On the exact shape of the horizontal profile of a topographically rectified tidal flow     

L. R. M. Maas  J. T. F. Zimmerman  N. M. Temme 《地球物理与天体物理流体动力学》2013,107(2):105-129

Abstract

Starting from the nonlinear shallow water equations of a homogeneous rotating fluid we derive the equation describing the evolution of vorticity by a fluctuating bottom topography of small amplitude, using a multiple scale expansion in a small parameter, which is the topographic length scale relative to the tidal wave length. The exact response functions of residual vorticity for a sinusoidal bottom topography are compared with those obtained by a primitive perturbation series and by harmonic truncation, showing the former to be invalid for small topographic length scales and the latter to be only a fair approximation for vorticity produced by planetary vortex stretching. In deriving the exact shape of the horizontal residual velocity profile at a step-like break in the bottom topography, it is shown that the Lagrangian profile only exists in a strip having the width of the amplitude of the tidal excursion at both sides of the break, and that it vanishes outside that interval. Moreover, in the limit of small amplitude topography at least, it vanishes altogether for the generation mechanism by means of planetary vortex stretching. The Eulerian profile is shown to extend over twice the interval of the Lagrangian profile both for production by vortex stretching and by differential bottom friction. These finite intervals over which the residual velocity profiles exist for a step-like topography are not reproduced by harmonic truncation of the basic equation. This method gives exponentially decaying profiles, indicating spurious horizontal diffusion of vorticity. In terms of orders of magnitude, the method of harmonic truncation is reliable for residual velocity produced by vortex stretching but it overestimates the residual velocity produced by differential bottom friction by a factor 2.  相似文献   

Importance of wave-induced bed liquefaction in the fine sediment budget of Cleveland Bay,Great Barrier Reef   总被引：3，自引：0，他引：3  

J. Lambrechts  C. Humphrey  L. McKinna  O. Gourge  K.E. Fabricius  A.J. Mehta  S. Lewis  E. Wolanski 《Estuarine, Coastal and Shelf Science》2010

Data from a three-year long field study of fine sediment dynamics in Cleveland Bay show that wave-induced liquefaction of the fine sediment bed on the seafloor in shallow water was the main process causing bed erosion under small waves during tradewinds, and that shear-induced erosion prevailed during cyclonic conditions. These data were used to verify a model of fine sediment dynamics that calculates sediment resuspension by both excess shear stress and wave-induced liquefaction of the bed. For present land-use conditions, the amount of riverine sediments settling on the bay may exceed by 50–75% the amount of sediment exported from the bay. Sediment is thus accumulating in the bay on an annual basis, which in turn may degrade the fringing coral reefs. For those years when a tropical cyclone impacted the bay there may be a net sediment outflow from the bay. During the dry, tradewind season, fine sediment was progressively winnowed out of the shallow, reefal waters.  相似文献   

Theoretical and experimental study of breaking wave on sloping bottoms     

Kuei-Sen Yang  Yang-Yih Chen  Meng-Syue Li  Hung-Chu Hsu 《中国海洋工程》2013,27(6):737-750

This paper studies the continuous evolution of breaking wave for the surface water waves propagating on a sloping beach. A Lagrangian asymptotic solution is derived. According to the solution coupled with the wave breaking criteria and the equations of water particles motion, the wave deformation and the continuous wave breaking processes for the progressive water waves propagating on a sloping bottom can be derived. A series of experiments are also conducted to compare with the theoretical solution. The results show that the present solution can reasonably describe the plunging or spilling wave breaking phenomenon.  相似文献   

Non linear waves in two dimensional keplerian flows     

E. Siregar  J. Léorat  J. P. Poyet  A. Pouquet 《地球物理与天体物理流体动力学》2013,107(2):69-104

Abstract

Accretion discs in astrophysics are fundamental for converting gravitational binding energy into observed electromagnetic radiation. We study the behavior of waves in a two dimensional supersonic Keplerian flow inside a given gravitational potential. We present the effects of shearing and rotation on short waves, and the numerical study of the dynamical stability of such flows with respect to various perturbations. We show that a large class of dynamical effects, due to pressure and associated to short time scales, may be excited.  相似文献   

Jet instability and the stabilizing effect of topography on jets in two-layer rotating systems     

Don L. Boyer  Rui-Rong Chen 《地球物理与天体物理流体动力学》2013,107(1-3):45-70

Abstract

Laboratory experiments concerning azimuthal jets in two-layer rotating systems in the absence and presence of bottom topography aligned along the jets have been conducted. The jets were forced by the selective withdrawal of fluid from the upper layer of a two-fluid system contained in a circular dishpan geometry. The principal parameters measured in the experiments were the jet Rossby number, Ro, and a stratification parameter F = r ₁/(λ₁λ₂)^1/2 where r ₁ is the radius of the circular disc used for the selective withdrawal (i.e., r ₁ is the approximate radius of curvature of the jet) and λ₁,λ₂ are the internal Rossby radii of deformation in the upper and lower fluids, respectively.

The no-topography experiments show that for a sufficiently small F, the particular value depending on Ro, the jet is stable for the duration of the experiment. For sufficiently large F, again as a function of Ro, the jet becomes unstable, exhibiting horizontal wave disturbances from modes three to seven. An Ro against F flow regime diagram is presented.

Experiments are then conducted in the presence of a bottom topography having constant cross-section and extending around a mid-radius of the dishpan. The axis of the topography is in the vicinity of the jet axis forced in the no-topography experiments and the crest of the topography is in the vicinity of the interface between the two fluids (i.e., the front associated with the jet). The experiments show that in all cases investigated the jet tends to be stabilized by the bottom topography. Experiments with the topography in place, but with the interface between the fluids being above the topography crest, are shown to be unstable but more irregular than their no-topography counterparts.

Various quantitative measurements of the jet are presented. It is shown, for example, that the jet Rossby number defined in terms of the fluid withdrawal rate from the tank. Q, can be well correlated with a dimensionless vorticity gradient, V_G , across the upper layer jet. This allows for an assessment of the stability characteristics of a jet based on a knowledge of V_G (which can be estimated given a jet profile) and F.  相似文献   

The behavior of magneto-acoustic-gravity waves near the cusp resonance in a lossless,compressible, isothermal,stratified, electrically conducting and uniformly magnetized atmosphere. II: The valve effect     

Leon P. J. Kamp 《地球物理与天体物理流体动力学》2013,107(4):257-271

Abstract

In the present paper the behavior of (internal) magneto-acoustic-gravity waves near the cusp resonance in a lossless, compressible, isothermal, stratified, electrically conducting atmosphere that is permeated by a uniform, nearly horizontal magnetic field is re-addressed (Kamp, 1989). The previously analyzed linear conversion of long acoustic-gravity waves into short magneto-acoustic waves that carry off the energy from the resonance region along the magnetic field, is re-analyzed with boundary layer techniques that are based on the smallness of the vertical component of the magnetic field. More specifically the existence of the so-called valve effect for the generated magneto-acoustic mode near the critical level is explicitly demonstrated and shown to be governed by two rivalling effects.  相似文献   

Long waves due to a symmetrical wind stress on the surface of a rotating ocean     

C. R. Mondal 《地球物理与天体物理流体动力学》2013,107(4):295-313

Abstract

The problem of unsteady long waves generated by any horizontal and symmetrically distributed, time-periodic surface wind on a rotating ocean is analysed for large times and distances. Uniform asymptotic estimates of the surface displacement in the unsteady state are obtained. The steady-state wave and velocity fields at any distance are also determined. Some characteristics of the unsteady and steady motions are described. Also noted are the features that distinguish the motion from its one-dimensional analogue for which a non-uniform analysis in the unsteady state along with a large-distance form of the surface elevation are already known.  相似文献   

Finite-amplitude mountain waves in a compressible atmosphere including the effects of dissipation     

William Blumen 《地球物理与天体物理流体动力学》2013,107(1-3):89-104

Abstract

Adiabatic, two-dimensional, steady-state finite-amplitude, hydrostatic gravity waves produced by flow over a ridge are considered. Nonlinear self advection steepens the wave until the streamlines attain a vertical slope at a critical height z_c. The height z_c , where this occurs, depends on the ridge crest height and adiabatic expansion of the atmosphere. Dissipation is introduced in order to balance nonlinear self advection, and to maintain a marginal state above z_c. The approach is to assume that the wave is inviscid except in a thin layer, small compared to a vertical wavelength, where dissipation cannot be neglected. The solutions in each region are matched to obtain a continuous solution for the streamline displacement δ. Solutions are presented for different values of the nondimensional dissipation parameter β. Eddy viscosity coefficients and the thickness of the dissipative layer are expressed as functions of β, and their magnitudes are compared to other theoretical evaluations and to values inferred from radar measurements of the stratosphere.

The Fourier spectrum of the solution for z ≫ z_c is shown to decay exponentially at large vertical wave numbers n. In comparison, a spectral decay law n ^?-8/3 characterizes the marginal state of the wave at z = z_c .  相似文献   

Planetons: An example of large amplitude solitary waves     

William K. Dewar 《地球物理与天体物理流体动力学》2013,107(1-4):53-85

Abstract

The term ‘‘solitary wave'’ is usually used to denote a steadily propagating permanent form solution of a nonlinear wave equation, with the permanency arising from a balance between steepening and dispersive tendencies. It is known that large-scale thermal anomalies in the ocean are subject to a steepening mechanism driven by the beta effect, while at the smaller deformation scale, such phenomena are highly dispersive. It is shown here that the evolution of a physical system subject to both effects is governed by the ‘‘frontal semi-geostrophic equation'’ (FSGE), which is valid for large amplitude thermocline disturbances. Solitary wave solutions of the FSGE (here named planetons) are calculated and their properties are described with a view towards examining the behavior of finite amplitude solitary waves. In contrast, most known solitary wave solutions belong to weakly nonlinear wave equations (e.g., the Korteweg—deVries (KdV) equation).

The FSGE is shown to reduce to the KdV equation at small amplitudes. Classical sech² solitons thus represent a limiting class of solutions to the FSGE. The primary new effect on planetons at finite amplitudes is nonlinear dispersion. It is argued that due to this effect the propagation rates of finite amplitude planetons differ significantly from the ‘‘weak planeton'', or KdV, dispersion relation. Planeton structure is found to be simple and reminiscent of KdV solitons. Numerical evidence is presented which suggests that collisions between finite amplitude solitary waves are weakly inelastic, indicating the loss of true soliton behavior of the FSGE at moderate amplitudes. Lastly, the sensitivity of solitary waves to the existence of a nontrivial far field is demonstrated and the role of this analysis in the interpretation of lab experiments and the evolution of the thermocline is discussed.  相似文献   

Baroclinic nonlinear exchanges of energy and potential enstrophy in the quasi-geostrophic two-layer model     

Hal G. Marshall  Tsing-Chang Chen 《地球物理与天体物理流体动力学》2013,107(1-2):71-84

Abstract

Merilees and Warn's (1975) nonlinear interaction analysis of two-dimensional nondivergent flow is extended to examine the quasi-geostrophic two-layer model. Two sets of triads exist in this model (Salmon, 1978). The purely barotropic triads are the same as the triads examined by Merilees and Warn. Baroclinic-barotropic triads are found to exchange more energy or potential enstrophy with smaller or larger scales depending on the scale of motion as compared with the internal Rossby deformation radius and the relative wavenumber position of baroclinic and barotropic components.  相似文献