Unsteady stress partitioning and momentum transfer in the wave bottom boundary layer over movable rippled beds

Rodriguez-Abudo, S.; Foster, D. L.

doi:10.1002/2014jc010240

Cited by 15 publications

(26 citation statements)

References 44 publications

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“…The velocity profiles for the three data sets also show a slip condition at the bed that is consistent with visual observations of a highly mobile bed. For a discussion on the effect of such mobile sediment layer on the analysis technique, please see Rodriguez‐Abudo and Foster [].…”

Section: Resultsmentioning

confidence: 88%

“…Consistent with wave dynamics in intermediate waters, RMS vertical velocities are nonzero at the free‐stream and slightly increase near the bed for both rippled bed data sets likely due to the large scale circulations cells resulting from the presence of bed forms [ Van der Werf et al ., ; Nichols and Foster , ; Rodriguez‐Abudo and Foster , ]. A nearbed increase in

〈 w_{r m s} 〉

is also seen for the flat bed data set, although this may be due to the mildly sloping bottom.…”

Section: Resultsmentioning

confidence: 99%

“…A nearbed increase in

〈 w_{r m s} 〉

is also seen for the flat bed data set, although this may be due to the mildly sloping bottom. Although assessment of the Stokes number suggests no settling bias on the observations [ Rodriguez‐Abudo and Foster , ], higher amplitude laser reflections associated with the flat bed case may have induced noise in the estimates, which show up in the RMS signals.…”

Section: Resultsmentioning

confidence: 99%

“…The time varying spatially averaged shear stress contributions are examined following the stress partitioning scheme presented in Coleman et al . [] and Rodriguez‐Abudo and Foster []:

τ_{x z} (z, \overset{t}{true}) = μ \frac{\partial 〈 \overset{u}{true} 〉}{\partial z} - ρ 〈 \overset{u}{true} 〉 〈 \overset{w}{true} 〉 - ρ 〈 {false(\tilde{u} false)}_{b} {false(\tilde{w} false)}_{b} 〉 - ρ 〈 \overset{u^{'} w^{'}}{true} 〉,

where u is the horizontal velocity ( x ‐coordinate), w is the vertical velocity ( z ‐coordinate),

\tilde{t}

represents the wave phase, over tilde (

\overset{}{true}

) denotes phase average, prime (

'

) represents departure from the phase average (

u_{i} = {\overset{u}{true}}_{i} + u_{i}^{'}

), angle brackets (

〈 〉

) denote spatial average, and the subscript b represents departure from the spatial average (

{\overset{u}{true}}_{i} = 〈 {\overset{u}{true}}_{i} 〉 + {false(\tilde{u} false)}_{b}

). Expression (4) partitions the shear stress into a viscous component (first term), a convective momentum transfer term induced by the large scale hydrodynamics presented by waves and currents (and any other physics coherent with

{\overset{u}{true}}_{i}

, second term), a bed form‐induced momentum transfer term that arises due to the presence of an uneven boundary (third term), and the Reynolds (turbulent) stress (fourth term).…”

Section: Resultsmentioning

confidence: 99%

“…Please note that the convective momentum transfer term does not partition waves from mean flows (currents) given that latter are, for the most part, negligible in this effort. The reader is referred to Rodriguez‐Abudo and Foster [] for a thorough discussion on the theoretical development and implications on the stress quantification resulting from the different decomposition schemes. The bed form‐induced stress is the spatial analogy to the Reynolds stress, as it represents the correlations of

{\overset{u}{true}}_{i}

that deviate from the spatial average.…”

Section: Resultsmentioning

confidence: 99%

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Direct estimates of friction factors for a mobile rippled bed

Rodriguez-Abudo

Foster

2017

JGR Oceans

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New friction factor estimates are computed from the total momentum transfer applied to a rippled sediment bed. The total time‐dependent momentum flux is achieved by implementing the double‐averaged horizontal momentum equation on the nearbed flow field collected with PIV. Time‐independent friction factors are obtained by regressing the total momentum flux to the common quadratic stress law given by 12ρu∞|u∞|. The resulting friction factors compare favorably with available analysis techniques including energy dissipation, vertical turbulence intensity, and maximum shear stress, but can be 2‐6 times smaller than estimates determined with the model by Madsen (1994) and the formula of Swart (1974) using the ripple roughness.

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Section: Resultsmentioning

confidence: 88%

〈 w_{r m s} 〉

is also seen for the flat bed data set, although this may be due to the mildly sloping bottom.…”

Section: Resultsmentioning

confidence: 99%

“…A nearbed increase in

〈 w_{r m s} 〉

Section: Resultsmentioning

confidence: 99%

“…The time varying spatially averaged shear stress contributions are examined following the stress partitioning scheme presented in Coleman et al . [] and Rodriguez‐Abudo and Foster []:

τ_{x z} (z, \overset{t}{true}) = μ \frac{\partial 〈 \overset{u}{true} 〉}{\partial z} - ρ 〈 \overset{u}{true} 〉 〈 \overset{w}{true} 〉 - ρ 〈 {false(\tilde{u} false)}_{b} {false(\tilde{w} false)}_{b} 〉 - ρ 〈 \overset{u^{'} w^{'}}{true} 〉,

where u is the horizontal velocity ( x ‐coordinate), w is the vertical velocity ( z ‐coordinate),

\tilde{t}

represents the wave phase, over tilde (

\overset{}{true}

) denotes phase average, prime (

'

) represents departure from the phase average (

u_{i} = {\overset{u}{true}}_{i} + u_{i}^{'}

), angle brackets (

〈 〉

) denote spatial average, and the subscript b represents departure from the spatial average (

{\overset{u}{true}}_{i} = 〈 {\overset{u}{true}}_{i} 〉 + {false(\tilde{u} false)}_{b}

{\overset{u}{true}}_{i}

, second term), a bed form‐induced momentum transfer term that arises due to the presence of an uneven boundary (third term), and the Reynolds (turbulent) stress (fourth term).…”

Section: Resultsmentioning

confidence: 99%

{\overset{u}{true}}_{i}

that deviate from the spatial average.…”

Section: Resultsmentioning

confidence: 99%

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Direct estimates of friction factors for a mobile rippled bed

Rodriguez-Abudo

Foster

2017

JGR Oceans

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Parameterization of intrawave ripple‐averaged sediment pickup above steep ripples

et al. 2016

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Near‐bed sediment pickup is critical for predictions of intrawave suspension and in turn net sediment transport in coastal models. In the present study, numerical results from a two‐dimensional Reynolds‐averaged Navier‐Stokes model are used to assess the functional relationship of intrawave ripple‐averaged sediment pickup above steep ripples. The numerical model provides intrawave time histories of ripple‐averaged near‐bed velocities and turbulence, which are qualitatively interrogated to determine pickup functional relationships. Several specific sediment pickup formulations are implemented within the numerical model: expressions relating pickup to near‐bed velocity or near‐bed turbulent kinetic energy via the bed shear stress; and expressions relating pickup to near‐bed shear production of turbulent kinetic energy. These are then tested via model‐data comparisons of near‐bed suspended sediment concentration. The results show that the traditional functions relating sediment pickup to near‐bed velocity cannot lead to reasonable intrawave suspension predictions above vortex ripples under a ripple‐averaged framework. Instead, relating sediment pickup to near‐bed turbulence quantities, such as turbulent kinetic energy or shear production of turbulent kinetic energy, significantly improves the numerical predictions for these conditions.

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Simultaneous velocity and concentration measurements over a rippled boundary subjected to oscillating fluid forcing

Vargas-Martinez,

Rodríguez-Abudo

2024

Exp Fluids

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Unsteady stress partitioning and momentum transfer in the wave bottom boundary layer over movable rippled beds

Cited by 15 publications

References 44 publications

Direct estimates of friction factors for a mobile rippled bed

Direct estimates of friction factors for a mobile rippled bed

Parameterization of intrawave ripple‐averaged sediment pickup above steep ripples

Simultaneous velocity and concentration measurements over a rippled boundary subjected to oscillating fluid forcing

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