Ripple formation induced by biogenic moundsðcomment

Transcription

1 Marine Geology 168 (2000) 145±151 Discussion Ripple formation induced by biogenic moundsðcomment Jaco H. Baas*, James L. Best School of Earth Sciences, University of Leeds, Leeds LS2 9JT, UK Received 25 January 2000; accepted 29 March Introduction Fries et al. (1999), hereafter referred to as FBW, present interesting experimental data showing that biogenic mounds, formed by the conveyor-belt feeding polychaete Cistenides (Pectinaria) gouldii, can be reshaped into asymmetric bedforms at bed shear stresses below the Shields threshold of sediment movement. The nal geometry of the current ripples was found to depend on the spatial density of the mounds (number of mounds per unit area), mound height and the imposed bed shear velocity. In a series of ume experiments at different boundary conditions, FBW distinguish between beds with migrating ripples (MR), beds with stationary ripples (SR) and beds without ripples (NR). We believe, however, that such a distinction is awed. Recent advances in the stability analysis of current ripples demonstrate the existence of predictable sequences of current-ripple geometry during evolution towards equilibrium bed morphology (Baas, 1994, 1999; Oost and Baas, 1994). This discussion illustrates how the principles of time-dependent bedform development can be applied to FBW's data. In addition, we discuss the physical parameters governing the generation of current ripples from bed defects, which de ne the threshold conditions (in terms of mound height, spacing and ow strength) for which biogenic mounds are expected to generate current ripples. Finally, we highlight the inappropriateness of the terms * Corresponding author. addresses: j.baas@earth.leeds.ac.uk (J.H. Baas), j.best@earth.leeds.ac.uk (J.L. Best). ªsubcriticalº and ªsupercriticalº for describing the threshold of sediment movement. 2. Shields criterion and roughness effects on the estimation of bed shear stress Before discussing the development and stability of current ripples and consequences for the nomenclature used by FBW, it is worthy of note that Shields threshold of sediment movement (and its modi cation by Miller et al. (1977)), as used widely in hydrodynamic research, is to some extent an arbitrary threshold. Indeed, the drawing of a single threshold line through a scatter of points was performed by Rouse in his later manipulation of Shields data, which itself had some averaging performed on the original data points (Kennedy, 1995). The threshold is thus a line drawn within a scatter of points between an upper and lower limit, with this range being a factor of 1.5 to 2.2 (Kennedy, 1995). The Shields threshold is equivalent to ªfrequent to permanent movement of particles at all locations on a at bedº, as de ned by Delft Hydraulics (1972) or the movement of 200±400 particles per square metre at bed, as quanti ed by Graf and Pazis (1977). The number of particles moving on a bed with increased form roughness (such as biogenic mounds and current ripples) is probably even higher. The Shields threshold has only been de ned, and is indeed very useful, for practical purposes such as the calculation of bedload transport rates. Grass (1970) outlined how the initiation of sediment movement can be viewed as the overlapping of two distributions, one for the imposed uid shear stress and one /00/$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S (00)

2 146 J.H. Baas, J.L. Best / Marine Geology 168 (2000) 145±151 Fig. 1. Changes in bedform spacing as a function of shear velocity in the biogenic mound experiments of Fries et al. (1999). The shear velocities for total drag were estimated from grain-related shear velocities, mound height, and mound spacing (Tables 1 and 2 of Fries et al. (1999)), using the CheÂzy and BeÂlanger equations for steady, non-uniform ow (i.e. change from at bed to bed with bedforms; see Van Rijn (1990), for methodology). Bedform spacing incorporates initial mound spacing and nal ripple spacing, connected by a vertical arrow for each ume run, if applicable. The dash±dotted line separates regions with and without a signi cant increase in bedform spacing (see text for explanation). One MR-type run (initial mound spacing: 14.7 cm; initial mound height: 1.36 cm; grain-related shear velocity: 1.03 cm s 21 ) was not included in the calculations, because the standard deviation of ripple spacing was more than two times the increase in spacing. representing the shear stress required to entrain sediment. The beginning of the overlap of these distributions, which corresponds to the effect of rare, highmagnitude turbulent sweeps on a at bed (Grass, 1970), dictates the point at which infrequent sediment transport occurs, and which will be below the bed shear stress at which more general motion is observed. This rationale is also implicit in the work of Lavelle and Mofjeld (1987), who question the existence of critical conditions for the initiation of motion. They argue that, given adequate time and a range of bed shear stresses, particle movement will occur somewhere, since turbulent ow is basically a stochastic process and at conditions below the Shields threshold there may thus be an instantaneous bed shear stress event large enough to move a particle. It follows from the above that sediment movement can occur below the Shields threshold, albeit at an increasingly smaller rate. On a at bed of sand with a median diameter of mm and a shear velocity, u*, of,0.95 cm s 21 (the typical constraints applied by FBW), the number of particles moving is small (around 1 per m 2 according to the methods of Graf and Pazis (1977)). FBW, however, calculated shear velocities from velocity pro les taken over a plane bed area situated one metre upstream of the test area. All calculated shear velocities thus underestimate the shear over the mounds and bedforms in the test area, since the form roughness is not taken into account by the authors. Using the CheÂzy and BeÂlanger equations for steady, non-uniform ow (e.g. Van Rijn, 1990), we estimated the shear velocities up to 18% higher in the test area at 0.9±1.3 cm s 21 (as opposed to the 0.75±1.1 cm s 21 in the plane bed area; Fig. 1), which may be expected to move up to several tens of particles per m 2 (Graf and Pazis, 1977). In our calculations, the form roughness of the biogenic mounds was assumed to be identical to that of current ripples of equal height and spacing (Van Rijn, 1993). However, it is likely that these cone-shaped mounds may have been ªrougherº than streamlined ripples, and thus produce even higher shear velocities and rates of particle transport: our recalculated shear velocities may thus still underestimate the true u* imposed on the bed. In any case, the movement of several tens of particles per m 2 may not be obvious visually, yet inevitably this will lead to the formation of current

3 J.H. Baas, J.L. Best / Marine Geology 168 (2000) 145± Fig. 2. Plot of initial and nal defect Reynolds number (Re d ) using the parameter values given in Tables 1 and 2 of Fries et al. (1999). Note that all mound heights produce Re d values considerably in excess of the critical value of 4.5. ripples, since lower stage plane beds do not exist in medium-grained sand (Best, 1996). 3. Bed defects and the development of current ripples from biogenic mounds: bedform stability and nomenclature Much past work has shown how the initiation of current ripples from a at bed is linked to the presence of small defects in the surface roughness (Southard and Dingler, 1971; Williams and Kemp, 1971, 1972; Mantz, 1978; Gyr and Schmid, 1989; Best, 1992, Best, 1996; Gyr and MuÈller, 1996), which may be produced through turbulence-related, high bed shear stress events or naturally-imposed bed irregularities, perhaps by biogenic activity as in FBW's work. However, regardless of the origin of the bed defect, the instability of this mound is governed by the defect height and shear velocity, and may lead to leeside ow separation, downstream bed scour and further ripple initiation. Such a sequence is evident in FBW's Fig. 5a. Bed defects trigger ow separation when the dimensionless defect Reynolds number, Re d (where Re d ˆ h m u*/n, in which h m is the defect (mound) height, u* is shear velocity and n is the kinematic viscosity of the uid) exceeds a value of approximately 4.5 (see Williams and Kemp, 1971; Best, 1992; Gyr and MuÈller, 1996). Calculation of Re d for the initial and nal mound/ripple heights (Fig. 2) shows that all of the initial mounds in the authors experiments far exceeded Re d ˆ 4.5, and thus may be expected to develop a downstream morphology similar to incipient ripples. These values are calculated using the upstream at bed shear velocity and would be even larger if the shear velocity over the mound roughness was used (see above). The data points on Fig. 2 are also classi ed according to the description given to the bed state by the authors, where it can be seen that all mounds which are stated to develop `no ripples' are still above the Re d threshold of ~4.5. However, this statement should be examined in the light of the authors description and photographs, in which it is clear that some runs that are described as developing `no ripples' (for instance Figs. 3 and 5a in FBW) do possess well-developed incipient ripples, identical to those described in past work on ripple initiation (see Mantz, 1978; Gyr and Schmid, 1989). It is therefore clear from this plot that all these bed defects, given suf cient time (see below), would begin to develop an incipient ripple morphology. Additionally, it is noticeable that even though all the bed defects for which sediment transport was described became lower in height as the runs proceeded, the nal dimensionless defect heights still far exceeded Re d ˆ 4.5 (Fig. 2), and thus may still be expected to be developing a ripple morphology, even if at a slow rate. The formation of current ripples is an extremely slow process at low shear velocities (Gyr and Schmid, 1989; Baas, 1994, 1999) and the formation of equilibrium linguoid ripples from at bed conditions may take several hundreds of hours at shear velocities just above the Shields threshold (Baas, 1994, Baas, 1999). However, current ripples have been shown to go through distinct stages of development towards an equilibrium geometry (Fig. 3). The rst development stage consists of solitary, incipient ripples, mostly linked to locations of pre-existing or ow-induced bed defects (see above). In time, these incipient ripples coalesce to form ripple trains with straight crest lines, with subsequent stages including sinuous ripples, non-equilibrium linguoid ripples and ultimately

4 148 J.H. Baas, J.L. Best / Marine Geology 168 (2000) 145±151 Fig. 3. Standardised curve for the development of current ripple height and wavelength from a at sand bed. Ripple plan morphology changes from incipient (stage 1) through straight-crested, sinuous (stage 2) and non-equilibrium linguoid (stage 3) to equilibrium linguoid (stage 4) at all shear stresses within the current ripple stability eld. H t ˆ ripple height at time t; H e ˆ ripple height at equilibrium time T e ; L t ˆ ripple wavelength at time t; L 0 ˆ wavelength of rst ripples appearing on the at bed; L e ˆ equilibrium ripple wavelength (after Baas, 1994). equilibrium linguoid ripples. Current ripple height and spacing gradually increase, albeit at a decreasing rate, during development towards equilibrium (Fig. 3). A similar type of development may be expected to take place below the Shields threshold of sediment movement, but at a slower rate, provided at least some particles are moving and the bed defects/incipient ripples stay above the threshold Re d. It was shown above (Figs. 1 and 2) that these conditions are present in FBW's experiments, including those in which the current ripples were described as ªstationaryº. A contradiction now emerges since ripples exist only by virtue of the fact that they migrate. Hence, the term stationary ripple is inappropriate for such a ow and it is likely these ripples are developing at an extremely slow rate because of the limited sediment transport. FBW state in several places that SR in their experiments did migrate, but within the test area only. They thus erroneously de ned the contradictio in terminis ªmigrating stationary rippleº. We argue that FBW's data should be reinterpreted by considering the bedforms in each run to be in a different stage of development, but part of the same continuum of bedform geometries (Fig. 3). As stated above, this is most obvious from the photographs shown in FBW's Figs. 3±5. Although the bedforms in Figs. 3 and 5a were classi ed as NR (no ripples), they clearly have the asymmetrical geometry typical of current ripples: the term NR is therefore a misnomer. These bedforms closely resemble solitary, early incipient ripples, formed by erosion of the stoss side and crest and development of a slip face on the leeside of the original mounds (cf. Southard and Dingler, 1971; Gyr and Schmid, 1989). Some ripples in Fig. 5a even show evidence for ow separation from the presence of newly formed ripples immediately downstream of the original mounds. Ripple crests have started to coalesce in Fig. 5b, which suggests that the ripples were in a late incipient stage of development when the photograph was taken. Finally, the bedforms in Fig. 4 clearly resemble straight-crested ripples, and hence are in a relatively mature stage of development. The rate of development of these bedforms, as well as those in all other runs, depends on the shear velocity in the test section and on the initial height and spacing of the biogenic mounds. The relationship between shear velocity and bedform spacing is plotted in Fig. 1. The data show that bedform development is con ned predominantly to shear velocities higher than 1.06 cm s 21 and initial

5 J.H. Baas, J.L. Best / Marine Geology 168 (2000) 145± mound spacings below ~10 cm (i.e. the lower-right quadrant of Fig. 1). For other values, the nal bedform spacing was not signi cantly different from the initial mound spacing. This morphological behaviour is compatible with the empirical bedform stability model of Baas (1994) described above. FBW's experiments did not last long enough to acquire any measurable increase in bedform spacing at u*, 1.06 cm s 21. At higher shear velocities and initial mound spacings larger than 10 cm, the bedform spacing increased at a rate that may well have been too slow to be detectable within the duration of the experiments. This is apparent from the standardised development curve (Fig. 3), as bedforms spaced 10± 15 cm apart would have completed 33±80% of their development path towards equilibrium spacing (using L 0 ˆ 7.0 cm (Coleman and Melville, 1996) and L e ˆ,16.5 cm (Raudkivi, 1997), both for mm sand), which is within the range where bedform development begins to slow down signi cantly. The ow treats the biogenic mounds with a spacing,10 cm (and u* cm s 21 ), on the other hand, as bedforms with a potentially high development rate, thus explaining the relatively large change in bedform spacing in the lower right quadrant of Fig. 1 and FBW's observation that an increase in mound density led to an increased tendency of coalescence of mounds into ripples (or from solitary, incipient ripples to straight-crested ripples in terms of the bedform stability model). If it is assumed that the length of the ow separation zone behind a mound/ripple is approximately four times the mound height (see Bennett and Best, 1996), then the high shear stresses present in the region of ow reattachment would result in greater entrainment, and more rapid development, over mounds that are closer together (i.e. for the initial mound heights at spacings of less than approximately 2.5±6.2 cm). Flow separation thus causes more densely spaced mounds to be more quickly eroded and reshaped into asymmetrical ripples of a smaller height. The application of the bedform stability model can also be used to explain the following observations in the formation of current ripples from biogenic mounds: 1. FBW used the term ªequilibrium rippleº for bedforms generated after 6 h from a plane bed at a shear velocity of 2 cm s 21. The ripples formed were,10.8 cm long and,1.1 cm high, and probably had a straight or sinuous planform (cf. FBW's Fig. 2). It should be stressed, however, that these ripples are much smaller than ripples formed in mm sand that are in full equilibrium with the ow conditions. Such ripples are,17 cm long (Raudkivi, 1997),,1.8 cm high (Ackers, 1964; Guy et al., 1966), and have a linguoid planform. The authors thus described current ripples that have reached about 35±60% of their ultimate equilibrium height and spacing. Model calculations indicate that an additional period of 2 days would have been required to reach full equilibrium bed morphology. 2. A second argument used by FBW to distinguish ªstationaryº and ªmigratingº ripples (the rst being the migration distance discussed earlier) was the larger spacing of the latter bedforms. In our opinion, however, this argument is untenable, since the difference in spacing is simply a consequence of the larger initial spacing of the biogenic mounds from which MR were formed (7.4± 14.7 cm for MR versus 3.7±7.4 cm for SR). As a result of their denser spacing, SR developed at a higher rate than MR (see above), but they did not succeed in closing the gap in spacing within the imposed experimental time. 3. We do not support the authors' suggestion that the SR strive after a ªlocal equilibriumº spacing that corresponds to the sand wavelet length of Coleman and Melville (1996). The underlying argument that ªmost stationary ripple wavelengths fall within one standard deviation of the overall meanº is trivial, since by de nition 68% of any data population will fall within one standard deviation of the mean ( g. 6 in FBW; cf. Fig. 1). There is no obvious reason why bedform development should cease at the wavelet length, which is equivalent to the initial ripple length, L 0, in the bedform stability model. It is to be expected that a train of bedforms with an initial spacing smaller than L 0 will be subject to bedform convergence processes and thereby increase their average spacing. However, this process will continue beyond the wavelet length until, as far as time allows, the equilibrium spacing (i.e. L e in Fig. 3) is attained and the bedforms are in full equilibrium with the ow.

6 150 J.H. Baas, J.L. Best / Marine Geology 168 (2000) 145± FBW refer to an experiment with ªinterruptedº bed development, in which the bedforms were classi- ed as SR, but MR would have been the ultimate bed state if given more time to develop. This is an excellent illustration of the importance of the time factor in ripple development. Other SR-type experiments may therefore have to be reinterpreted as MR-type ripples, if the bedforms had been given suf cient time to develop, in accordance with the bedform stability model. The uncertainty in the distinction between SR and MR has major implications for the validity of the authors' comparison with the work of Southard and Dingler (1971) on the propagation of ripples behind mounds (cf. FBW's Fig. 7). If the experiment with interrupted bed development, and possibly other SR-type experiments, would have lasted long enough to classify the bed state as MR, the threshold shear stress separating migrating from non-migrating ripples in mm sand would be much closer than suggested by FBW to the original threshold of Southard and Dingler (1971) for mm sand. 4. Subcritical and supercritical ow FBW use the terms `subcritical' and `supercritical' to describe ows with bed shear stresses below and above the threshold of sediment movement, respectively. However, this terminology is likely to lead to confusion since the terms `subcritical' and `supercritical' are commonly used to distinguish ows with a Froude number below and above unity, respectively, the latter being an entirely different ow regime than in the present experiments with biogenic mounds. Although we acknowledge there is no established term for the low-velocity ows in FBW's study, we suggest a different terminology is more appropriate. The solution adopted in past papers is to use a short description instead of a single term, such as ªbelow the critical shear stress for sediment entrainmentº. As a shorter alternative, the terms ªentrainingº and ªnon-entrainingº or `sub' and `supra-threshold' ows could be chosen, although even these are not fully satisfactory (see discussion above). 5. Conclusions That sediment transport occurs at shear stresses below the Shields criterion is not surprising and supports past work on the entrainment threshold (Grass, 1970; Lavelle and Mofjeld, 1987). Additionally, given a range of shear stresses that may entrain only a few grains, and a defect height that may trigger ow separation, current ripples may be expected to propagate downstream from biogenically-induced mounds. The processes and patterns of ripple formation will be identical to those well established in past work. However, the rate at which such bedforms develop will depend on the bed defect height and the applied bed shear stress (which itself may vary greatly because of changing form roughness), and hence the rate of development will be much lower at lower bed shear stresses. This highlights the fact that suf cient time must be given to allow ripples to develop fully, and at very low threshold shear stresses this period may be several days in duration. References Ackers, P., Experiments on small streams in alluvium. Journal of the Hydraulics Division, ASCE 90 (HY4), 1±37. Baas, J.H., A ume study on the development and equilibrium morphology of small-scale bedforms in very ne sand. Sedimentology 41, 185±209. Baas, J.H., An empirical model for the development and equilibrium morphology of current ripples in ne sand. Sedimentology 46, 123±138. Bennett, S.J., Best, J.L., Mean ow and turbulence structure over xed ripples and the ripple-dune transition. In: Ashworth, P.J., Bennett, S.J., Best, J.L., McLelland, S.J. (Eds.). Coherent Flow Structures in Open Channels, Wiley and Sons, Chichester, pp. 281±304. Best, J.L., On the entrainment of sediment and initiation of bed defects: insights from recent developments within turbulent boundary layer research. Sedimentology 39, 797±811. Best, J.L., The uid dynamics of small-scale alluvial bedforms. In: Carling, P.A., Dawson, M. (Eds.). Advances in Fluvial Dynamics and Stratigraphy, Wiley and Sons, Chichester, pp. 67±125. Coleman, S.E., Melville, B.W., Initiation of bed forms on a at sand bed. Journal of Hydraulic Engineering 122, 301±310. Delft Hydraulics, Systematic Investigation of Two-dimensional and Three-Dimensional Scour (in Dutch). Report M648/M863, Delft, Netherlands. Fries, J.S., Butman, C.A., Wheatcroft, R.A., Ripple formation induced by biogenic mounds. Marine Geology 159, 287±302. Graf, W.H., Pazis, G.G., Les phenomenes de deposition et

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