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  • Internal solitary waves  (2)
  • Nonlinear internal waves  (2)
  • Buoyant gravity currents  (1)
  • Differential equations  (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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    Synthetic Aperture Radar observations of resonantly generated internal solitary waves at Race Point Channel (Cape Cod) (2010)
    American Geophysical Union
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    Publication Date: 2022-05-25
    Description: Author Posting. © American Geophysical Union, 2008. 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 113 (2008): C11016, doi:10.1029/2008JC005004.
    Description: Synthetic Aperture Radar images revealed the two-dimensional propagation characteristics of short-period internal solitary waves in Race Point Channel in Massachusetts Bay. The images and in situ measurements of the flow in the channel are used to infer the likely generation mechanism of the waves. The solitary waves are generated during the ebb phase of the tide within the channel. On some occasions, two trains of internal waves are generated presumably at the same location but at slightly different phases of the ebb tide. The main characteristics of the (two-layer) flow are described based on the criticality of the Froude number. It is suggested that these two individual packets of waves result from flow passage through resonance (where the Froude number is one). One packet is generated as the flow passes through the transcritical regime during the acceleration phase of the (ebb) tidal current, and another packet is generated during the deceleration phase. Both packets propagate upstream when the tide slacks, but with slightly different propagation directions.
    Description: J. C. B. da Silva is grateful to FCT for sabbatical leave support (BSAB/610/2006) and the Calouste Gulbenkian Foundation for partial support. J. C. B. da Silva was supported by FCT projects ‘‘SPOTIWAVE-II’’ (project code POCI/MAR/57836/2004) and ‘‘AMAZING’’ (project code PDCTE/CTA/49953/2003). K. R. Helfrich was supported by ONR grant N000140610798. This research was partially supported by the Woods Hole Sea Grant Program (2008– 2010 cycle), under a grant from the U.S. National Oceanic and Atmospheric Administration (NOAA), U.S. Department of Commerce, Grant No. NA06OAR4170021, project number R/O-40.
    Keywords: Internal solitary waves ; Resonant generation ; Flow through straits ; Variable Froude ; Synthetic aperture radar ; Massachusetts Bay
    Repository Name: Woods Hole Open Access Server
    Type: Article
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  • 3
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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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  • 4
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    Large-scale, realistic laboratory modeling of M2 internal tide generation at the Luzon Strait (2014)
    John Wiley & Sons
    Details
    Publication Date: 2022-05-25
    Description: Author Posting. © American Geophysical Union, 2013. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geophysical Research Letters 40 (2013): 5704–5709, doi:10.1002/2013GL058064.
    Description: The complex double-ridge system in the Luzon Strait in the South China Sea (SCS) is one of the strongest sources of internal tides in the oceans, associated with which are some of the largest amplitude internal solitary waves on record. An issue of debate, however, has been the specific nature of their generation mechanism. To provide insight, we present the results of a large-scale laboratory experiment performed at the Coriolis platform. The experiment was carefully designed so that the relevant dimensionless parameters, which include the excursion parameter, criticality, Rossby, and Froude numbers, closely matched the ocean scenario. The results advocate that a broad and coherent weakly nonlinear, three-dimensional, M2 internal tide that is shaped by the overall geometry of the double-ridge system is radiated into the South China Sea and subsequently steepens, as opposed to being generated by a particular feature or localized region within the ridge system.
    Description: This work is funded by ONR grants N00014-09- 1-0282 and N00014-09-1-0227, CNRS-PICS grant 5860, ANR grant 08- BLAN-0113-01, and the MIT-France Program.
    Description: 2014-05-04
    Keywords: Internal tide ; Luzon Strait ; Internal solitary waves ; Laboratory experiments
    Repository Name: Woods Hole Open Access Server
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  • 5
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    Some new aspects of the joint effect of rotation and topography on internal solitary waves. (2019)
    American Meteorological Society
    Details
    Publication Date: 2022-05-26
    Description: Author Posting. © American Meteorological Society, 2019. 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 49(6), (2019): 1639-1649, doi: 10.1175/JPO-D-18-0154.1.
    Description: Using a recently developed asymptotic theory of internal solitary wave propagation over a sloping bottom in a rotating ocean, some new qualitative and quantitative features of this process are analyzed for internal waves in a two-layer ocean. The interplay between different singularities—terminal damping due to radiation and disappearing quadratic nonlinearity, and reaching an “internal beach” (e.g., zero lower-layer depth)—is discussed. Examples of the adiabatic evolution of a single solitary wave over a uniformly sloping bottom under realistic conditions are considered in more detail and compared with numerical solutions of the variable-coefficient, rotation-modified Korteweg–de Vries (rKdV) equation.
    Description: LAO is thankful to Yu. Stepanyants for broad discussions of mutual benefit. KRH was supported by Grant N00014-18-1-2542 from the Office of Naval Research.
    Description: 2020-06-13
    Keywords: Internal waves ; Differential equations ; Nonlinear models ; Ocean models
    Repository Name: Woods Hole Open Access Server
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  • 6
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    Buoyant gravity currents along a sloping bottom in a rotating fluid (2005)
    Cambridge University Press
    Details
    Publication Date: 2022-05-26
    Description: Author Posting. © Cambridge University Press, 2002. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 464 (2002): 251-278, doi:10.1017/S0022112002008868.
    Description: The dynamics of buoyant gravity currents in a rotating reference frame is a classical problem relevant to geophysical applications such as river water entering the ocean. However, existing scaling theories are limited to currents propagating along a vertical wall, a situation almost never realized in the ocean. A scaling theory is proposed for the structure (width and depth), nose speed and flow field characteristics of buoyant gravity currents over a sloping bottom as functions of the gravity current transport Q, density anomaly g[prime prime or minute], Coriolis frequency f, and bottom slope [alpha]. The nose propagation speed is cp [similar] cw/ (1 + cw/c[alpha]) and the width of the buoyant gravity current is Wp [similar] cw/ f(1 + cw/c[alpha]), where cw = (2Qg[prime prime or minute] f)1/4 is the nose propagation speed in the vertical wall limit (steep bottom slope) and c[alpha] = [alpha]g/f is the nose propagation speed in the slope-controlled limit (small bottom slope). The key non-dimensional parameter is cw/c[alpha], which indicates whether the bottom slope is steep enough to be considered a vertical wall (cw/c[alpha] [rightward arrow] 0) or approaches the slope-controlled limit (cw/c[alpha] [rightward arrow] [infty infinity]). The scaling theory compares well against a new set of laboratory experiments which span steep to gentle bottom slopes (cw/c[alpha] = 0.11–13.1). Additionally, previous laboratory and numerical model results are reanalysed and shown to support the proposed scaling theory.
    Description: This research was supported by NSF grant OCE-0095059.
    Keywords: Buoyant gravity currents ; Scaling theory ; Sloping bottom
    Repository Name: Woods Hole Open Access Server
    Type: Article
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