Upstream-propagating waves induced by steady current over a rippled bottom: theory and experimental observation

Fan, Jun; Zheng, Jinhai; Tao, Aifeng; Liu, Yuming

doi:10.1017/jfm.2020.1006

Cited by 14 publications

(5 citation statements)

References 20 publications

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“…Both φ and η are a combination of an unsteady solution, denoted by subscript 'u', and a steady solution, denoted by subscript 's' (Kirby 1988;Fan et al 2021). The quantities φ…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…The expressions (4.2a)-(4.2b) denote the particular (steady) solution, and have been previously investigated by many authors in various contexts (Lamb 1932;Kennedy 1963;Kirby 1988;Sammarco, Mei & Trulsen 1994;Fan et al 2021). Equations (4.2a)-(4.2b) result from the presence of the non-homogeneous term V 0 η b,y in the right-hand side of (4.1b).…”

Section: Lagrangian Drift and Eulerian Return Flowmentioning

confidence: 99%

“…The velocity potential and surface elevation can then be expressed in terms of and as Both and are a combination of an unsteady solution, denoted by subscript ‘’, and a steady solution, denoted by subscript ‘’ (Kirby 1988; Fan et al. 2021). The quantities and are , while and are .…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…At , we obtain the following steady, non-homogeneous system of equations: The steady surface elevation and velocity potential, which results from the interaction between the wavy bottom boundary and the uniform alongshore current, and obtained by solving – along with , are respectively given by and Here, and The expressions – denote the particular (steady) solution, and have been previously investigated by many authors in various contexts (Lamb 1932; Kennedy 1963; Kirby 1988; Sammarco, Mei & Trulsen 1994; Fan et al. 2021). Equations – result from the presence of the non-homogeneous term in the right-hand side of .…”

Section: Case-ii: Wavy Seabed Steepness Dominates Over Wave Steepness ()mentioning

confidence: 99%

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A new Lagrangian drift mechanism due to current–bathymetry interactions: applications in coastal cross-shelf transport

Gupta

Guha²

2022

J. Fluid Mech.

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We show that in free surface flows, a uniform, streamwise current over small-amplitude wavy bottom topography generates cross-stream drift velocity. This drift mechanism, referred to as the current–bathymetry interaction-induced drift (CBIID), is specifically understood in the context of a simplified nearshore environment consisting of a uniform alongshore current, onshore-propagating surface waves and monochromatic wavy bottom making an oblique angle with the shoreline. The CBIID is found to originate from the steady, non-homogeneous solution of the governing system of equations. Similar to Stokes drift induced by surface waves, CBIID also generates a compensating Eulerian return flow to satisfy the no-flux lateral boundaries, e.g. the shoreline. The CBIID increases with an increase in particle's initial depth, bottom undulation amplitude and the strength of the alongshore current. Additionally, CBIID near the free (bottom) surface increases (decreases) with an increase in bottom undulation's wavelength. Maximum CBIID is obtained for long-wavelength bottom topography that makes an angle of approximately ${\rm \pi} /4$ with the shoreline. Unlike Stokes drift, particle excursions due to current–bathymetry interactions might not be small, and hence analytical expressions based on the small-excursion approximation could be inaccurate. We provide an alternative $z$ -bounded approximation, which leads to highly accurate expressions for drift velocity and time period of particles especially located near the free surface. Realistic parametric analysis reveals that in some nearshore environments, CBIID's contribution to the net Lagrangian drift can be as important as Stokes drift, implying that CBIID can have major implications in cross-shelf tracer transport.

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“…Both φ and η are a combination of an unsteady solution, denoted by subscript 'u', and a steady solution, denoted by subscript 's' (Kirby 1988;Fan et al 2021). The quantities φ…”

Section: Mathematical Formulationmentioning

confidence: 99%

Section: Lagrangian Drift and Eulerian Return Flowmentioning

confidence: 99%

Section: Mathematical Formulationmentioning

confidence: 99%

Section: Case-ii: Wavy Seabed Steepness Dominates Over Wave Steepness ()mentioning

confidence: 99%

See 2 more Smart Citations

A new Lagrangian drift mechanism due to current–bathymetry interactions: applications in coastal cross-shelf transport

Gupta

Guha²

2022

J. Fluid Mech.

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show abstract

“…The shoreface nourishment can be regarded as a local perturbation that involves complicated feedbacks between the evolving morphology and driving forces. Both wave nonlinearity and setup will evolve differently on beaches without shoreface nourishments [26][27][28]. So far, the studies regarding detailed sediment transport of shoreface nourishment are scarce, to the best of the authors' knowledge.…”

Section: Of 22mentioning

confidence: 99%

Wave Dissipation and Sediment Transport Patterns during Shoreface Nourishment towards Equilibrium

Zhang

Cai

et al. 2021

JMSE

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Implementing shoreface nourishment is an effective method to protect sandy beaches. A better understanding of the equilibrium mechanism of shoreface nourishments is necessary for coastal engineering designs and constructions. Two experiments on the beach profile equilibrium of the shoreface nourishment are carried out under mild wave conditions on the reflective and intermediate beach. It is observed that the shoreface nourishment increases local wave height and strengthens wave nonlinearity by its shallow water depth. The most intense wave breaking dissipation has been found on the crest of the shoreface nourishment, and the distribution of wave energy dissipation rate is more uniform on the quasi-equilibrium profile than that on the initial profile. A process-based numerical model is used to reproduce bed profile evolution successfully. On that basis, it is found that onshore bedload transport is the primary cause for the onshore migration of the shoreface nourishment. The magnitude of bedload transport decreases during the evolution of the shoreface nourishment towards equilibrium. The most intense sediment transport rate occurs over the shoreface nourishment or in front of the shoreline, depending on the ’lee effect’ of the nourishment. Furthermore, the effects of incident wave height, wave period, and sea-level rise on the equilibrium profile of the shoreface nourishment under mild wave conditions are analyzed.

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On the Downshift of Wave Frequency for Bragg Resonance

Tao

Fan

et al. 2022

China Ocean Eng

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Upstream-propagating waves induced by steady current over a rippled bottom: theory and experimental observation

Abstract: Abstract

Cited by 14 publications

References 20 publications

A new Lagrangian drift mechanism due to current–bathymetry interactions: applications in coastal cross-shelf transport

A new Lagrangian drift mechanism due to current–bathymetry interactions: applications in coastal cross-shelf transport

Wave Dissipation and Sediment Transport Patterns during Shoreface Nourishment towards Equilibrium

On the Downshift of Wave Frequency for Bragg Resonance

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