Lee waves in stratified flows with simple harmonic time dependence

Bell, Thomas H.

doi:10.1017/s0022112075000560

Cited by 260 publications

(340 citation statements)

References 10 publications

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“…The effect of superposition of the basic flow forces the propagation of internal waves in the tidal direction much more than in other directions. This shows that the effect of the basic flow is not only the reason for the occurrence of higher harmonics as proposed first by Bell (1975a) but also enhances the wave strength in the direction of basic flow.…”

Section: (A) P >supporting

confidence: 67%

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Spatial structure of internal tidal waves generated on weak topographies

Ping¹,

Singh²

2010

Dynamics of Atmospheres and Oceans

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a b s t r a c tThe generation of internal gravity waves by barotropic tidal flow passing over a two-dimensional topography is investigated. Rather than calculating the conversion of tidal energy, this study focuses on delineating the geometric characteristics of the spatial structure of the resulting internal wave fields (i.e., the configurations of the internal beams and their horizontal projections) which have usually been ignored. It is found that the various possible wave types can be demarcated by three characteristic frequencies: the tidal frequency, ω 0 ; the buoyancy frequency, N; and the vertical component of the Coriolis vector or earth's rotation, f. When different possibilities arising from the sequence of these frequencies are considered, there occur 12 kinds of wave structures in the full 3D space in contrast to the 5 kinds identified by the 2D theory. The constant wave phase lines may form as ellipses or hyperbolic lines on the horizontal plane, provided the buoyancy frequency is greater or less than the tidal frequency. The effect that stems from the consideration of the basic flow is also found, which not only serves as the reason for the occurrence of higher harmonics but also increases the wave strength in the direction of basic flow.

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Section: (A) P >supporting

confidence: 67%

“…Following Bell (1975a) and Khatiwala (2003), the BC (16) motivates us to seek a series solution of the form:…”

Section: Dispersion Relationmentioning

confidence: 99%

Spatial structure of internal tidal waves generated on weak topographies

Ping¹,

Singh²

2010

Dynamics of Atmospheres and Oceans

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“…Here, the cascade of tidal energy is examined for the large-scale linear tide. By neglecting nonlinearity, the physics of wave-wave interactions (Mü ller et al 1986;MacKinnon and Winters 2005;Alford et al 2007); large-amplitude internal waves (Buijsman et al 2010); and tide-topography interactions with long tidal excursions (Bell 1975), high Froude number (Legg and Klymak 2008), and turbulent boundary layers along critical slopes (Gayen and Sarkar 2010) are omitted. However, linearizing the equations of motion isolates the physics of small tidal-excursion tide-topography interactions (Garrett and Kunze 2007), which can be used to describe observed topographic scattering from rough and steep topography (Johnston et al 2003;Nash et al 2004Nash et al , 2007.…”

Section: Introductionmentioning

confidence: 99%

The Cascade of Tidal Energy from Low to High Modes on a Continental Slope

Kelly

Nash

Martini

et al. 2012

Journal of Physical Oceanography

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The linear transfer of tidal energy from large to small scales is quantified for small tidal excursion over a near-critical continental slope. A theoretical framework for low-wavenumber energy transfer is derived from ''flat bottom'' vertical modes and evaluated with observations from the Oregon continental slope. To better understand the observations, local tidal dynamics are modeled with a superposition of two idealized numerical simulations, one forced by local surface-tide velocities and the other by an obliquely incident internal tide generated at the Mendocino Escarpment 315 km southwest of the study site. The simulations reproduce many aspects of the observed internal tide and verify the modal-energy balances. Observed transfer of tidal energy into high-mode internal tides is quantitatively consistent with observed turbulent kinetic energy (TKE) dissipation. Locally generated and incident simulated internal tides are superposed with varying phase shifts to mimic the effects of the temporally varying mesoscale. Altering the phase of the incident internal tide alters (i) internal-tide energy flux, (ii) internal-tide generation, and (iii) energy conversion to high modes, suggesting that tidally driven TKE dissipation may vary between 0 and 500 watts per meter of coastline on 3-5-day time scales. Comparison of observed in situ internal-tide generation and satellite-derived estimates of surface-tide energy loss is inconclusive.

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“…The simplest, a plane wave, is the basis of many theoretical studies that provide fundamental insight (see Thorpe 1987Thorpe , 1998Dauxois & Young 1999, for instance), especially as any linear wave structure can be decomposed into independent plane waves via Fourier transforms. While plane wave solutions are the focus of many theoretical studies, laboratory experiments and field observations reveal that internal waves generated by a localized source, such as the tidal flow past an ocean ridge (Bell 1975;Martin, Rudnick & Pinkel 2006) or deep tropical convection in the atmosphere (Walterscheid, Schubert & Brinkman 2001), produce coherent wave beams that radiate away from the generation site. In vertically-finite domains, such as the ocean, the internal wave field can be conveniently described using vertical modes, i.e.…”

Section: Introductionmentioning

confidence: 99%

New wave generation

et al. 2010

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We present the results of a combined experimental and numerical study of the generation of internal waves using the novel internal wave generator design of . This mechanism, which involves a tunable source comprised of oscillating plates, has so far been used for a few fundamental studies of internal waves, but its full potential has yet to be realized. Our studies reveal that this approach is capable of producing a wide variety of two-dimensional wave fields, including plane waves, wave beams and discrete vertical modes in finite-depth stratifications. The effects of discretization by a finite number of plates, forcing amplitude and angle of propagation are investigated, and it is found that the method is remarkably efficient at generating a complete wave field despite forcing only one velocity component in a controllable manner. We furthermore find that the nature of the radiated wave field is well predicted using Fourier transforms of the spatial structure of the wave generator.

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Lee waves in stratified flows with simple harmonic time dependence

Cited by 260 publications

References 10 publications

Spatial structure of internal tidal waves generated on weak topographies

Spatial structure of internal tidal waves generated on weak topographies

The Cascade of Tidal Energy from Low to High Modes on a Continental Slope

New wave generation

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