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<p>An analytical model is developed to quantify Eulerian residual currents generated by tidal flow rectification over sloping bathymetry under quadratic bottom friction. Starting from the barotropic shallow-water equations, a perturbative framework is derived under weak nonlinearity and small-slope assumptions, allowing a systematic separation between fast tidal oscillations and slow residual motions. Closed-form expressions for the one-dimensional residual current are obtained, revealing its dependence on tidal flux amplitude, Coriolis parameter, bottom friction, and bathymetric gradients. The residual circulation emerges as a second-order response resulting from the interaction between oscillatory tidal currents and topography, with bottom friction controlling the associated phase lag. The analytical solutions are validated using numerical experiments with the MICOM ocean model in an idealized basin containing a finite topographic feature. The model–data comparison shows good agreement over a wide range of tidal, frictional, and latitudinal parameters. The influence of rotation is quantified through a dimensionless coefficient governing the strength of the residual flow. Extension to biharmonic tidal forcing demonstrates that residual currents can be approximated by a superposition of constituent contributions, while also exhibiting beat-like modulations for closely spaced tidal frequencies.</p>

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Analytical study of barotropic tidal residual current in one dimension, accounting for frictional effects

  • 期刊论文

  • 发表日期：

    2026年1月15日

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  • Logueminda Sabaga,
  • Hoavo Hova,
  • Yago Ya Hilaire Amemou,
  • Essowè Panassa

摘要

An analytical model is developed to quantify Eulerian residual currents generated by tidal flow rectification over sloping bathymetry under quadratic bottom friction. Starting from the barotropic shallow-water equations, a perturbative framework is derived under weak nonlinearity and small-slope assumptions, allowing a systematic separation between fast tidal oscillations and slow residual motions. Closed-form expressions for the one-dimensional residual current are obtained, revealing its dependence on tidal flux amplitude, Coriolis parameter, bottom friction, and bathymetric gradients. The residual circulation emerges as a second-order response resulting from the interaction between oscillatory tidal currents and topography, with bottom friction controlling the associated phase lag. The analytical solutions are validated using numerical experiments with the MICOM ocean model in an idealized basin containing a finite topographic feature. The model–data comparison shows good agreement over a wide range of tidal, frictional, and latitudinal parameters. The influence of rotation is quantified through a dimensionless coefficient governing the strength of the residual flow. Extension to biharmonic tidal forcing demonstrates that residual currents can be approximated by a superposition of constituent contributions, while also exhibiting beat-like modulations for closely spaced tidal frequencies.