Grimshaw Roger H. J.

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Grimshaw
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Roger H. J.
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  • Article
    Large amplitude internal waves in the coastal ocean (Preface)
    (Copernicus Publications on behalf of the European Geosciences Union and the American Geophysical Union, 2011-10-07) Grimshaw, Roger H. J. ; Helfrich, Karl R. ; Scotti, Alberto
    The flow in the coastal ocean, and especially on the continental shelf and slope is often characterized by the presence of very large-amplitude internal waves. These are waves which occur in the interior of the ocean, and propagate horizontally with a concentration of their energy around the oceanic pcynocline. They are usually generated by the interaction of the barotropic tide with the shelf break, topographic sill or with other prominent bottom features. This leads to the formation of an internal tide, which then deforms and evolves into a train of very large-amplitude internal waves, with associated large pycnocline displacements and strong currents. They are highly significant for sediment transport and for the biology on the continental shelf, their associated currents cause strong forces on marine platforms and submersibles, the associated strong distortion of the density field has a severe impact on acoustic signaling and their capacity to break and form microstructure has major consequences for the understanding of interior ocean mixing.
  • Preprint
    Experimental study of the effect of rotation on nonlinear internal waves
    ( 2013-03-01) Grimshaw, Roger H. J. ; Helfrich, Karl R. ; Johnson, Edward R.
    Large amplitude internal waves are commonly observed in the coastal ocean. In the weakly nonlinear long wave r egime, they are often modeled by the Korteweg-de Vries equation, which predicts that the long-time outcome of generic localised initial conditions is a train of internal solitary waves. However, when the e ect of background rotation is taken into account, it is known from several theoretical and numerical studies that the formation of solitary waves is inhibited, and instead nonlinear wave packets form. In this paper, we report the results from a laboratory experiment on the Coriolis platform which describes this process.
  • Preprint
    Internal solitary wave generation by tidal flow over topography
    ( 2017-12-21) Grimshaw, Roger H. J. ; Helfrich, Karl R.
    Oceanic internal solitary waves are typically generated by barotropic tidal flow over localised topography. Wave generation can be characterised by the Froude number F = U/c(0), where U is the tidal flow amplitude and c(0) is the intrinsic linear long wave phase speed, that is the speed in the absence of the tidal current. For steady tidal flow in the resonant regime, Delta(m) < F - 1 < Delta(M), a theory based on the forced Korteweg-de Vries equation shows that upstream and downstream propagating undular bores are produced. The bandwidth limits Delta(m,M) depend on the height (or depth) of the topographic forcing term, which can be either positive or negative depending on whether the topography is equivalent to a hole or a sill. Here the wave generation process is studied numerically using a forced Korteweg-de Vries equation model with time-dependent Froude number, F(t), representative of realistic tidal flow. The response depends on Delta(max) = F-max - 1, where F-max is the maximum of F(t) over half of a tidal cycle. When Delta(max) < Delta(m) the flow is always subcritical and internal solitary waves appear after release of the downstream disturbance. When Delta(m) < Delta(max) < Delta(M) the flow reaches criticality at its peak, producing upstream and downstream undular bores that are released as the tide slackens. When Delta(max) > Delta(M) the tidal flow goes through the resonant regime twice, producing undular bores with each passage. The numerical simulations are for both symmetrical topography, and for asymmetric topography representative of Stellwagen Bank and Knight Inlet.
  • Article
    Combined effect of rotation and topography on shoaling oceanic internal solitary waves
    (American Meteorological Society, 2014-04) Grimshaw, Roger H. J. ; Guo, Chuncheng ; Helfrich, Karl R. ; Vlasenko, Vasiliy
    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.
  • Preprint
    The reduced Ostrovsky equation : integrability and breaking
    ( 2012-05-10) Grimshaw, Roger H. J. ; Helfrich, Karl R. ; Johnson, Edward R.
    The reduced Ostrovsky equation is a modi cation of the Korteweg-de Vries equation, in which the usual linear dispersive term with a third-order deriva- tive is replaced by a linear non-local integral term, which represents the e ect of background rotation. This equation is integrable provided a certain curvature constraint is satis ed. We demonstrate, through theoretical analysis and numeri- cal simulations, that when this curvature constraint is not satisfi ed at the initial time, then wave breaking inevitably occurs.
  • Article
    Nonlinear disintegration of the internal tide
    (American Meteorological Society, 2008-03) Helfrich, Karl R. ; Grimshaw, Roger H. J.
    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.
  • Article
    Atmospheric gravity waves in the Red Sea : a new hotspot
    (Copernicus Publications on behalf of the European Geosciences Union and the American Geophysical Union, 2011-02-03) Magalhaes, Jorge M. ; Araujo, I. B. ; da Silva, Jose C. B. ; Grimshaw, Roger H. J. ; Davis, Kate ; Pineda, Jesus
    The region of the Middle East around the Red Sea (between 32° E and 44° E longitude and 12° N and 28° N latitude) is a currently undocumented hotspot for atmospheric gravity waves (AGWs). Satellite imagery shows evidence that this region is prone to relatively high occurrence of AGWs compared to other areas in the world, and reveals the spatial characteristics of these waves. The favorable conditions for wave propagation in this region are illustrated with three typical cases of AGWs propagating in the lower troposphere over the sea. Using weakly nonlinear long wave theory and the observed characteristic wavelengths we obtain phase speeds which are consistent with those observed and typical for AGWs, with the Korteweg-de Vries theory performing slightly better than Benjamin-Davis-Acrivos-Ono theory as far as phase speeds are concerned. ERS-SAR and Envisat-ASAR satellite data analysis between 1993 and 2008 reveals signatures consistent with horizontally propagating large-scale internal waves. These signatures cover the entire Red Sea and are more frequently observed between April and September, although they also occur during the rest of the year. The region's (seasonal) propagation conditions for AGWs, based upon average vertical atmospheric stratification profiles suggest that many of the signatures identified in the satellite images are atmospheric internal waves.