for bedforms to retain a twodimensional geometry while translating downstream". Jerolmack and Mohrig (2005) maintain quasi two dimensional bedforms with a nonlinear Exner equation (see their Eq. 8 and Fig 4). How do you reconcile their successful nonlinear formulation of bedform dynamics with your statement about linearity ($q_s ~ x$) being required? It seems to me so long as there is no crossstream variation in sediment transport trends (i.e. $q_s(x,y)=q_s(x)$), it does not matter how $q_s$ scales with $x$, provided it has a positive gradient on the stoss side of the bedform (i.e., degradational) and a negative gradient at the crest and on the lee side of the bedform (i.e., depositional) this will produce a downstream migrating bedform with some two dimensional profile (which depends on the specific gradient values), regardless of whether these gradients are constant or not. Maybe I am missing the point  in this case a clarification may benefit others. I otherwise agree that any lateral variation in $q_s$ can destabilize a 2D bedform.
 233: $x^a$ is algebraically, not exponentially  $ a^x$  this requires corrections in the figures and elsewhere in the text
 292: typos
 294: "Considering the results presented herein, we suggest two potential mechanisms that drive the transition from twodimensional to threedimensional bedform geometries: (1) splat events near flow reattachment and (2) localized, nonlinear increases in bedload transport rates along the stoss side of the bedform." Jerolmack and Mohrig (2005) show that stochasticity in sediment transport drives transitions to three dimensional geometries.
 "(splat events near flow reattachment) and (localized, nonlinear increases in bedload transport rates) may be genetically linked, and we suggest that (1) could drive (2)." Can you investigate the timescales separating sequential splat events and compare these with the timescales separating what you believe are splatassociated transport events? How do they compare?
 Isn't it strange that Reynolds stresses and mean bedload transport are anticorrelated? Can you clarify this? Are the Reynolds stresses near the bed irrelevant to the mean bedload transport rate over dunes?
Citation: https://doi.org/10.5194/esurf20233RC1 
RC2: 'Comment on esurf20233', Anonymous Referee #2, 27 Mar 2023
reply
General comments:
This paper presents experimental results regarding the turbulent structure and bedload transport pattern over a twodimensional ripple using LDV velocity measurement and camerabased particle tracking techniques. More specifically, the authors showed the presence of a “splat event” at the flow separation and reattachment point behind ripple crest, and discussed its importance for the bedload transport and morphodynamics of ripple. Understanding the relationship between the flow turbulence and bedload transport provides some important insight into the mechanics and dynamics of bedforms; however, this has not been deeply understood because of the difficulty of measurement. Therefore, this paper will be a nice contribution to our understanding of fluvial morphodynamics, and the paper's topic well fits the scope of ESurf. I would like to point out some unclear points about the experimental method and analysis and some interpretations of the results as follows.
Detailed comments:
 The discussion on the bedload transport pattern and bedform geometry needs to be checked carefully. For example, sentence like Lines 134135 sounds OK for a necessary condition for downstream migration of bedforms, but is not really applicable to explain twodimensional features. If there is no variation of streamwise bedload transport rate in crossstream direction, any streamwise distribution of bedload transport (either linear or nonlinear) could sustain twodimensional bedform. So, I am not sure the discussion at Lines 211238 makes sense. To discuss above, the authors presented Exner equation (2). Normally, \partial q_s/\partial y is not included in the Exner equation. What is the control volume for deriving this equation? Please check carefully since referee #1 also pointed out a similar issue regarding Equation (2).
 The importance of splat event on the bedload transport over ripple bed should be clearly explained. This is because that one of the main contributions of this paper may be that the authors use the concept of splat event, which was previously pointed out by the same team (Leary and Schmeeckle, 2017, JGR) using a flume with backward facing step, to understand real bedform fields. In addition, I am not sure about the discussion on the importance of the splat event to the threedimensional bedform mentioned at Lines 294297. The authors suggested an interesting mechanism, but I am unsure whether or not the experimental result supports this. The bedload transport feature at downstream of the crest indeed shows complex crossstream pattern, but even though bedload transport pattern at more downstream shows a strong streamwise dominated feature. This may be because of the condition selected in this study: under the same but purely movable bed condition, the bedform presented by Nelson et al. (2011) seems to show twodimensional feature. More clear discussion with some literature review will be beneficial to highlight the discussion here.
 There are some unclear points in the experimental work and its analysis. For example, the LDV measurement are performed along the centerline of the flume above 1 and 3 mm from the bed. How did the authors calculate mean velocity and Reynolds stress using this measurement? This is unclear since one velocity quantity is only shown at single streamwise location. Is there any difference of velocity feature at 1 and 3 mm above the bed? Also, Line 127 mentioned crossstream fluid velocity, but I think there is no LDV measurement in crossstream velocity. Please confirm. In addition to the flow measurement, a detailed explanation of bedload transport measurement should be added in the text. As referee #1 pointed out, the sampling time is important for calculating bedload flux. It might be better to explain the direction, length and velocity of sediment particles at the method section not around Line 251 since these are also important quantities to characterize the bedload transport pattern.
Linebyline comments:
Lines 77 and 80: 3 and 2 should be superscript.
Line 81: This flow depth is an averaged value over 1 ripple or others? And how did the authors control the water depth. Please confirm.
Table 1: The grain shape is assumed as a spherical to conovert the unit from grains/(cm*s) to cm^2/s? Also, did the authors check this value reasonably like by comparing sediment supply rate or sediment transport rate at the downstream end.
Line 122: “being downstream at the crest” will be better.
Lines 259260: Is there any reference for previous study?
Line 269: What is the definition of concentration of sediment?
Line 303: in creased should be increased
Citation: https://doi.org/10.5194/esurf20233RC2
Kate C. P. Leary et al.
Kate C. P. Leary et al.
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