Modified Stokes drift due to resonant interactions between surface waves and corrugated sea floor with and without a mean current

Gupta, Akanksha; Guha, Anirban

doi:10.1103/physrevfluids.6.024801

Cited by 4 publications

(3 citation statements)

References 23 publications

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“…. denotes averaging over one wave period (in the moving frame), T = 2π/ ω. Equations analogous to (3.5a)-(3.5c) can be found in Ursell (1953) and Gupta & Guha (2021). The small-excursion approximation, which serves the basis for (3.5a)-(3.5c), yields a highly accurate solution -for deep and shallow water waves, the errors are respectively O( 6) (Longuet-Higgins 1987; Van den Bremer & Breivik 2017) and O( 4) (Clamond 2007).…”

Section: Stokes Drift: Small-excursion Approximation In the Presence ...mentioning

confidence: 99%

“…The solution – is generally known as the homogeneous (unsteady) solution of progressive surface gravity waves in the presence of a constant background current in a constant water depth. Related (but not the same) set-ups have been thoroughly studied in Peregrine (1976), Dommermuth & Yue (1987), Kirby (1988), Raj & Guha (2019) and Gupta & Guha (2021).…”

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

confidence: 99%

“…A closed elliptical trajectory is obtained at , but inclusion of terms reveals an open trajectory, shown in figure 3( b ), and yields the Stokes drift velocity: where denotes averaging over one wave period (in the moving frame), . Equations analogous to – can be found in Ursell (1953) and Gupta & Guha (2021). The small-excursion approximation, which serves the basis for –, yields a highly accurate solution – for deep and shallow water waves, the errors are respectively (Longuet-Higgins 1987; Van den Bremer & Breivik 2017) and (Clamond 2007).…”

Section: Case-i: Wave Steepness Dominates Over Wavy Seabed 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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Section: Stokes Drift: Small-excursion Approximation In the Presence ...mentioning

confidence: 99%

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

confidence: 99%

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

confidence: 99%

See 1 more Smart Citation

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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Bilinear auto-Bäcklund transformations and soliton solutions of a (3+1)-dimensional generalized nonlinear evolution equation for the shallow water waves

Shen

Tian

2021

Applied Mathematics Letters

160

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Role of detuned frequency on Bragg scattering of surface gravity waves over an array of sinusoidal bottom patches: An analytic study

Kar,

Sahoo,

Ning

2024

Applied Ocean Research

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Modified Stokes drift due to resonant interactions between surface waves and corrugated sea floor with and without a mean current

Cited by 4 publications

References 23 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

Bilinear auto-Bäcklund transformations and soliton solutions of a (3+1)-dimensional generalized nonlinear evolution equation for the shallow water waves

Role of detuned frequency on Bragg scattering of surface gravity waves over an array of sinusoidal bottom patches: An analytic study

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