Spectral estimates of bed shear stress using suspended‐sediment concentrations in a wave‐current boundary layer

Abstract

[1] High-resolution time series of suspended-sediment profiles have been obtained using an acoustic backscatter system at an inner shelf site (North Carolina) where flows are dominated by wind-driven currents and waves. We analyzed the spatial and temporal structure of near-bed turbulence in particle-transporting flows and scalar-like fluctuations of suspended-sediment concentrations. An important element of our analysis is a new inertial dissipation method for passive tracers to estimate the shear stress acting on the seabed, using the spectral properties of suspended sediment concentrations observed by acoustic backscatter sensors. In flows that provide adequate separation of the scales of turbulence production and dissipation, a sufficiently thick constant stress wall layer, and significant sediment suspension, frequency (or associated wave number) spectra of nearbed sediment concentration exhibit a À5/3 slope in the inertial subrange that spans frequencies of order 1 Hz. This observation suggests that the suspended sediment is effectively a passive tracer of turbulent fluid motions. Inversion of the relevant, Kolmogorov scaling equations yields estimates of the shear velocity that agree reasonably well with other, independent and widely used measures. High-and low-frequency limits on application of the inertial dissipation method to sediment concentration are related to the inertial response time of sediment particles and the sediment settling timescale. We propose that, in future applications, the inertial dissipation method for passive tracers can be used to estimate either the shear velocity, effective settling velocity of suspended sediment (or equivalent particle size) or dynamic bed roughness if two of these three quantities are independently known.

Multiscale Superposition and Decomposition of Field‐Measured Suspended Sediment Concentrations: Implications for Extending 1DV Models to Coastal Oceans With Advected Fine Sediments

“…The three main sources contributing to the C ( t ) variations (i.e., C M4_res ( t ), C M2_adv ( t ), and C w_res ( t )) are identified in Section 4.1. These components have unique periods (time scales) (Vercruysse et al., 2017), which inspire the possibility of using spectral analyses (e.g., Lee et al., 2003; Schoellhamer, 1996; Venditti & Bennett, 2000) and band‐pass filtering to quantitatively distinguish the components and estimate the contributions via the ratio of variance.…”

Multiscale Superposition and Decomposition of Field‐Measured Suspended Sediment Concentrations: Implications for Extending 1DV Models to Coastal Oceans With Advected Fine Sediments

“…The three main sources contributing to the C ( t ) variations (i.e., C M4_res ( t ), C M2_adv ( t ), and C w_res ( t )) are identified in Section 4.1. These components have unique periods (time scales) (Vercruysse et al., 2017), which inspire the possibility of using spectral analyses (e.g., Lee et al., 2003; Schoellhamer, 1996; Venditti & Bennett, 2000) and band‐pass filtering to quantitatively distinguish the components and estimate the contributions via the ratio of variance.…”

Implications of intermittent turbulent bursts for sediment resuspension in a coastal bottom boundary layer: A field study in the western Yellow Sea, China

“…Previous studies have shown that suspended sediments can be regarded as a passive scalar in the well-developed turbulent boundary flows (Lee et al, 2003). The variance spectrum of the sediment concentration also show a wide inertial subrange with a '−5/3' slope.…”

“…The advantage of ADV in measuring flow velocity and suspended sediment concentration rapidly and synchronously in the same sampling volume has prompted a renewal of interest in sediment dynamics in turbulent boundary layer (Fugate and Friedrichs, 2002;Nikora and Goring, 2002;Lee et al, 2003;Voulgaris and Meyers, 2004;Scully and Friedrichs, 2003;Trevethan et al, 2007;Maa and Kwon, 2007). ADVs work by emitting fixed-frequency acoustic pulses and recording the amount of reflection from suspended particulate matter (SPM) in the sampling volume.…”

Sediment eddy diffusivity and selective suspension under waves and currents on the inner shelf

“…According to Lee et al (2002;2003), cases with R > 1 generally correspond to weak currents, but waves strong enough to suspend sediment high above the bed, such that u * ≈u *cw . In contrast, periods with R < 1 correspond to strong current conditions for which u * ≈u *c .…”

“…Rearrangement of the diffusion equation (Eq. 1) and introduction of the flow velocity scale u* and wave boundary layer length scale δ w yield a dimensionless measure of eddy diffusivity K + which can be evaluated directly from observations of suspendedsediment concentration and flow intensity in a wave-current boundary layer (Lee et al, 2003). The expression is given as…”

Multiscale Superposition and Decomposition of Field‐Measured Suspended Sediment Concentrations: Implications for Extending 1DV Models to Coastal Oceans With Advected Fine Sediments

“…The three main sources contributing to the C ( t ) variations (i.e., C M4_res ( t ), C M2_adv ( t ), and C w_res ( t )) are identified in Section 4.1. These components have unique periods (time scales) (Vercruysse et al., 2017), which inspire the possibility of using spectral analyses (e.g., Lee et al., 2003; Schoellhamer, 1996; Venditti & Bennett, 2000) and band‐pass filtering to quantitatively distinguish the components and estimate the contributions via the ratio of variance.…”

Implications of intermittent turbulent bursts for sediment resuspension in a coastal bottom boundary layer: A field study in the western Yellow Sea, China

“…Previous studies have shown that suspended sediments can be regarded as a passive scalar in the well-developed turbulent boundary flows (Lee et al, 2003). The variance spectrum of the sediment concentration also show a wide inertial subrange with a '−5/3' slope.…”

“…The advantage of ADV in measuring flow velocity and suspended sediment concentration rapidly and synchronously in the same sampling volume has prompted a renewal of interest in sediment dynamics in turbulent boundary layer (Fugate and Friedrichs, 2002;Nikora and Goring, 2002;Lee et al, 2003;Voulgaris and Meyers, 2004;Scully and Friedrichs, 2003;Trevethan et al, 2007;Maa and Kwon, 2007). ADVs work by emitting fixed-frequency acoustic pulses and recording the amount of reflection from suspended particulate matter (SPM) in the sampling volume.…”

Sediment eddy diffusivity and selective suspension under waves and currents on the inner shelf

“…According to Lee et al (2002;2003), cases with R > 1 generally correspond to weak currents, but waves strong enough to suspend sediment high above the bed, such that u * ≈u *cw . In contrast, periods with R < 1 correspond to strong current conditions for which u * ≈u *c .…”

“…Rearrangement of the diffusion equation (Eq. 1) and introduction of the flow velocity scale u* and wave boundary layer length scale δ w yield a dimensionless measure of eddy diffusivity K + which can be evaluated directly from observations of suspendedsediment concentration and flow intensity in a wave-current boundary layer (Lee et al, 2003). The expression is given as…”

Multiscale Superposition and Decomposition of Field‐Measured Suspended Sediment Concentrations: Implications for Extending 1DV Models to Coastal Oceans With Advected Fine Sediments

“…The three main sources contributing to the C ( t ) variations (i.e., C M4_res ( t ), C M2_adv ( t ), and C w_res ( t )) are identified in Section 4.1. These components have unique periods (time scales) (Vercruysse et al., 2017), which inspire the possibility of using spectral analyses (e.g., Lee et al., 2003; Schoellhamer, 1996; Venditti & Bennett, 2000) and band‐pass filtering to quantitatively distinguish the components and estimate the contributions via the ratio of variance.…”

Implications of intermittent turbulent bursts for sediment resuspension in a coastal bottom boundary layer: A field study in the western Yellow Sea, China

“…Previous studies have shown that suspended sediments can be regarded as a passive scalar in the well-developed turbulent boundary flows (Lee et al, 2003). The variance spectrum of the sediment concentration also show a wide inertial subrange with a '−5/3' slope.…”

“…The advantage of ADV in measuring flow velocity and suspended sediment concentration rapidly and synchronously in the same sampling volume has prompted a renewal of interest in sediment dynamics in turbulent boundary layer (Fugate and Friedrichs, 2002;Nikora and Goring, 2002;Lee et al, 2003;Voulgaris and Meyers, 2004;Scully and Friedrichs, 2003;Trevethan et al, 2007;Maa and Kwon, 2007). ADVs work by emitting fixed-frequency acoustic pulses and recording the amount of reflection from suspended particulate matter (SPM) in the sampling volume.…”

Sediment eddy diffusivity and selective suspension under waves and currents on the inner shelf

“…According to Lee et al (2002;2003), cases with R > 1 generally correspond to weak currents, but waves strong enough to suspend sediment high above the bed, such that u * ≈u *cw . In contrast, periods with R < 1 correspond to strong current conditions for which u * ≈u *c .…”

“…Rearrangement of the diffusion equation (Eq. 1) and introduction of the flow velocity scale u* and wave boundary layer length scale δ w yield a dimensionless measure of eddy diffusivity K + which can be evaluated directly from observations of suspendedsediment concentration and flow intensity in a wave-current boundary layer (Lee et al, 2003). The expression is given as…”