Scattering of internal tides by irregular bathymetry of large extent

Li, Yile; Mei, Chiang C.

doi:10.1017/jfm.2014.159

Cited by 12 publications

(14 citation statements)

References 27 publications

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“…One motivation to this study is the possibility to capture and predict processes that affect the propagation of the internal tides—such as topographic scattering—for example, for the construction of accurate parameterization of the associated mixing for general circulation models (Eden & Olbers, 2014; Lavergne et al., 2020; MacKinnon et al., 2017). Analytical expectations have been derived using different approaches and assumptions (Buhler & Holmes‐Cerfon, 2011; Y. Li & Mei, 2014), showing that the energy density of a given mode follows an exponential decay when passing over topographic irregularities with given statistical properties. The typical decay length scale λ depends on the latter: for instance Buhler and Holmes‐Cerfon (2011) obtained the following equality (their Equation 5.4)

λ^{- 1} = \frac{π {normalΓ}_{0}}{2 H^{2}} \sqrt{E | h |^{2} E | h^{'} |^{2}},

where h is the topographic deviation from the mean value H and

h^{'}

its (one‐dimensional) gradient.…”

Section: Discussionmentioning

confidence: 99%

Internal Tide Cycle and Topographic Scattering Over the North Mid‐Atlantic Ridge

2020

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Internal tides are a key component of the ocean circulation. They are responsible for a large portion of the diapycnal mixing in the deep ocean (Kunze, 2017b; Polzin et al., 1997). Thereby, they greatly impact the large scale circulation (Kunze, 2017a; Melet et al., 2012) as well as vertical fluxes of nutrients in some regions-in particular near the surface (Sharples et al., 2009; Tuerena et al., 2019). They also contribute significantly to coastal shelf dynamics, where they have large amplitude and variability associated with nonlinear effects (

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λ^{- 1} = \frac{π {normalΓ}_{0}}{2 H^{2}} \sqrt{E | h |^{2} E | h^{'} |^{2}},

where h is the topographic deviation from the mean value H and

h^{'}

its (one‐dimensional) gradient.…”

Section: Discussionmentioning

confidence: 99%

Internal Tide Cycle and Topographic Scattering Over the North Mid‐Atlantic Ridge

2020

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“…As Melet et al (2013) found this fraction to vary regionally, global calculations of internal tide generation as well as subsequent breaking and Resolving the horizontal direction of internal tide generation 403 mixing might rely on including a spectral model like that of Goff & Jordan (1988) for the small-scale roughness (e.g. Goff & Arbic 2010;Li & Mei 2014;Guo & Holmes-Cerfon 2016), noting, however, that such models involve further uncertainties themselves.…”

Section: Discussionmentioning

confidence: 99%

Resolving the horizontal direction of internal tide generation

et al. 2019

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The mixing induced by breaking internal gravity waves is an important contributor to the ocean’s energy budget, shaping, inter alia, nutrient supply, water mass transformation and the large-scale overturning circulation. Much of the energy input into the internal wave field is supplied by the conversion of barotropic tides at rough bottom topography, which hence needs to be described realistically in internal gravity wave models and mixing parametrisations based thereon. A new semi-analytical method to describe this internal wave forcing, calculating not only the total conversion but also the direction of this energy flux, is presented. It is based on linear theory for variable stratification and finite depth, that is, it computes the energy flux into the different vertical modes for two-dimensional, subcritical, small-amplitude topography and small tidal excursion. A practical advantage over earlier semi-analytical approaches is that the new one gives a positive definite conversion field. Sensitivity studies using both idealised and realistic topography allow the identification of suitable numerical parameter settings and corroborate the accuracy of the method. This motivates the application to the global ocean in order to better account for the geographical distribution of diapycnal mixing induced by low-mode internal gravity waves, which can propagate over large distances before breaking. The first results highlight the significant differences of energy flux magnitudes with direction, confirming the relevance of this more detailed approach for energetically consistent mixing parametrisations in ocean models. The method used here should be applicable to any physical system that is described by the standard wave equation with a very wide field of sources.

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“…The scarcity of statistical theories may be due to the fact that information such as the wavenumber spectra of sea bathymetry is readily available only for some ocean basins ( [3], [15]). Such information has been only recently used in the studies of long-lasting tides and internal waves ( [4], [28]), but not yet applied to tsunamis.…”

Section: Introductionmentioning

confidence: 99%

Modified Kadomtsev–Petviashvili equation for tsunami over irregular seabed

Mei

2016

Nat Hazards

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We derive an asymptotic equation governing the trans-ocean propagation of tsunami from source to the continental shelf. Focus is on disturbances originated from a slender fault of finite length. The variable sea depth is assumed to consist of a slowly varying mean and random fluctuations. The method of multiple scales is used to derive a Kadomtsev-Petviashivili equation with variable coefficients. Modifications by one and two dimensional random irregularities are shown to affect the wave speed, dissipation and additional dispersion. The result can be used to facilitate physical insight with modest numerical efforts.

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Scattering of internal tides by irregular bathymetry of large extent

Cited by 12 publications

References 27 publications

Internal Tide Cycle and Topographic Scattering Over the North Mid‐Atlantic Ridge

Internal Tide Cycle and Topographic Scattering Over the North Mid‐Atlantic Ridge

Resolving the horizontal direction of internal tide generation

Modified Kadomtsev–Petviashvili equation for tsunami over irregular seabed

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