Internal wave attractors over random, small-amplitude topography

2015 ◽  
Vol 787 ◽  
pp. 148-174 ◽  
Author(s):  
Yuan Guo ◽  
Miranda Holmes-Cerfon
Keyword(s):  
Internal Wave ◽  
Small Amplitude ◽  
Wave Beam ◽  
Internal Tide ◽  
Boussinesq Equations ◽  
Numerical Code ◽  
Zero Crossings ◽  
Covariance Functions ◽  
Closed Orbits ◽  
Arbitrary Topography

We consider whether small-amplitude topography in a two-dimensional ocean may contain internal wave attractors. These are closed orbits formed by the characteristics (or wave beam paths) of the linear, inviscid, steady-state Boussinesq equations, and their existence may imply enhanced scattering and energy decay for the internal tide when dissipation is present. We develop a numerical code to detect attractors over arbitrary topography, and apply this to random, Gaussian topography with different covariance functions. The rate of attractors per length of topography increases with the fraction of supercritical topography, but surprisingly, it also increases as the amplitude of the topography is decreased, while the supercritical fraction is held constant. This can partly be understood by appealing to Rice’s formula for the rate of zero crossings of a stochastic process. We compute the rate of attractors for a covariance function typical of ocean bathymetry away from large features and find it is about 10 attractors per 1000 km. This could have implications for the overall energy budget of the ocean.

scholarly journals Climate Process Team on Internal Wave–Driven Ocean Mixing

2017 ◽  
Vol 98 (11) ◽  
pp. 2429-2454 ◽  
Author(s):  
Jennifer A. MacKinnon ◽  
Zhongxiang Zhao ◽  
Caitlin B. Whalen ◽  
Amy F. Waterhouse ◽  
David S. Trossman ◽  
...  
Keyword(s):  
Internal Wave ◽  
Turbulent Mixing ◽  
Low Frequency ◽  
Internal Tide ◽  
Deep Ocean ◽  
Global Ocean ◽  
Primary Role ◽  
Inverse Models ◽  
Lee Waves ◽  
Mixing Rates

Abstract Diapycnal mixing plays a primary role in the thermodynamic balance of the ocean and, consequently, in oceanic heat and carbon uptake and storage. Though observed mixing rates are on average consistent with values required by inverse models, recent attention has focused on the dramatic spatial variability, spanning several orders of magnitude, of mixing rates in both the upper and deep ocean. Away from ocean boundaries, the spatiotemporal patterns of mixing are largely driven by the geography of generation, propagation, and dissipation of internal waves, which supply much of the power for turbulent mixing. Over the last 5 years and under the auspices of U.S. Climate Variability and Predictability Program (CLIVAR), a National Science Foundation (NSF)- and National Oceanic and Atmospheric Administration (NOAA)-supported Climate Process Team has been engaged in developing, implementing, and testing dynamics-based parameterizations for internal wave–driven turbulent mixing in global ocean models. The work has primarily focused on turbulence 1) near sites of internal tide generation, 2) in the upper ocean related to wind-generated near inertial motions, 3) due to internal lee waves generated by low-frequency mesoscale flows over topography, and 4) at ocean margins. Here, we review recent progress, describe the tools developed, and discuss future directions.

A viscous internal wave in a stratified fluid whose buoyancy frequency varies with altitude

1975 ◽  
Vol 69 (3) ◽  
pp. 615-624 ◽  
Author(s):  
D. Gordon ◽  
U. R. Klement ◽  
T. N. Stevenson
Keyword(s):  
Internal Wave ◽  
Small Amplitude ◽  
Wave Amplitude ◽  
Stratified Fluid ◽  
Similarity Solutions ◽  
Buoyancy Frequency ◽  
Experimental Measurements ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Curved Paths

A viscous incompressible stably stratified fluid with a buoyancy frequency which varies slowly with altitude is considered. A simple harmonic localized disturbance generates an internal wave in which the energy propagates along curved paths. Small amplitude similarity solutions are obtained for two-dimensional and axisymmetric waves. It is found that under certain conditions the wave amplitude can increase with height. The two-dimensional theory compares quite well with experimental measurements.

Internal-Wave-Driven Mixing: Global Geography and Budgets

2017 ◽  
Vol 47 (6) ◽  
pp. 1325-1345 ◽  
Author(s):  
Eric Kunze
Keyword(s):  
Internal Wave ◽  
Internal Tide ◽  
Internal Tides ◽  
Tidal Mixing ◽  
Linear Wave ◽  
Power Sources ◽  
The North ◽  
Dissipation Rates ◽  
Thickness Variability ◽  
Significant Pathway

AbstractInternal-wave-driven dissipation rates ε and diapycnal diffusivities K are inferred globally using a finescale parameterization based on vertical strain applied to ~30 000 hydrographic casts. Global dissipations are 2.0 ± 0.6 TW, consistent with internal wave power sources of 2.1 ± 0.7 TW from tides and wind. Vertically integrated dissipation rates vary by three to four orders of magnitude with elevated values over abrupt topography in the western Indian and Pacific as well as midocean slow spreading ridges, consistent with internal tide sources. But dependence on bottom forcing is much weaker than linear wave generation theory, pointing to horizontal dispersion by internal waves and relatively little local dissipation when forcing is strong. Stratified turbulent bottom boundary layer thickness variability is not consistent with OGCM parameterizations of tidal mixing. Average diffusivities K = (0.3–0.4) × 10−4 m2 s−1 depend only weakly on depth, indicating that ε = KN2/γ scales as N2 such that the bulk of the dissipation is in the pycnocline and less than 0.08-TW dissipation below 2000-m depth. Average diffusivities K approach 10−4 m2 s−1 in the bottom 500 meters above bottom (mab) in height above bottom coordinates with a 2000-m e-folding scale. Average dissipation rates ε are 10−9 W kg−1 within 500 mab then diminish to background deep values of 0.15 × 10−9 W kg−1 by 1000 mab. No incontrovertible support is found for high dissipation rates in Antarctic Circumpolar Currents or parametric subharmonic instability being a significant pathway to elevated dissipation rates for semidiurnal or diurnal internal tides equatorward of 28° and 14° latitudes, respectively, although elevated K is found about 30° latitude in the North and South Pacific.

Evidence of internal-wave and internal-tide deposits in the Middle Ordovician Xujiajuan Formation of the Xiangshan Group, Ningxia, China

2011 ◽  
Vol 31 (5-6) ◽  
pp. 509-523 ◽  
Author(s):  
You-Bin He ◽  
Jin-Xiong Luo ◽  
Xiang-Dong Li ◽  
Zhen-Zhong Gao ◽  
Zhan Wen
Keyword(s):  
Internal Wave ◽  
Internal Tide ◽  
Middle Ordovician

scholarly journals Internal wave beam propagation in non-uniform stratifications

2009 ◽  
Vol 639 ◽  
pp. 133-152 ◽  
Author(s):  
MANIKANDAN MATHUR ◽  
THOMAS PEACOCK
Keyword(s):  
Internal Wave ◽  
Laboratory Experiments ◽  
Close Agreement ◽  
Wave Beam ◽  
Reflection Coefficients ◽  
Uniform Density ◽  
Finite Width ◽  
Transmission And Reflection Coefficients ◽  
Physical Quantities ◽  
Transmission And Reflection

In addition to being observable in laboratory experiments, internal wave beams are reported in geophysical settings, which are characterized by non-uniform density stratifications. Here, we perform a combined theoretical and experimental study of the propagation of internal wave beams in non-uniform density stratifications. Transmission and reflection coefficients, which can differ greatly for different physical quantities, are determined for sharp density-gradient interfaces and finite-width transition regions, accounting for viscous dissipation. Thereafter, we consider even more complex stratifications to model geophysical scenarios. We show that wave beam ducting can occur under conditions that do not necessitate evanescent layers, obtaining close agreement between theory and quantitative laboratory experiments. The results are also used to explain recent field observations of a vanishing wave beam at the Keana Ridge, Hawaii.

scholarly journals Internal Tide Convergence and Mixing in a Submarine Canyon

2017 ◽  
Vol 47 (2) ◽  
pp. 303-322 ◽  
Author(s):  
Amy F. Waterhouse ◽  
Jennifer A. Mackinnon ◽  
Ruth C. Musgrave ◽  
Samuel M. Kelly ◽  
Andy Pickering ◽  
...  
Keyword(s):  
Continental Shelf ◽  
Internal Wave ◽  
Wave Energy ◽  
Internal Tide ◽  
Submarine Canyon ◽  
Internal Tides ◽  
North Coast ◽  
Semidiurnal Tide ◽  
The North ◽  
Tidally Driven

AbstractObservations from Eel Canyon, located on the north coast of California, show that elevated turbulence in the full water column arises from the convergence of remotely generated internal wave energy. The incoming semidiurnal and bottom-trapped diurnal internal tides generate complex interference patterns. The semidiurnal internal tide sets up a partly standing wave within the canyon due to reflection at the canyon head, dissipating all of its energy within the canyon. Dissipation in the near bottom is associated with the diurnal trapped tide, while midwater isopycnal shear and strain is associated with the semidiurnal tide. Dissipation is elevated up to 600 m off the bottom, in contrast to observations over the flat continental shelf where dissipation occurs closer to the topography. Slope canyons are sinks for internal wave energy and may have important influences on the global distribution of tidally driven mixing.

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