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Microstructure measurements in Drake Passage and on the flanks of Kerguelen Plateau find turbulent dissipation rates ε on average factors of 2–3 smaller than linear lee-wave generation predictions, as well as a factor of 3 smaller than the predictions of a well-established parameterization based on finescale shear and strain. Here, the possibility that these discrepancies are a result of conservation of wave action E/ ωL= E/| kU| is explored. Conservation of wave action will transfer a fraction of the lee-wave radiation back to the mean flow if the waves encounter weakening currents U, where the intrinsic or Lagrangian frequency ωL= | kU| ↓ | f| and k the along-stream horizontal wavenumber, where kU ≡ k ⋅ V. The dissipative fraction of power that is lost to turbulence depends on the Doppler shift of the intrinsic frequency between generation and breaking, hence on the topographic height spectrum and bandwidth N/ f. The partition between dissipation and loss to the mean flow is quantified for typical topographic height spectral shapes and N/ f ratios found in the abyssal ocean under the assumption that blocking is local in wavenumber. Although some fraction of lee-wave generation is always dissipated in a rotating fluid, lee waves are not as large a sink for balanced energy or as large a source for turbulence as previously suggested. The dissipative fraction is 0.44–0.56 for topographic spectral slopes and buoyancy frequencies typical of the deep Southern Ocean, insensitive to flow speed U and topographic splitting. Lee waves are also an important mechanism for redistributing balanced energy within their generating bottom current.
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This content will become publicly available on May 1, 2026
Oceanic Lee Waves in a Linearly Sheared Flow
Abstract We find a Green’s function solution for the propagation of two-dimensional oceanic lee waves in a linearly sheared background flow and use it to study the remote dissipation of waves. This Green’s function approach combines normal modes in the vertical direction with solving a coupled system of ODEs in the horizontal direction in an up-winding fashion. This leads to a solution for isolated topography that is valid on an infinite horizontal domain, in sharp contrast with the standard lee wave solution method based on horizontal Fourier series, which suffers from spurious resonances in a vertically bounded domain that must be controlled by artificial damping. Moreover, in the case of a negatively sheared background flow with an inertial critical layer present, the singularity normally associated with these layers is significantly modified when following the Green’s function approach. In this setting, we confirm ray-tracing estimates for lee wave absorption and highlight the ability for waves to propagate far from their generation site, even with critical layers present, which could help explain observed discrepancies between lee wave generation and dissipation. Elsewhere in the oceanographic literature, viscosity is used to deal with critical layers, and also more broadly to avoid resonant solutions in their absence, which can significantly affect the conclusions drawn if not handled correctly. This emphasizes the need for nonperiodic solvers in studies of oceanic lee waves and for care when incorporating any damping mechanism.
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- Award ID(s):
- 2108225
- PAR ID:
- 10633274
- Publisher / Repository:
- American Meteorological Society
- Date Published:
- Journal Name:
- Journal of Physical Oceanography
- Volume:
- 55
- Issue:
- 5
- ISSN:
- 0022-3670
- Page Range / eLocation ID:
- 543 to 558
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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