--- _id: '9149' abstract: - lang: eng text: "The interaction of tidal currents with sea-floor topography results in the radiation of internal gravity waves into the ocean interior. These waves are called internal tides and their dissipation due to nonlinear wave breaking and concomitant three-dimensional turbulence could play an important role in the mixing of the abyssal ocean, and hence in controlling the large-scale ocean circulation.\r\nAs part of on-going work aimed at providing a theory for the vertical distribution of wave breaking over sea-floor topography, in this paper we investigate the instability of internal tides in a very simple linear model that helps us to relate the formation of unstable regions to simple features in the sea-floor topography. For two-dimensional tides over one-dimensional topography we find that the formation of overturning instabilities is closely linked to the singularities in the topography shape and that it is possible to have stable waves at the sea floor and unstable waves in the ocean interior above.\r\nFor three-dimensional tides over two-dimensional topography there is in addition an effect of geometric focusing of wave energy into localized regions of high wave amplitude, and we investigate this focusing effect in simple examples. Overall, we find that the distribution of unstable wave breaking regions can be highly non-uniform even for very simple idealized topography shapes." article_processing_charge: No article_type: original author: - first_name: Oliver full_name: Bühler, Oliver last_name: Bühler - first_name: Caroline J full_name: Muller, Caroline J id: f978ccb0-3f7f-11eb-b193-b0e2bd13182b last_name: Muller orcid: 0000-0001-5836-5350 citation: ama: Bühler O, Muller CJ. Instability and focusing of internal tides in the deep ocean. Journal of Fluid Mechanics. 2007;588:1-28. doi:10.1017/s0022112007007410 apa: Bühler, O., & Muller, C. J. (2007). Instability and focusing of internal tides in the deep ocean. Journal of Fluid Mechanics. Cambridge University Press. https://doi.org/10.1017/s0022112007007410 chicago: Bühler, Oliver, and Caroline J Muller. “Instability and Focusing of Internal Tides in the Deep Ocean.” Journal of Fluid Mechanics. Cambridge University Press, 2007. https://doi.org/10.1017/s0022112007007410. ieee: O. Bühler and C. J. Muller, “Instability and focusing of internal tides in the deep ocean,” Journal of Fluid Mechanics, vol. 588. Cambridge University Press, pp. 1–28, 2007. ista: Bühler O, Muller CJ. 2007. Instability and focusing of internal tides in the deep ocean. Journal of Fluid Mechanics. 588, 1–28. mla: Bühler, Oliver, and Caroline J. Muller. “Instability and Focusing of Internal Tides in the Deep Ocean.” Journal of Fluid Mechanics, vol. 588, Cambridge University Press, 2007, pp. 1–28, doi:10.1017/s0022112007007410. short: O. Bühler, C.J. Muller, Journal of Fluid Mechanics 588 (2007) 1–28. date_created: 2021-02-15T14:41:45Z date_published: 2007-10-10T00:00:00Z date_updated: 2022-01-24T13:43:36Z day: '10' doi: 10.1017/s0022112007007410 extern: '1' intvolume: ' 588' keyword: - mechanical engineering - mechanics of materials - condensed matter physics language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1017/S0022112007007410 month: '10' oa: 1 oa_version: None page: 1-28 publication: Journal of Fluid Mechanics publication_identifier: issn: - 0022-1120 - 1469-7645 publication_status: published publisher: Cambridge University Press quality_controlled: '1' status: public title: Instability and focusing of internal tides in the deep ocean type: journal_article user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 588 year: '2007' ...