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  • Internal solitary waves  (2)
  • Nonlinear waves  (2)
  • Buoyant gravity currents  (1)
  • Differential equations  (1)
  • 1
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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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  • 2
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    Nonlinear adjustment of a localized layer of buoyant, uniform potential vorticity fluid against a vertical wall (2007)
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    Publication Date: 2022-05-25
    Description: Author Posting. © Elsevier B.V., 2006. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Dynamics of Atmospheres and Oceans 41 (2006): 149-171, doi:10.1016/j.dynatmoce.2006.02.001.
    Description: The nonlinear evolution of a localized layer of buoyant, uniform potential vorticity fluid of uniform depth H, width w0 and length L released adjacent to a wall in a rotating system is studied using reduced-gravity shallow-water theory and numerical modeling. In the interior, far from the two ends of the layer, the initial adjustment gives, after ignoring inertia-gravity waves, a geostrophic flow of width w∞ and layer velocities parallel to the wall directed in the downstream direction (defined by Kelvin wave propagation). This steady geostrophic flow serves as the initial condition for a semigeostrophic solution using the method of characteristics. At the downstream end, the theory shows that the fluid intrudes along the wall as rarefaction terminating at a nose of vanishing width and depth. However, in a real fluid the presence of the lower layer leads to a blunt gravity current head. The theory is amended by introducing a gravity current head condition that has a blunt bore joined to the rarefaction by a uniform gravity current. The upstream termination of the initial layer produces a Kelvin rarefaction that propagates downstream, decreasing the layer depth along the wall, and initiating upstream flow adjacent to the wall. The theoretical solution compares favorably to numerical solutions of the reduced-gravity shallow-water equations. The agreement between theory and numerical solutions occurs regardless of whether the numerical runs are initiated with an adjusted geostrophic solution or with the release of a stagnant layer. The latter case excites inertia-gravity waves that, despite their large amplitude and breaking, do not significantly affect the evolution of the geostrophic flow. At times beyond the validity of the semigeostrophic theory, the numerical solutions evolve into a stationary arrays of vortices. The vortex formation can be interpreted as the finite-amplitude manifestation of a linear instability of the new flow established by the passage of the Kelvin wave. The Kelvin wave ultimately reduces the flux into the downstream gravity current and the vortices retain buoyant in the neighborhood of the initial layer.
    Description: This work was supported by NSF Grant OCE-0325102.
    Keywords: Geostrophic adjustment ; Gravity currents ; Kelvin waves ; Nonlinear waves ; Vortices
    Repository Name: Woods Hole Open Access Server
    Type: Preprint
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  • 3
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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
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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
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    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
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