Papers › Disentangling discrete and continuous spectra of tidally forced internal waves in shear flow
Disentangling discrete and continuous spectra of tidally forced internal waves in shear flow
Yohei Onuki, Antoine Venaille
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Generation of internal waves driven by barotropic tides over seafloor topography is a central issue in developing mixing and wave drag parameterizations for ocean circulation models. Traditional analytical approaches estimate the energy conversion rate from barotropic tides to internal waves using a modal expansion of the wave field. However, this framework becomes inadequate if a background shear flow is present, as singular solutions associated with critical levels emerge. To uncover the distinct roles of regular eigenmodes and singular solutions in tidal energy conversion, this study analytically investigates wave generation over a localized small topography in the presence of shear flow without Coriolis force. Applying horizontal Fourier and temporal Laplace transforms, we identify regions in the topographic wavenumber and forcing frequency space where unbounded energy growth occurs. These regions coincide with the spectrum of an operator governing free wave propagation and consist of discrete and continuous parts, which correspond to regular eigenmodes and singular solutions, respectively. Asymptotic evaluation of the Fourier integral reveals that the far-field response comprises standing wave trains linked to the discrete spectrum and evolving wave packets associated with the continuous spectrum. While the velocity amplitudes of the wave packets decay, their vertical velocity gradients grow during propagation, potentially leading to wave breaking. Finally, we derive a formula for the net barotropic-to-baroclinic energy conversion rate, extending the classical one by incorporating the contributions from both the discrete and continuous spectra.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections