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

TL;DR

This paper introduces a novel drift mechanism called CBIID caused by current-bathymetry interactions, significantly affecting cross-shelf transport in nearshore environments, with implications comparable to Stokes drift.

Contribution

The study identifies and characterizes the CBIID mechanism, providing analytical expressions and demonstrating its importance in coastal tracer transport.

Findings

CBIID increases with particle depth, bottom amplitude, and current strength.

Maximum CBIID occurs at long bottom wavelengths at a $rac{ ext{pi}}{4}$ angle.

CBIID can rival Stokes drift in influencing net Lagrangian drift.

Abstract

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. 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. CBIID increases with an increase in the particle's initial depth, bottom undulation's 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 approximately makes $\pi/4$ angle with the shoreline. Unlike Stokes drift, particle excursions due to current-bathymetry interactions might not be small, 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.