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1.
R. Grimshaw 《地球物理与天体物理流体动力学》2013,107(2):131-148
Nonlinear internal gravity waves in a slightly dissipative, slightly compressible fluid are discussed for the case when the properties of the medium vary slowly on a scale determined by the local wave structure. A two‐timing technique is used to obtain transport equations which describe the changes in amplitude, phase and mean flow of a wave packet. Various solutions of these transport equations are discussed, with relevance to critical layer absorption. 相似文献
2.
R. H. J. Grimshaw 《Dynamics of Atmospheres and Oceans》1985,9(2):85-120
We consider the three-dimensional reflection and diffraction properties of internal waves in a continuously stratified rotating fluid which are incident on the junction of a vertical slit and a half-space. This geometry is a model for submarine canyons on continental slopes in the ocean, where various physical phenomena embodying reflection and diffraction effects have been observed. Three types of incident wave are considered: (1) Kelvin waves in the slit (canyon); (2) Kelvin waves on the slope; and (3) plane internal waves incident from the half-space (ocean). These are scattered into Kelvin and Poincaré waves in the slit, a Kelvin wave on the slope and Poincaré waves in the half-space. Most of the discussion is centered around case (1). Various properties of the wave field are calculated for ranges of the parameters c/cot θ, γα and ƒ/ω where cot θ is the topographic slope, c is the internal wave ray slope, α is the canyon half-width, γ is the down-slope wave-number, ƒ is the Coriolis parameter and ω is the wave frequency. Analytical results are obtained for small γα and some approximate results for larger values of γα. The results show that significant wave trapping may occur in oceanic situations, and that submarine canyons may act as source regions for internal Kelvin waves on the continental slope. 相似文献
3.
L. Grimshaw 《Earth, Moon, and Planets》1982,26(3):305-310
In this paper the dynamics of individual dust particles and the effects on their motion caused by insolation and consequent evaporation is considered. Evaporation rates and the radii of dust-free zones have been computed using thermodynamic data from various sources. Some doubt is thrown on the validity of the process of matching observed thermal emission peaks with theoretical evaporation zone radii. 相似文献
4.
The transformation of a weakly nonlinear interfacial solitary wave in an ideal two-layer flow over a step is studied. In the vicinity of the step the wave transformation is described in the framework of the linear theory of long interfacial waves, and the coefficients of wave reflection and transmission are calculated. A strong transformation arises for propagation into shallower water, but a weak transformation for propagation into deeper water. Far from the step, the wave dynamics is described by the Korteweg-de Vries equation which is fully integrable. In the vicinity of the step, the reflected and transmitted waves have soliton-like shapes, but their parameters do not satisfy the steady-state soliton solutions. Using the inverse scattering technique it is shown that the reflected wave evolves into a single soliton and dispersing radiation if the wave propagates from deep to shallow water, and only dispersing radiation if the wave propagates from shallow to deep water. The dynamics of the transmitted wave is more complicated. In particular, if the coefficient of the nonlinear quadratic term in the Korteweg-de Vries equation is not changed in sign in the region after the step, the transmitted wave evolves into a group of solitons and radiation, a process similar to soliton fission for surface gravity waves at a step. But if the coefficient of the nonlinear term changes sign, the soliton is destroyed completely and transforms into radiation. The effects of cubic nonlinearity are studied in the framework of the extended Korteweg-de Vries (Gardner) equation which is also integrable. The higher-order nonlinear effects influence the amplitudes of the generated solitons if the amplitude of the transformed wave is comparable with the thickness of lower layer, but otherwise the process of soliton fission is qualitatively the same as in the framework of the Korteweg-de Vries equation. 相似文献
5.
Although tsunamis in the deep ocean are very long waves of quite small amplitudes, as they propagate shorewards into shallow water, nonlinearity becomes important and the structure of the leading waves depends on the polarity of the incident wave from the deep ocean. In this paper, we use a variable-coefficient Korteweg–de Vries equation to examine this issue, for an initial wave which is either elevation, or depression, or a combination of each. We show that the leading waves can be described by a reduction of the Whitham modulation theory to a solitary wave train. We find that for an initial elevation, the leading waves are elevation solitary waves with an amplitude which varies inversely with the depth, with a pre-factor which is twice the maximum amplitude in the initial wave. By contrast, for an initial depression, the leading wave is a depression rarefaction wave, followed by a solitary wave train whose maximum amplitude of the leading wave is determined by the square root of the mass in the initial wave. 相似文献
6.
R. Grimshaw 《Pure and Applied Geophysics》1980,119(4):780-797
Evolution equations for long nonlinear internal waves in a compressible fluid are derived, with the aim of comparing these equations with their counterparts in an incompressible fluid. Both the Korteweg-de Vries equation, and the deep fluid equation are discussed, for both dry and moist atmospheres. It is shown that the effects of compressibility, or non-Boussinesq terms, are generally small, but measurable, and are manifested mainly in the nonlinear term of the evolution equation. For the case of a moist atmosphere the effect of a gain in energy by latent heat release is compared with the energy lost by radiation damping. 相似文献
7.
Colin C. Turner Philip C. Richards John L. Swallow Stephanie P. Grimshaw 《Marine and Petroleum Geology》1984,1(2):105-117
The Upper Jurassic of the Outer Moray Firth Basin can be divided into two main stratigraphic units — the Piper and Kimmeridge Clay Formations. In each of these formations five major sedimentary facies can be recognized. The Piper Formation, of late Oxfordian to early Kimmeridgian age, comprises very fine to coarse-grained sandstones and minor mudstone of clastic shelf to shoreline origin. Large scale upward-coarsening sequences are well developed in some areas, particularly in the reservoir sands of the Tartan oilfield, and are interpreted as regressive, possibly deltaic deposits. The unconformably overlying Kimmeridge Clay Formation ranges in age from late Oxfordian through Volgian to Ryazanian. The formation is predominantly argillaceous, but also contains locally thick accumulations of sandstone deposited by gravity flow processes. The Claymore Sandstone Member is proposed as a new name for these sandstones in the region of the Claymore oilfield, where they form the major reservoir. Sands of the Piper Formation were derived mainly from the south-west, although some input from the north may also have occurred. Deposition may have extended further eastwards than the present erosional limit of the sands. Thick sand sequences in the Kimmeridge Clay Formation are probably restricted to the margins of the Witch Ground Graben, where contemporaneous faulting occurred. 相似文献
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9.
R. Grimshaw 《地球物理与天体物理流体动力学》2013,107(1):3-16
Abstract Continental shelf waves are examined in the long wavelength limit, and the effects of weak topographic dispersion calculated. These dispersive effects are then balanced against nonlinear terms and a Korteweg-de Vries equation is derived to describe the evolution of the wave amplitude. Two particular cases are worked in detail. 相似文献
10.
Abstract We consider the linearized stability of a barotropic coastal current flowing parallel to a straight coastline over a continental shelf and slope whose depth varies monotonically with distance from the coast. Some necessary conditions for stability and various semi-circle theorems are reviewed for general current profiles and bottom topography. A criterion for topography to be a destabilizing influence is derived. Some general results for stable waves are also described. Analytic solutions are obtained for a piece-wise linear current profile and the exponential depth profile (Buchwald and Adams, 1968). Dispersion diagrams are obtained for a monotonic current profile, where it is shown that the effect of topography is destabilizing, and for a triangular current profile. The dispersion diagrams generally contain a finite number (usually one or two) of unstable waves, and a set of stable waves, which may be infinite in number. The results are applied to some specific coastal regimes. 相似文献