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  • Solitary waves  (5)
  • Nonlinear internal waves  (2)
  • Black Sea  (1)
  • Delay coordinate embedding  (1)
  • 1
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    Decay and return of internal solitary waves with rotation (2007)
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    Publication Date: 2022-05-25
    Description: Author Posting. © The Author, 2007. This is the author's version of the work. It is posted here by permission of American Institute of Physics for personal use, not for redistribution. The definitive version was published in Physics of Fluids 19 (2007): 026601, doi:10.1063/1.2472509.
    Description: The effect of rotation on the propagation of internal solitary waves is examined. Wave evolution is followed using a new rotating extension of a fully-nonlinear, weakly nonhydrostatic theory for waves in a two-layer system. When a solitary wave solution of the non-rotating equations is used as the initial condition the wave initially decays by radiation of longer inertia-gravity waves. The radiated inertia-gravity wave always steepens, leading to the formation a secondary solitary-like wave. This decay and re-emergence process then repeats. Eventually a nearly localized wavepacket emerges. It consists of a longwave envelope and shorter, faster solitary-like waves that propagate through the envelope. The radiation from this mature state is very weak, leading to a robust, long-lived structure that may contain as much as 50% of the energy in the initial solitary wave. Interacting packets may either pass through one another, or merge to form a longer packet. The packets appear to be modulated, fully-nonlinear versions of the steadily translating quasi-cnoidal waves.
    Description: This work was supported by a Woods Hole Oceanographic Institution Mellon Independent Study Award and ONR Grant N000140610798.
    Keywords: Nonlinear internal waves ; Solitary waves ; Rotation
    Repository Name: Woods Hole Open Access Server
    Type: Preprint
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  • 2
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    Long nonlinear internal waves (2006)
    Annual Reviews
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    Publication Date: 2022-05-25
    Description: Author Posting. © Annual Reviews, 2006. This article is posted here by permission of Annual Reviews for personal use, not for redistribution. The definitive version was published in Annual Review of Fluid Mechanics 38 (2006): 395-425, doi:10.1146/annurev.fluid.38.050304.092129.
    Description: Over the past four decades, the combination of in situ and remote sensing observations has demonstrated that long nonlinear internal solitary-like waves are ubiquitous features of coastal oceans. The following provides an overview of the properties of steady internal solitary waves and the transient processes of wave generation and evolution, primarily from the point of view of weakly nonlinear theory, of which the Korteweg-de Vries equation is the most frequently used example. However, the oceanographically important processes of wave instability and breaking, generally inaccessible with these models, are also discussed. Furthermore, observations often show strongly nonlinear waves whose properties can only be explained with fully nonlinear models.
    Description: KRH acknowledges support from NSF and ONR and an Independent Study Award from the Woods Hole Oceanographic Institution. WKM acknowledges support from NSF and ONR, which has made his work in this area possible, in close collaboration with former graduate students at Scripps Institution of Oceanography and MIT.
    Keywords: Solitary waves ; Nonlinear waves ; Stratified flow ; Physical Oceanography
    Repository Name: Woods Hole Open Access Server
    Type: Article
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  • 3
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    Nonlinear disintegration of the internal tide (2010)
    American Meteorological Society
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    Publication Date: 2022-05-25
    Description: Author Posting. © American Meteorological Society, 2008. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 38 (2008): 686-701, doi:10.1175/2007JPO3826.1.
    Description: The disintegration of a first-mode internal tide into shorter solitary-like waves is considered. Since observations frequently show both tides and waves with amplitudes beyond the restrictions of weakly nonlinear theory, the evolution is studied using a fully nonlinear, weakly nonhydrostatic two-layer theory that includes rotation. In the hydrostatic limit, the governing equations have periodic, nonlinear inertia–gravity solutions that are explored as models of the nonlinear internal tide. These long waves are shown to be robust to weak nonhydrostatic effects. Numerical solutions show that the disintegration of an initial sinusoidal linear internal tide is closely linked to the presence of these nonlinear waves. The initial tide steepens due to nonlinearity and sheds energy into short solitary waves. The disintegration is halted as the longwave part of the solution settles onto a state close to one of the nonlinear hydrostatic solutions, with the short solitary waves superimposed. The degree of disintegration is a function of initial amplitude of the tide and the properties of the underlying nonlinear hydrostatic solutions, which, depending on stratification and tidal frequency, exist only for a finite range of amplitudes (or energies). There is a lower threshold below which no short solitary waves are produced. However, for initial amplitudes above another threshold, given approximately by the energy of the limiting nonlinear hydrostatic inertia–gravity wave, most of the initial tidal energy goes into solitary waves. Recent observations in the South China Sea are briefly discussed.
    Description: KRH was supported by a Woods Hole Oceanographic Institution Mellon Independent Study Award and ONR Grant N000140610798.
    Keywords: Tides ; Internal waves ; Solitary waves ; Inertia–gravity waves ; Rotation
    Repository Name: Woods Hole Open Access Server
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  • 4
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    Whales and waves : humpback whale foraging response and the shoaling of internal waves at Stellwagen Bank (2015)
    John Wiley & Sons
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    Publication Date: 2022-05-25
    Description: Author Posting. © American Geophysical Union, 2015. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Oceans 120 (2015): 2555–2570, doi:10.1002/2014JC010564.
    Description: We tested the hypothesis that humpback whales aggregate at the southern flank of Stellwagen Bank (SB) in response to internal waves (IWs) generated semidiurnally at Race Point (RP) channel because of the presence of their preferred prey, planktivorous fish, which in turn respond to zooplankton concentrated by the predictable IWs. Analysis of synthetic aperture radar (SAR) images indicates that RP IWs approach the southern flank of SB frequently (∼62% of the images). Published reports of whale sighting data and archived SAR images point to a coarse spatial coincidence between whales and Race Point IWs at SB's southern flank. The responses of whales to IWs were evaluated via sightings and behavior of humpback whales, and IWs were observed in situ by acoustic backscatter and temperature measurements. Modeling of IWs complemented the observations, and results indicate a change of ∼0.4 m/s in current velocity, and ∼1.5 Pa in dynamic pressure near the bottom, which may be sufficient for bottom fish to detect the IWs. However, fish were rare in our acoustic observations, and fish response to the IWs could not be evaluated. RP IWs do not represent the leading edge of the internal tide, and they may have less mass-transport potential than typical coastal IWs. There was large interannual variability in whale sightings at SB's southern flank, with decreases in both numbers of sightings and proportion of sightings where feeding was observed from 2008 to 2013. Coincidence of whales and IWs was inconsistent, and results do not support the hypothesis.
    Description: We would also like to acknowledge funding from the National Oceanic and Atmospheric Administration Sea Grant (Woods Hole), the Woods Hole Oceanographic Institution, the ESA, and the German Aerospace Center.
    Description: 2015-10-02
    Keywords: Humpback whales ; Nonlinear internal waves ; Shallow temperate bank ; Ecological hotspots
    Repository Name: Woods Hole Open Access Server
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  • 5
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    Testing the physical oceanographic implications of the suggested sudden Black Sea infill 8400 years ago (2010)
    American Geophysical Union
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    Publication Date: 2022-05-25
    Description: Author Posting. © American Geophysical Union, 2004. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Paleoceanography 19 (2004): PA1024, doi:10.1029/2003PA000903.
    Description: We apply a shock-capturing numerical model based on the single-layer shallow water equations to an idealized geometry of the Black Sea and the Sea of Marmara in order to test the implications of a suggested sudden Black Sea infill 8400 years ago. The model resolves the two-dimensional flow upstream and downstream of the hydraulic jump provoked by the cascade of water from the Sea of Marmara into the Black Sea, which would occur during a sudden Black Sea infill. The modeled flow downstream of the hydraulic jump in the Black Sea would consist of a jet that is in part constrained by bathymetric contours. Guided by the Bosporus Canyon, the modeled jet reaches depths of up to 2000 m and could explain the origin of the sediment waves observed at this depth. At a late stage of the infill the modeled jet is attached to the coast and might account for the course of a submerged channel at the mouth of the Bosporus. The preservation of continuous barrier-washover-lagoonal fill systems occurring on the Black Sea shelf is, however, not easily reconcilable with the large flows over the southwest Black Sea shelf predicted by the model. Intensified flow in the upstream basin (Sea of Marmara) is restricted to the immediate vicinity of the Bosporus, suggesting that a sudden reconnection need not have disturbed sediments in the wider Sea of Marmara.
    Description: L. Pratt and K. Helfrich were supported under O.N.R. grant N00014-010100167 and N.S.F. grant OCE-0132903. L. Giosan was supported by a postdoctoral scholarship grant from CICOR (a Joint Institute of Woods Hole Oceanographic Institution and NOAA).
    Keywords: Black Sea ; Flood hypothesis ; Dam break
    Repository Name: Woods Hole Open Access Server
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  • 6
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    Optimal transient growth in thin-interface internal solitary waves (2018)
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    Publication Date: 2022-05-26
    Description: Author Posting. © The Author(s), 2018. This is the author's version of the work. It is posted here under a nonexclusive, irrevocable, paid-up, worldwide license granted to WHOI. It is made available for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 840 (2018): 342-378, doi:10.1017/jfm.2018.19.
    Description: The dynamics of perturbations to large-amplitude Internal Solitary Waves (ISW) in two-layered ows with thin interfaces is analyzed by means of linear optimal transient growth methods. Optimal perturbations are computed through direct-adjoint iterations of the Navier-Stokes equations linearized around inviscid, steady ISWs obtained from the Dubreil-Jacotin-Long (DJL) equation. Optimal perturbations are found as a function of the ISW phase velocity c (alternatively amplitude) for one representative stratification. These disturbances are found to be localized wave-like packets that originate just upstream of the ISW self-induced zone (for large enough c) of potentially unstable Richardson number, Ri 〈 0:25. They propagate through the base wave as coherent packets whose total energy gain increases rapidly with c. The optimal disturbances are also shown to be relevant to DJL solitary waves that have been modi ed by viscosity representative of laboratory experiments. The optimal disturbances are compared to the local WKB approximation for spatially growing Kelvin-Helmholtz (K-H) waves through the Ri 〈 0:25 zone. The WKB approach is able to capture properties (e.g., carrier frequency, wavenumber and energy gain) of the optimal disturbances except for an initial phase of non-normal growth due to the Orr mechanism. The non-normal growth can be a substantial portion of the total gain, especially for ISWs that are weakly unstable to K-H waves. The linear evolution of Gaussian packets of linear free waves with the same carrier frequency as the optimal disturbances is shown to result in less energy gain than found for either the optimal perturbations or the WKB approximation due to nonnormal effects that cause absorption of disturbance energy into the leading face of the wave. Two-dimensional numerical calculations of the nonlinear evolution of optimal disturbance packets leads to the generation of large-amplitude K-H billows that can emerge on the leading face of the wave and that break down into turbulence in the lee of the wave. The nonlinear calculations are used to derive a slowly varying model of ISW decay due to repeated encounters with optimal or free wave packets. Field observations of unstable ISW by Moum et al. (2003) are consistent with excitation by optimal disturbances.
    Description: PYP and BLW acknowledge the support by the National Science Foundation Grant Number OCE-1155558 and OCE{1736989. KRH acknowledges support from Independent Research and Development and Investment in Science Program awards from the Woods Hole Oceanographic Institution.
    Keywords: Solitary waves ; Internal waves ; Instability
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  • 7
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    Estimating the predictability of an oceanic time series using linear and nonlinear methods (2010)
    American Geophysical Union
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    Publication Date: 2022-05-26
    Description: Author Posting. © American Geophysical Union, 2004. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 109 (2004): C08002, doi:10.1029/2003JC002148.
    Description: This study establishes a series of tests to examine the relative utility of nonlinear time series analysis for oceanic data. The performance of linear autoregressive models and nonlinear delay coordinate embedding methods are compared for three numerical and two observational data sets. The two observational data sets are (1) an hourly near-bottom pressure time series from the South Atlantic Bight and (2) an hourly current-meter time series from the Middle Atlantic Bight (MAB). The nonlinear methods give significantly better predictions than the linear methods when the underlying dynamics have low dimensionality. When the dimensionality is high, the utility of nonlinear methods is limited by the length and quality of the time series. On the application side we mainly focus on the MAB data set. We find that the slope velocities are much less predictable than shelf velocities. Predictability on the slope after several hours is no better than the statistical mean. On the other hand, significant predictability of shelf velocities can be obtained for up to at least 12 hours.
    Description: This research was supported by Office of Naval Research grants N00014-01-1-0260, N00014-92-J-1481, and N10014-99-1-0258.
    Keywords: Predictability ; Delay coordinate embedding ; Shelf break
    Repository Name: Woods Hole Open Access Server
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  • 8
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    Combined effect of rotation and topography on shoaling oceanic internal solitary waves (2014)
    American Meteorological Society
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    Publication Date: 2022-05-26
    Description: Author Posting. © American Meteorological Society, 2014. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 44 (2014): 1116–1132, doi:10.1175/JPO-D-13-0194.1.
    Description: Internal solitary waves commonly observed in the coastal ocean are often modeled by a nonlinear evolution equation of the Korteweg–de Vries type. Because these waves often propagate for long distances over several inertial periods, the effect of Earth’s background rotation is potentially significant. The relevant extension of the Kortweg–de Vries is then the Ostrovsky equation, which for internal waves does not support a steady solitary wave solution. Recent studies using a combination of asymptotic theory, numerical simulations, and laboratory experiments have shown that the long time effect of rotation is the destruction of the initial internal solitary wave by the radiation of small-amplitude inertia–gravity waves, and the eventual emergence of a coherent, steadily propagating, nonlinear wave packet. However, in the ocean, internal solitary waves are often propagating over variable topography, and this alone can cause quite dramatic deformation and transformation of an internal solitary wave. Hence, the combined effects of background rotation and variable topography are examined. Then the Ostrovsky equation is replaced by a variable coefficient Ostrovsky equation whose coefficients depend explicitly on the spatial coordinate. Some numerical simulations of this equation, together with analogous simulations using the Massachusetts Institute of Technology General Circulation Model (MITgcm), for a certain cross section of the South China Sea are presented. These demonstrate that the combined effect of shoaling and rotation is to induce a secondary trailing wave packet, induced by enhanced radiation from the leading wave.
    Description: KH was supported by Grants N00014-09-10227 and N00014-11-0701 from the Office of Naval Research.
    Description: 2014-10-01
    Keywords: Circulation/ Dynamics ; Internal waves ; Solitary waves ; Models and modeling ; Nonlinear models
    Repository Name: Woods Hole Open Access Server
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