Non-dispersive Wave Research Articles

Quasi-geostrophic oceanic adjustment in the presence of mean currents

The effect of mean currents on the adjustment of the ocean to a change in the winds is studied using a quasigeostrophic shallow water model. In an inviscid ocean the eigenmodes that affect the oceanic adjustment fall into two groups: a finite discrete number of Rossby waves with speeds greater than that of the mean flow, and a continuum of modes that have critical layers where the wave speed equals that of the mean current. In the case of a baroclinic mean current there exists large-scale latitudinal modes that propagate at the speed of long non-dispersive Rossby waves. Because of their presence, the adjustment in the presence of mean baroclinic currents is very similar to the adjustment in the absence of any currents provided that the forcing has large latitudinal scale. If the continuum of modes with critical layers is important in the adjustment—this is the case if the mean current is barotropic—then the adjustment occurs at approximately the Doppler-shifted Rossby wave speed.

Quasi-geostrophic oceanic adjustment in the presence of mean currents

The effect of mean currents on the adjustment of the ocean to a change in the winds is studied using a quasigeostrophic shallow water model. In an inviscid ocean the eigenmodes that affect the oceanic adjustment fall into two groups: a finite discrete number of Rossby waves with speeds greater than that of the mean flow, and a continuum of modes that have critical layers where the wave speed equals that of the mean current. In the case of a baroclinic mean current there exists large-scale latitudinal modes that propagate at the speed of long non-dispersive Rossby waves. Because of their presence, the adjustment in the presence of mean baroclinic currents is very similar to the adjustment in the absence of any currents provided that the forcing has large latitudinal scale. If the continuum of modes with critical layers is important in the adjustment—this is the case if the mean current is barotropic—then the adjustment occurs at approximately the Doppler-shifted Rossby wave speed.

Trajectories of two-particle states for the harmonic oscillator

Using the example of a harmonic oscillator and nondispersive wave packets, we derive, in the frame of the causal interpretation, the equations of motion and particle trajectories in one- and two-particle systems. The role of the symmetry or antisymmetry of the wave function is analyzed as it manifests itself in the specific types of corelated trajectories. This simple example shows that the concepts of the quantum potential and the quantum forces prove to be essential for the specification of the dynamics of a microsystem and the resulting statistical behavior.

Spinup toward Communication between Large Oceanic Subpolar and Subtropical Gyres

Abstract An interpretation in terms of planetary waves is proposed, which sheds light on the dynamics underlying the large-scale cross-gyre geostrophic flow recently developed in a two-layer ventilated thermocline model. The cross-gyre communication flow is the result of an arrested nondispersive baroclinic Rossby wave in the presence of zonal Sverdrup transport along the line of vanishing Ekman pumping. A baroclinic adjustment is described in which a resting ocean settles to a steady communicating solution.

Observations and events

Whether a space-time event is observed or not, its physical nature will not depend on the inertial frame of reference used for its mathematical description. Hence one can produce a non-dispersive de Broglie wave packet whose center adds a localising function to the wave mechanical description of a particle. Once observed, the past history of this function will describe the track of the particle up to the observation. It is here shown that this packet turns the quantum mechanical description of a single particle from mathematical tool to understandable physical theory.

Hindcast/forecast of ENSO events based upon the redistribution of observed and model dynamic height in the Western Tropical Pacific, 1964–1986

Anomalous sea level, anomalous observed dynamic height (0/400 db) and anomalous model dynamic height are examined at the locations of 13 island sea level stations in the tropical Pacific for each bimonth of the four year period 1979 to 1982. Starting in 1981, the anomalous dynamic height data show off-equatorial Rossby waves propagated toward the W boundary of the Pacific basin. At the W boundary, the model Rossby wave activity was found to have excited coastally trapped Kelvin-Munk waves which transmitted the anomalous dynamic height equatorward. At the equator, coastally trapped wave activity excited eastward propagating equatorial Kelvin waves, yielding a pair of anomalous peaks in dynamic height variability in the E equatorial Pacific associated with the 1982–1983 ENSO event. The evolution of the peaks in dynamic height associated with the Rossby and Kelvin wave activity reflects the redistribution of observed upper-ocean heat content in the W tropical Pacific, providing a qualitative hindcast for the 1982–1983 ENSO event. In consequence of these results, and the results of a related study (Inoue et al. 1985), the redistribution of both observed and model heat content, as evidenced in dynamic height in the W Pacific during the 23-year period 1964–1985, is examined for its ability to hindcast and forecast ENSO events in this period. Complex EOF analysis is applied to the Onset Phase of ENSO events occurring in 1968–69, 1972–73, 1976–77, and 1982–83; it is used to determine the characteristic redistribution of heat content (dynamic height) prior to the Mature Phase of ENSO events. This analysis found both model and observed dynamic height in the N hemisphere to be characterized by wind-driven, westward propagating, baroclinic Rossby wave activity, having a remarkably stable period of 3 years over the 23-year period. The complex time series associated with these first spatial eigen-functions are used to construct observed and model hindcast indices that yield high values one year prior to the Mature Phase of ENSO events of the period. These indices achieve these values due to the incidence upon the Philippine coast in fall/winter of a positive anomaly in dynamic height propagating from the east at nondispersive Rossby long wave speeds.

The equatorial source of propagating variability along the Peru coast During the 1982–1983 El Niño

Using data obtained from tide gages in South America, current meters along the equator and the Peru coast, and an array of pressure gages and inverted echo sounders within and around the Galapagos archipelago, we have analyzed the equatorial origin of coastal trapped waves observed by Cornejo‐Rodriquez and Enfield (this issue) along the Peru coast during the intense 1982–1983 El Niño. The propagating fluctuations along the coast were much stronger at that time than either before or after the El Niño, and the variability was not locally forced by coastal winds. We find that the coastal variability was also more energetic during previous El Niño occurrences. At periods of 1–2 weeks the meridional component of currents on the equator is up to an order of magnitude more energetic than the zonal fluctuations and is consistently associated with sea level that fluctuates antisymmetrically between hemispheres. At periods longer than 2 weeks the zonal velocity component is more energetic, and the cross‐equatorial sea level variability is symmetric. The meridional and zonal phase structures of cross spectra involving the currents and sea level establish the 1‐ to 2‐week equatorial fluctuations as mixed Rossby‐gravity (Yanai) waves of low wave number with infinite phase speed (standing oscillations) in the middle of the band (10 days); the corresponding structures for longer periods are consistent with nondispersive Kelvin waves. Frequency domain EOF modes of the sea level and current data establish the mixed Rossby‐gravity waves as the principal source of the strong trapped wave variability in the 1‐ to 2‐week band along the Ecuador‐Peru coast during the 1982–1983 El Niño episode.

Coupled KdV equations with multi-Hamiltonian structures

We present a large class of systems of N-equations which possess ( N+1) purely differential, compatible Hamiltonian structures. Our generic equations are isospectral to [( Σ N−1 0 ε i λ 2 i ) ∂ 2+ Σ N−1 0 υ i λ 2 i ] ψ= λ 2 N ψ, but our class also includes degenerate, nondispersive systems which are unrelated to this linear problem. Embedded in this class, for each N, there are N distinct coupled KdV systems. When N = 2 our class includes 3 known equations: dispersive water waves, Ito's equation and reduced Benney's equations. These equations are thus tri-Hamiltonian. We also present 2 examples of 3-component quadri-Hamiltonian systems, which generalise the above mentioned dispersive and nondispersive water waves.

Scattering of Continental Shelf Waves at a Discontinuity in Shelf Width

Abstract An analytical solution is presented for the scattering of a free shelf wave incident upon a discontinuity in shelf width in a barotropic ocean. The discussion of solutions relying on backscattered free-waves with large wavenumbers which may not exist in a realistically stratified ocean is avoided by considering only the range of parameters over which energy transmission is nearly 100%. There is a substantial transfer of energy to modes other than that of the incident wave. The mode most readily excited is that which has the cross-shelf structure most closely coinciding with that of the incident wave. The resultant presence of multiple modes produces a strong alongshelf modulation in flow intensity and phase progression downstream of the scattering region which may affect the interpretation of shelf wave observations. A nondispersive long shelf wave pulse is shown to scatter into a train of pulses of differing mode number, each propagating at its own flee wave speed.

Nondispersive MSFVW propagation in an inhomogeneously magnetized YIG film (abstract)

The present paper reports a theoretical and experimental study of the realizability of bandwidth enhancement for nondispersive magnetostatic forward volume wave (MSFVW) propagation in a YIG film via bias-field inhomogeneity. The theory assumes that the bias field varies linearly and weakly with distance along the direction normal to the sagittal plane. In agreement with expectation, the MSFVW signal profile along this direction is channelized, i.e., the MSFVW profile corresponding to a fixed frequency exists predominantly over a confined spatial region which shifts in the direction of increasing bias field as the frequency is increased. An in-depth characterization of the channelization process, which is crucial in unraveling the MSW dispersion control capability afforded by bias-field inhomogeneity, will be presented. Interestingly, the MSFVW wave-number variation over the confinement region is such that an essentially nondispersive propagation is achieved. The theoretical prediction of significant enhancement in the bandwidth for nondispersive MSFVW propagation as a result of bias-field inhomogeneity was verified experimentally utilizing specially machined pole pieces.

Weakly dispersive spectral theory of transients, part I: Formulation and interpretation

Dispersive effects in transient propagation and scattering are usually negligible over the high frequency portion of the signal spectrum, and for certain configurations, they may be neglected altogether. The source-excited field may then be expressed as a continuous spatial spectrum of nondispersive time-harmonic local plane waves, which can be inverted in closed form into the time domain to yield a fundamental field representation in terms of a spatial spectrum of transient local plane waves. By exploiting its analytic properties, one may evaluate the basic spectral integral in terms of its singularities-real and complex, time dependent and time independent-in the complex spectral plane. These singularities describe distinct features of the propagation and scattering process appropriate to a given environment. The theory is developed in detail for the generic local plane wave spectra representative of a broad class of two-dimensional propagation and diffraction problems, with emphasis on physical interpretation of the various spectral contributions. Moreover, the theory is compared with a similar approach that restricts all spectra to be real, thereby forcing certain wave processes into a spectral mold less natural than that admitting complex spectra. Finally, application of the theory is illustrated by specific examples. The presentation is divided into three parts. Part I, in this paper, deals with the formulation of the theory and the classification of the singularities. Parts II and III, to appear subsequently, contain the evaluation and interpretation of the spectral integral and the applications, respectively.

Topographic Scattering of Equatorial Kelvin Waves

Abstract We develop a linear, reduced-gravity model with two active layers above a deep, resting layer to examine the scattering of equatorial Kelvin waves from meridional submarine ridges. Model ridges, idealized as infinitely long in the meridional direction and infinitesimally thin in the zonal direction, completely obstruct flow in the lower active layer. The equatorial long-wave approximation is made, which restricts the class of motions considered to nondispersive Kelvin and Rossby waves in each of two internal modes. Thus, coastal and topographically trapped phenomena are filtered out, but variability far from the ridge is accurately modeled. The scattering of Kelvin wave energy depends on two parameters, r = H0/H1 and γ = (ρ1 − ρ0)/(ρ2 − ρ1), where H0 and H1 are the equilibrium thicknesses of the upper and lower active layers, respectively, and ρ0≲ρ1≲ρ2 are the layer densities. Incident first internal mode Kelvin waves are little affected by a deep ridge (i.e., for large r) and strongly reflected ...

A non-negative distribution function in relativistic quantum mechanics

Abstract We generalize to a Lorentz covariant formalism (with proper-time dependence) the non-negative phase-space distribution proposed by Kuryshkin and make a specific proposal to define the corresponding correspondence rule between functions of phase-space and quantum operators on the basis of the introduction of a non-dispersive soliton wave surrounding particles in space-time.

Acceleration and heating in quasi-linear diffusion

Quasi-linear diffusion of charged particles due to a stationary and homogeneous spectrum of electrostatic field fluctuations is investigated via a Fokker-Planck approach. The energy of a given distribution of test particles is found to be conserved whenever the wave spectrum is isotropic and none of the spectral components of the field has a phase speed that equals the speed of any test particle. Quite generally, the energy is monotonically increasing for isotropic spectra. An interesting quantum mechanical interpretation of these results is given, and the special case of beam evolution in an isotropic spectrum of non-dispersive waves is studied in some detail. Conditions for isotropization of directed electron and ion beams from Coulomb collisions and collective oscillations are discussed in the context of the quasi-linear description. Some promising results from a beam-plasma experiment are quoted.

On a submerged sphere in a viscous fluid excited by small-amplitude periodic motions

Higher-order nonlinear corrections to the Stokes pendulum problem are calculated in perturbation schemes for small values of Reynolds numbers R(2) = umd0/2ν. Here the controlling lengthscale ½d0 is the displacement amplitude of the undisturbed periodic motion, um is the velocity amplitude and ν is the kinematic viscosity. Solutions for two general types of periodic motion are found; namely orbital motion as under deep water waves and oscillatory motion as under shallow water or acoustic waves. These solutions are found by matched asymptotic expansions using the fundamental irrotational oscillation to drive a thin Stokes a.c. boundary layer over the surface of the sphere. From the boundary layer several secondary motions are excited which die away in the neighbouring fluid. Among these are an orthogonal system of steady, rotational Eulerian streaming currents, and two outwardly radiating non-dispersive waves, one having the frequency of the fundamental but with a phase shift, the other appearing at the second harmonic.With these solutions the forces and torques on a fixed sphere were computed. One of the orthogonal components of the rotational streaming field was found to produce a rotary lift force which opposed virtual-mass forces and diminished the resultant force component in quadrature to the fundamental oscillation. The other streaming component contributed damping terms which, unlike leading-order Stokes drag, vary nonlinearly with the displacement amplitude. Steady and second-harmonic torques were found to act on the sphere about the horizontal axis transverse to the fundamental oscillation.

The Resonant Response of Interannual Baroclinic Rossby Waves to Wind Forcing in the Eastern Midlatitude North Pacific

During the four year period 1976–80, mesoscale anomalies of 300 m temperature in the eastern midlatitude North Pacific were observed propagating westward from the coast of North America to 165°W at approximately 2 cm s−1, with characteristics similar to baroclinic, nondispersive Rossby waves. These mesoscale anomalies had a dominant period scale of approximately two years and a dominant wavelength scale of approximately 1000 km. In this study, a baroclinic, nondispersive Rossby wave model is driven by the observed wind stress curl in an attempt to simulate the amplitude and phase of these observed mesoscale anomalies over this period of time. Model/data intercomparison finds the frequency/zonal wavenumber spectra of model 300 m temperature to be similar in pattern to that observed for waves of periods greater than one year, with peak spectral energy density in both occurring at zonal wavelengths of 1000–1200 km and periods of 2–3 years. These spectral peaks occur on the Rossby wave dispersion curve at the frequency/wavenumber location where peak spectral energy density occurs in the wind-stress curl spectrum. Coherence between model and observed mesoscale anomalies is maximum at the frequency/wavenumber location of these spectral peaks, significant at the 70% confidence level, with approximately 0° phase difference. The response functions in frequency/wavenumber space of both model ocean and real ocean are nearly identical in pattern for periods greater than one year, with maximum values located along the Rossby wave dispersion curve. Therefore, a resonant response of the baroclinic, nondispersive, Rossby waves to the wind stress curl is indicated. These resonant waves begin at the coast of North America and propagate westward with amplitude increasing linearly. The zonal profile of rms differences of observed mesoscale anomalies from 125–165°W is very similar to the model profile, the latter dominated by the resonant response which explains 60–90% of the total model response. The off-resonant model response is small, even though the wind strew curl variability is largest at off-resonant frequencies and wavenumbers. In the real ocean the off-resonant response is much larger than in the model, with the largest off-resonant response occurring in the dispersive portion of the spectral domain where the model is not applicable. This, together with white noise in both model and observed data, accounts for the model's inability to explain more than 20% of the total observed mesoscale variance.

Edge diffraction of transient nondispersive wave—theory and experiment

Edge diffraction of transient nondispersive waves in two dimensions is considered. The characteristic single‐edge diffraction pattern for time‐harmonic waves is described by the Fresnel function. The time domain counterpart of the Fresnel function is derived. We argue that the time domain wavefield representation is more insightful than its frequency domain counterpart. It shows, for example, that the diffracted pulse which originates at the shadow casting edge is of opposite polarity in the illuminated and shadow regions. Theoretical and experimental results are compared. [Work supported by ONR.]

中規模渦の数値実験と木星南熱帯撹乱

Numerical experiments are carried out by using the Yamagata-Flierl equation for eddies of a scale intermediate between the Rossby deformation radius and the beta-scale. These experiments are performed for two types of zonal flows, one has a linear shear and the other is sinusoidal velocity profile along meridian. Through these experiments, we tried to investigate the motion and the life time of the intermediate scale eddies in the cases of linear shear zonal flow, and attempted to compare the results with the development of the South Tropical Disturbance (STrD) observed in 1979-81 on Jupiter for the cases of sinusoidal velocity profile.From the experiments for the case of linear shear flow, we found the following facts.(1) If the eddy and zonal flow have the same sign of vorticity, the eddy can survive stably. If the eddy and zonal flow have the opposite sign of vorticity, the eddy disappears or is deformed remarkably. (2) In the case of uniform zonal flow, a cyclonic eddy can survive stably in a high speed westward flow, whereas an anticyclonic eddy can survive in a low speed westward flow. When the westward zonal flow has the non-dispersive wave velocity, both cyclonic and anticyclonic eddies can survive stably. (3) In a low speed westward flow, a cyclonic eddy shifts poleward and an anticyclonic one equatorward. In a high speed westward flow, a cyclonic eddy shifts equatorward and an anticyclonic one poleward. (4) Anticyclonic eddies move westward with higher speed than that of non-dispersive wave. On the other hand, many of cyclonic eddies move westward with lower speed. In one of our experiments for the sinusoidal velocity profile, a cyclonic eddy, whose radius is comparable to the latitudinal width of the westward jet, can go poleward through this jet, and is elongated in northeast and southwest direction in the northern hemisphere before it disappears. The STrD seems to be this kind of cyclonic eddy, because the STrD also had cyclonic vorticity and developed poleward, and because the STrD also was elongated in the same direction as our results. The life time and longitudinal motion of this eddy is not consistent with those of the STrD, but through collisions with small vortices the STrD may get a long life time.

Dispersive waves and caustics

The Lagrange manifold (WKB) formalism enables the determination of the asymptotic series solution of linear, non‐dispersive wave equations at turning points. The formalism is adapted to include those equations which model dispersive waves.

Wave propagation and growth on a surface front in a two-layer geostrophic current

We study analytically and numerically small amplitude perturbations of a geostrophically balanced semi-infinite layer of light water having a surface front and lying above a heavier layer of finite vertical thickness which is at rest in the mean. In contrast with previous studies where the latter layer was infinitely deep we find that the equilibrium is always unstable regardless of the distribution of potential vorticity, and the maximum growth rates are generally much larger than in the one-layer case. The amplifying ageostrophic wave transfers kinetic energy from the basic shear flow as well as potential energy. Good quantitative agreement is found with the laboratory experiments of Griffiths and Linden (1982), and our model seems to be the simplest one for future investigations of cross frontal mixing processes by finite amplitude waves. The propagation speed of very low frequency and nondispersive frontal waves is also computed and is shown to decrease with increasing bottom layer depth.