Examination of reference concentration under waves and currents on the inner shelf

Abstract

[1] We examine reference concentration using three different data sets of near-bed suspended sediment concentration observed under combined waves and currents. The data include observations made at 15 and 20 m depth off Dounreay, Scotland, UK, and observations obtained at 13 m depth off Duck, North Carolina, USA. These data accommodate different dynamic conditions (from wave-dominated conditions at Dounreay to wind-driven, current-dominated conditions at Duck) and sediment properties (median size of bed sediment ranging from 120 to 350 mm). Near-bed concentration profiles to elevations of about 80 cm were obtained using acoustic backscatter sensors with 1 cm resolution. The reference concentrations (C r ) at 1 cm were then evaluated by regressing the observed suspended sediment concentrations against a Rouse-type model. Bed shear stresses associated with each estimate of C r were estimated using the wavecurrent interaction model of Grant and Madsen. Existing equations for reference concentration based on shear stress alone fail to accommodate all C r estimates from different environments. We introduce a new empirical relationship between C r and the product of Shields and inverse Rouse numbers. These dimensionless parameters represent the ratio of bed shear stress and submerged particle weight and the ratio of shear velocity and particle settling velocity, respectively. The new formula adjusts the amount of mobile sediment at the bed (related to the Shields number) to that available for suspension at the reference height (related to the inverse Rouse number). The new formula for reference concentration accommodates observations from different environments, suggesting that it may have wide applicability on sandy inner shelves.

Comparison of measurements and models of bed stress, bedforms and suspended sediments under combined currents and waves

“…This strong dependence on ripple steepness has recently been questioned by Dolphin and Vincent (2009), who did not observe such sensitivity in a field study on bedforms and suspended sediments off the Dutch coast. result which is very comparable to that of Lee et al (2004). The reduction in δ agrees, qualitatively, with Thorne et al (2002) who found that δ=2.5·10 -3 gave a better fit to their data.…”

“…Comparing the two predictions with the observations showed that the formulation of Lee et al (2004) out-performed that of Nielsen (1986), although a modified Nielsen calculation, with nominally constant steepness and δ=5·10 -4 , did compare as well with the observations as Lee et al (2004). The indication from the present study, and those of Lee et al (2004), Grasmeijer and Kleinhans (2004) and Dolphin and Vincent (2009), indicate that the reference concentration may not be as strongly coupled to the ripple steepness as suggested by Nielsen (1986).…”

“…The indication from the present study, and those of Lee et al (2004), Grasmeijer and Kleinhans (2004) and Dolphin and Vincent (2009), indicate that the reference concentration may not be as strongly coupled to the ripple steepness as suggested by Nielsen (1986).…”

Comparison of measurements and models of bed stress, bedforms and suspended sediments under combined currents and waves

“…This strong dependence on ripple steepness has recently been questioned by Dolphin and Vincent (2009), who did not observe such sensitivity in a field study on bedforms and suspended sediments off the Dutch coast. result which is very comparable to that of Lee et al (2004). The reduction in δ agrees, qualitatively, with Thorne et al (2002) who found that δ=2.5·10 -3 gave a better fit to their data.…”

“…Comparing the two predictions with the observations showed that the formulation of Lee et al (2004) out-performed that of Nielsen (1986), although a modified Nielsen calculation, with nominally constant steepness and δ=5·10 -4 , did compare as well with the observations as Lee et al (2004). The indication from the present study, and those of Lee et al (2004), Grasmeijer and Kleinhans (2004) and Dolphin and Vincent (2009), indicate that the reference concentration may not be as strongly coupled to the ripple steepness as suggested by Nielsen (1986).…”

“…The indication from the present study, and those of Lee et al (2004), Grasmeijer and Kleinhans (2004) and Dolphin and Vincent (2009), indicate that the reference concentration may not be as strongly coupled to the ripple steepness as suggested by Nielsen (1986).…”

Observed and predicted bed forms and their effect on suspended sand concentrations

“…As can be seen, changing the bottom concentration predictor from the Nielsen (1986) model to the Zyserman and Fredsøe (1994) model leads to an increase of the predicted suspended sand concentrations with about a factor 10 -100. The Lee et al (2004) model produces concentrations close to the values by the Nielsen (1986) model. Generally, best predictions are obtained with the latter two bottom concentration predictors.…”

Data-driven components in a model of inner-shelf sorted bedforms: a new hybrid model

“…5). Predictors generally show nonlinear dependence on U sig /d 50 , qualitatively similar to the predictors developed by Nielsen (1986) and Lee et al (2004), which both show dependence on the modified Shields parameter. We focus our analysis on the last cliff before the proliferation of very complex, nonlinear terms (solution 9):…”

Comparison of measurements and models of bed stress, bedforms and suspended sediments under combined currents and waves

“…This strong dependence on ripple steepness has recently been questioned by Dolphin and Vincent (2009), who did not observe such sensitivity in a field study on bedforms and suspended sediments off the Dutch coast. result which is very comparable to that of Lee et al (2004). The reduction in δ agrees, qualitatively, with Thorne et al (2002) who found that δ=2.5·10 -3 gave a better fit to their data.…”

“…Comparing the two predictions with the observations showed that the formulation of Lee et al (2004) out-performed that of Nielsen (1986), although a modified Nielsen calculation, with nominally constant steepness and δ=5·10 -4 , did compare as well with the observations as Lee et al (2004). The indication from the present study, and those of Lee et al (2004), Grasmeijer and Kleinhans (2004) and Dolphin and Vincent (2009), indicate that the reference concentration may not be as strongly coupled to the ripple steepness as suggested by Nielsen (1986).…”

“…The indication from the present study, and those of Lee et al (2004), Grasmeijer and Kleinhans (2004) and Dolphin and Vincent (2009), indicate that the reference concentration may not be as strongly coupled to the ripple steepness as suggested by Nielsen (1986).…”

Observed and predicted bed forms and their effect on suspended sand concentrations

“…As can be seen, changing the bottom concentration predictor from the Nielsen (1986) model to the Zyserman and Fredsøe (1994) model leads to an increase of the predicted suspended sand concentrations with about a factor 10 -100. The Lee et al (2004) model produces concentrations close to the values by the Nielsen (1986) model. Generally, best predictions are obtained with the latter two bottom concentration predictors.…”

Data-driven components in a model of inner-shelf sorted bedforms: a new hybrid model

“…5). Predictors generally show nonlinear dependence on U sig /d 50 , qualitatively similar to the predictors developed by Nielsen (1986) and Lee et al (2004), which both show dependence on the modified Shields parameter. We focus our analysis on the last cliff before the proliferation of very complex, nonlinear terms (solution 9):…”

Comparison of measurements and models of bed stress, bedforms and suspended sediments under combined currents and waves

“…This strong dependence on ripple steepness has recently been questioned by Dolphin and Vincent (2009), who did not observe such sensitivity in a field study on bedforms and suspended sediments off the Dutch coast. result which is very comparable to that of Lee et al (2004). The reduction in δ agrees, qualitatively, with Thorne et al (2002) who found that δ=2.5·10 -3 gave a better fit to their data.…”

“…Comparing the two predictions with the observations showed that the formulation of Lee et al (2004) out-performed that of Nielsen (1986), although a modified Nielsen calculation, with nominally constant steepness and δ=5·10 -4 , did compare as well with the observations as Lee et al (2004). The indication from the present study, and those of Lee et al (2004), Grasmeijer and Kleinhans (2004) and Dolphin and Vincent (2009), indicate that the reference concentration may not be as strongly coupled to the ripple steepness as suggested by Nielsen (1986).…”

“…The indication from the present study, and those of Lee et al (2004), Grasmeijer and Kleinhans (2004) and Dolphin and Vincent (2009), indicate that the reference concentration may not be as strongly coupled to the ripple steepness as suggested by Nielsen (1986).…”

Observed and predicted bed forms and their effect on suspended sand concentrations

“…As can be seen, changing the bottom concentration predictor from the Nielsen (1986) model to the Zyserman and Fredsøe (1994) model leads to an increase of the predicted suspended sand concentrations with about a factor 10 -100. The Lee et al (2004) model produces concentrations close to the values by the Nielsen (1986) model. Generally, best predictions are obtained with the latter two bottom concentration predictors.…”

Data-driven components in a model of inner-shelf sorted bedforms: a new hybrid model

“…5). Predictors generally show nonlinear dependence on U sig /d 50 , qualitatively similar to the predictors developed by Nielsen (1986) and Lee et al (2004), which both show dependence on the modified Shields parameter. We focus our analysis on the last cliff before the proliferation of very complex, nonlinear terms (solution 9):…”