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Abstract While lee-wave generation has been argued to be a major sink for the 1-TW wind work on the ocean’s circulation, microstructure measurements in the Antarctic Circumpolar Currents find dissipation rates as much as an order of magnitude weaker than linear lee-wave generation predictions in bottom-intensified currents. Wave action conservation suggests that a substantial fraction of lee-wave radiation can be reabsorbed into bottom-intensified flows. Numerical simulations are conducted here to investigate generation, reabsorption, and dissipation of internal lee waves in a bottom-intensified, laterally confined jet that resembles a localized abyssal current over bottom topography. For the case of monochromatic topography with |kU0| ≈ 0.9N, wherekis the along-stream topographic wavenumber, |U0| is the near-bottom flow speed, andNis the buoyancy frequency; Reynolds-decomposed energy conservation is consistent with linear wave action conservation predictions that only 14% of lee-wave generation is dissipated, with the bulk of lee-wave energy flux reabsorbed by the bottom-intensified flow. Thus, water column reabsorption needs to be taken into account as a possible mechanism for reducing the lee-wave dissipative sink for balanced circulation.
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Baroclinic tidal conversion: note on a paper of L.R.M. Maas
Maas ( J. Fluid Mech. , vol. 684, 2011, pp. 5–24) showed that, for an oscillating two-dimensional barotropic tide flowing over sub-critical topography of compact support, some topographic forms existed that produced non-radiating baroclinic disturbances. The problem is related to ‘stealth’ and ‘cloaking’ problems. Here Maas's result is derived using a simpler approach, not involving complicated mappings, but formally restricted to perturbation topography. Wider results come from the discussion of nearly compact support topographic disturbances provided by Schwartz functions with weak high-wavenumber radiation and by exploiting both a known functional equation formulation and Fourier methods. The problem is extended to disturbances on uniform slopes. A variety of non-radiating topographies can be found, although they are mathematically delicate and unlikely to be found in nature. Topography with weak radiation at high wavenumber is a much wider class of structures. Application of these solutions would lie with the ability to estimate dissipation over and near the topography from motions observed at a distance.
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- Award ID(s):
- 2054424
- PAR ID:
- 10412514
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 946
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2022.637
