- Email: [email protected]
Discussion by A. Roy
30
Michael Church
and sediment transport. Importantly, the experimental results of Pyrce and Ashmore do not necessarily eliminate the role of the flow field.
References Coterill, K., Coleman, J., Marotta, D., et al., 1998. Sinuosity in submarine channels; scale and geometries in seismic and outcrop indicating possible mechanisms for deposition (abstract). Am. Ass. Pet. Geol. Bull. 82 (10), 1904. Einstein, H.A., Shen, H.W., 1964. A study on meandering in straight alluvial channels. J. Geophys. Res. 69 (24), 5239–5247. Etling, D., 1990. On plume meandering under stable stratification. Atmos. Environ. 24A (8 Part 2), 1979–1985. Gorycki, M.A., 1973. Hydraulic drag: A meander initiating mechanism. Bull. Geol. Soc. Am. 84, 175–186. Holland, G.J., Lander, M., 1993. The meandering nature of tropical cyclone tracks. J. Atmos. Sci. 50 (9), 1254–1266. Johannesson, H., Parker, G., 1989. Linear theory of river meanders. In: Ikeda, S. and Parker, G. (Eds), River Meandering. American Geophysical Union, Washington, DC, pp. 181–213. Knighton, D., 1998. Fluvial forms and processes: A new perspective. Arnold, London. Leopold, L.B., Wolman, M.G., 1960. River meanders. Geol. Soc. Am. Bull. 71 (6), 769–793. Parker, G., 1976. On the cause and characteristic scales of meandering and braiding in rivers. J. Fluid Mech. 76, 457–480. Parker, G., 1998. Flow and deposits of turbidity currents and submarine debris flows (abstract). Am. Ass. Pet. Geol. Bull. 82 (10), 1948–1949. Pyrce, R.S., Ashmore, P.E., 2003a. Particle path length distributions in meandering gravel-bed streams: Results from physical models. Earth Surf. Process. Landf. 28 (9), 951–966. Pyrce, R.S., Ashmore, P.E., 2003b. The relation between particle path length distributions and channel morphology in gravel-bed streams: A synthesis. Geomorphology 56 (1–2), 167–187. Pyrce, R.S., Ashmore, P.E., 2005. Bedload path length and point bar development in gravel-bed river models. Sedimentology 52 (4), 839–857. Quick, M.C., 1974. Mechanism for streamflow meandering. J. Hydraul. Eng. 100 (HY6), 741–753. Seminara, G., Tubino, M., 1989. Alternate bars and meandering: Free, forced and mixed interactions. In: Ikeda, S. and Parker, G. (Eds), River Meandering. American Geophysical Union, Washington, DC, pp. 267–320. Thomson, J., 1878. On the origin of windings of rivers in alluvial plains, with remarks on the flow of water round bends in pipes. Proc. R. Soc. London, Ser. A. 25, 114–127.
Discussion by A. Roy I would like to raise three points concerning the turbulent scale. The author questions the usefulness of the integral length scale (LE) for determining the upper limit of turbulence. Because it is based on the integration of the autocorrelation function of the whole velocity signal, LE represents the scale of both the turbulent events and the ambient fluid. LE provides a very conservative estimate of the size of the turbulent flow structures. Our data from a range of gravel-bed rivers and of flow conditions show that LE for the streamwise velocity component averages around 0.9d with a standard deviation of 0.3. This scaling is the lowest estimate of eddy size when compared to values obtained from other methods that emphasize the scale of individual events. These latter methods should be preferred in establishing the maximum scale of turbulent eddies.
Multiple scales in rivers
31
As noted by the author, defining unambiguously a true turbulent event (e.g., ejection) from velocity time series is a prerequisite to any scaling or frequency analysis. It is interesting to note, however, that the detection of turbulent events from velocity records may be quite robust. It is known that the application of various methods used to detect individual flow structures to velocity data will yield different results. In spite of this variability and using thresholds for each method that have been developed from studies in laboratory flumes, it appears that the frequency of events in gravel-bed rivers remains relatively constant among the various detection schemes. For instance, Roy et al. (1996) reported that average bursting frequency (T) for four commonly used burst detection schemes varies between 0.30 and 0.35 event per second. In gravel-bed rivers, bursting frequency is not very sensitive to height above the bed. This suggests that the phenomenon under study may be quite robust in its global properties or that the large-scale events that dominate the turbulent flow field in gravel-bed rivers are equally well detected by the schemes. It is important, however, that detection schemes be used consistently and that similar threshold values be applied across various studies. The selection of adequate thresholds may be guided by flow visualization. Bursting frequency in gravel-bed rivers is often quite low with reported values typically between 0.2 and 0.6 depending on the thresholds used in the detection schemes. This indicates that the turbulent structures are quite large. Using Rao et al.’s formula, such low T values would imply that measurements were taken in shallow and/or fast currents. If one supposes that the size of the ejections scale with depth (say 5d) and one samples flows of different depth but with similar flow velocity, then T as estimated by uNT ¼ 5d would increase with increasing depth while the size of the structures would also increase. If larger structures take more time than smaller ones to fully develop and if they advect roughly at the mean flow velocity, it is difficult to imagine that bursting frequency would also increase. It seems to me that it may be difficult to reconcile both scalings as in L ¼ 5d ¼ uNT in many contexts encountered in gravel-bed rivers.
References Roy, A.G., Buffin-Be´langer, T., Deland, S., 1996. Scales of turbulent coherent flow structures in gravel-bed rivers. In: Ashworth, P.J., Bennett, S.J., Best, J.L., and McLelland, S.J. (Eds), Coherent Flow Structures in Open Channels. Wiley, Chichester, pp. 147–164.
Reply by the author I thank Rennie and Roy for their helpful amplification of some points in the paper. Together, the discussions emphasize that the essential connections between the flow field and the resulting channel morphology remain an important unresolved problem. Rennie points out that the demonstration by Pyrce and Ashmore (2003b) of a preferred riffle–riffle step length for sediment grain movements was made with
Michael Church
and sediment transport. Importantly, the experimental results of Pyrce and Ashmore do not necessarily eliminate the role of the flow field.
References Coterill, K., Coleman, J., Marotta, D., et al., 1998. Sinuosity in submarine channels; scale and geometries in seismic and outcrop indicating possible mechanisms for deposition (abstract). Am. Ass. Pet. Geol. Bull. 82 (10), 1904. Einstein, H.A., Shen, H.W., 1964. A study on meandering in straight alluvial channels. J. Geophys. Res. 69 (24), 5239–5247. Etling, D., 1990. On plume meandering under stable stratification. Atmos. Environ. 24A (8 Part 2), 1979–1985. Gorycki, M.A., 1973. Hydraulic drag: A meander initiating mechanism. Bull. Geol. Soc. Am. 84, 175–186. Holland, G.J., Lander, M., 1993. The meandering nature of tropical cyclone tracks. J. Atmos. Sci. 50 (9), 1254–1266. Johannesson, H., Parker, G., 1989. Linear theory of river meanders. In: Ikeda, S. and Parker, G. (Eds), River Meandering. American Geophysical Union, Washington, DC, pp. 181–213. Knighton, D., 1998. Fluvial forms and processes: A new perspective. Arnold, London. Leopold, L.B., Wolman, M.G., 1960. River meanders. Geol. Soc. Am. Bull. 71 (6), 769–793. Parker, G., 1976. On the cause and characteristic scales of meandering and braiding in rivers. J. Fluid Mech. 76, 457–480. Parker, G., 1998. Flow and deposits of turbidity currents and submarine debris flows (abstract). Am. Ass. Pet. Geol. Bull. 82 (10), 1948–1949. Pyrce, R.S., Ashmore, P.E., 2003a. Particle path length distributions in meandering gravel-bed streams: Results from physical models. Earth Surf. Process. Landf. 28 (9), 951–966. Pyrce, R.S., Ashmore, P.E., 2003b. The relation between particle path length distributions and channel morphology in gravel-bed streams: A synthesis. Geomorphology 56 (1–2), 167–187. Pyrce, R.S., Ashmore, P.E., 2005. Bedload path length and point bar development in gravel-bed river models. Sedimentology 52 (4), 839–857. Quick, M.C., 1974. Mechanism for streamflow meandering. J. Hydraul. Eng. 100 (HY6), 741–753. Seminara, G., Tubino, M., 1989. Alternate bars and meandering: Free, forced and mixed interactions. In: Ikeda, S. and Parker, G. (Eds), River Meandering. American Geophysical Union, Washington, DC, pp. 267–320. Thomson, J., 1878. On the origin of windings of rivers in alluvial plains, with remarks on the flow of water round bends in pipes. Proc. R. Soc. London, Ser. A. 25, 114–127.
Discussion by A. Roy I would like to raise three points concerning the turbulent scale. The author questions the usefulness of the integral length scale (LE) for determining the upper limit of turbulence. Because it is based on the integration of the autocorrelation function of the whole velocity signal, LE represents the scale of both the turbulent events and the ambient fluid. LE provides a very conservative estimate of the size of the turbulent flow structures. Our data from a range of gravel-bed rivers and of flow conditions show that LE for the streamwise velocity component averages around 0.9d with a standard deviation of 0.3. This scaling is the lowest estimate of eddy size when compared to values obtained from other methods that emphasize the scale of individual events. These latter methods should be preferred in establishing the maximum scale of turbulent eddies.
Multiple scales in rivers
31
As noted by the author, defining unambiguously a true turbulent event (e.g., ejection) from velocity time series is a prerequisite to any scaling or frequency analysis. It is interesting to note, however, that the detection of turbulent events from velocity records may be quite robust. It is known that the application of various methods used to detect individual flow structures to velocity data will yield different results. In spite of this variability and using thresholds for each method that have been developed from studies in laboratory flumes, it appears that the frequency of events in gravel-bed rivers remains relatively constant among the various detection schemes. For instance, Roy et al. (1996) reported that average bursting frequency (T) for four commonly used burst detection schemes varies between 0.30 and 0.35 event per second. In gravel-bed rivers, bursting frequency is not very sensitive to height above the bed. This suggests that the phenomenon under study may be quite robust in its global properties or that the large-scale events that dominate the turbulent flow field in gravel-bed rivers are equally well detected by the schemes. It is important, however, that detection schemes be used consistently and that similar threshold values be applied across various studies. The selection of adequate thresholds may be guided by flow visualization. Bursting frequency in gravel-bed rivers is often quite low with reported values typically between 0.2 and 0.6 depending on the thresholds used in the detection schemes. This indicates that the turbulent structures are quite large. Using Rao et al.’s formula, such low T values would imply that measurements were taken in shallow and/or fast currents. If one supposes that the size of the ejections scale with depth (say 5d) and one samples flows of different depth but with similar flow velocity, then T as estimated by uNT ¼ 5d would increase with increasing depth while the size of the structures would also increase. If larger structures take more time than smaller ones to fully develop and if they advect roughly at the mean flow velocity, it is difficult to imagine that bursting frequency would also increase. It seems to me that it may be difficult to reconcile both scalings as in L ¼ 5d ¼ uNT in many contexts encountered in gravel-bed rivers.
References Roy, A.G., Buffin-Be´langer, T., Deland, S., 1996. Scales of turbulent coherent flow structures in gravel-bed rivers. In: Ashworth, P.J., Bennett, S.J., Best, J.L., and McLelland, S.J. (Eds), Coherent Flow Structures in Open Channels. Wiley, Chichester, pp. 147–164.
Reply by the author I thank Rennie and Roy for their helpful amplification of some points in the paper. Together, the discussions emphasize that the essential connections between the flow field and the resulting channel morphology remain an important unresolved problem. Rennie points out that the demonstration by Pyrce and Ashmore (2003b) of a preferred riffle–riffle step length for sediment grain movements was made with