I will skip the derivation and just give the phase speeds for the two modes, respectively. Pdf stability of abstractwave equation with delay and a. Aug 26, 2014 stability of abstractwave equation with delay and a kelvinvoigt damping article pdf available in asymptotic analysis 9512 august 2014 with 286 reads how we measure reads. Jinyi yu coriolis force against a topographic boundary such as a coastline, or a waveguide such as the equator. In the generalized wave equation, the degree of viscoelasticity varies between zero and unity, and is defined by a controlling parameter. The unique feature of the kelvin wave is its unidirectional propagation. Generalized viscoelastic wave equation geophysical journal. Pdf on a kelvinvoigt viscoelastic wave equation with. The existence of the kelvin wave relies on a gravity and stable strati. Kelvin waves in the nonlinear shallow water equations on the sphere. There are two classes of solutions to equations 12.
That means that the net amplitude caused by two or more waves traversing the same space is the sum of the amplitudes which would have been produced by the individual waves separately. Lecture notes fluid dynamics of the atmosphere and ocean. Finish kelvin waves we were considering an ocean x 0 with a coast at x 0 in the northern hemisphere. Pdf frequency analysis of a wave equation with kelvin. We give a detailed spectrum analysis of the system operator, from which we show that the generalized eigenfunc. Kelvin wave propagation along an irregular coastline by l.
Nonhamiltonian kelvin wave generation on vortices in bose. There initially appears to be two solutions associated with the plus and minus signs in equation 12. Unlike the waves you see at the beach, kelvin waves do not curl over and then. In many cases for example, in the classic wave equation, the equation describing the wave is linear. March 2, 2018 ultracold quantum turbulence is expected to decay through a cascade of kelvin waves. Kelvin waves more north and south along coast from south america 4. However, since the xdependence of the kelvin wave is of the travelling wave form, its dispersion relation must be.
The wave equation is a secondorder linear hyperbolic pde that describesthe propagation of a variety of waves, such as sound or water waves. The equation can be written in terms of sea surface height ssh h ast2h 2 hd2 1 b xh 52r2h, 1a where d 5 cof. The kelvin wave let us take the linearized shallow water equation on a fplane with d constant. Linear and nonlinear kelvin wavestropical instability. A feature of a kelvin wave is that it is nondispersive, i. When the elasticity k is constant, this reduces to usual two term wave equation u tt c2u xx where the velocity c p k.
The kelvin wave is also not included in this dispersion relation because of the v6 0 assumption. Thistypeofwaveoccurs next to a lateral boundary such as a shore line in the ocean or a steep mountain range in the atmosphere. The kelvin wave is a special type of gravity wave that is affected by the earths rotation and trapped at the equator or along lateral vertical boundaries such. Wave equation in 1d part 1 derivation of the 1d wave equation vibrations of an elastic string solution by separation of variables three steps to a solution several worked examples travelling waves more on this in a later lecture dalemberts insightful solution to the 1d wave equation. In turn, appropriate corrections can easily be introduced as required. Frequency analysis of a wave equation with kelvinvoigt damping. The kelvin wave is a special type of gravity wave that is affected by the earths rotation and trapped at the equator or along lateral vertical boundaries such as coastlines or mountain ranges. Lindzen national center for atmospheric research, boulder, coio. The shallowwater kelvin wave solution is given in section 2, and the various balance equation approximations to the kelvin wave are given in section 3. Pdf frequency analysis of a wave equation with kelvinvoigt. Kelvin moves moves to the east at 3 ms across pacific in 70 days 2.
It is a wave in the ocean or atmosphere that balances the. Linear and nonlinear kelvin wavestropical instability waves. Kelvin waves the kelvin wave is a largescale wave motion of great practical importance in the earths atmosphere and ocean. When this is true, the superposition principle can be applied. A kelvin wave is a wave in the ocean or atmosphere that balances the earths coriolis force against a topographic boundary such as a coastline, or a. Notice the negative anomaly that starts towards the end of 1972 and propagates up the coast over the next month or so. Carr department of physics, colorado school of mines, 1523 illinois st. The fplane linear shallowwater equations support coastal kelvin waves. It would seem selfevident that the nonlinear dynamics of the kelvin wave needs to be understood as thoroughly as possible. This paper presents a generalized wave equation which unifies viscoelastic and pure elastic cases into a single wave equation. Tang institute of ocoanography, university of british columbia, vancouver received 1 june 1973 and in revised forin 31 december 1973 we discuss the theory of kelvin wave propagation along an infinitely long coast. Such patterns are nearly always the same and are referred to as kelvin ship waves after lord kelvin william thomson who was a leading. Stability and instability results of the wave equation. We would like to show you a description here but the site wont allow us.
The wave equation governs a wide range of phenomena, including gravitational waves, light waves, sound waves, and even the oscillations of strings in string theory. However, if v 0, then we are dealing with a kelvin mode, and we have already shown that the westwardmoving kelvin mode. Journal of physics a mathematical and general 18, 15511560 of the kelvin equation become physically obvious, notably the assumption that the liquid is incompressible, the vapour is an ideal gas, and the interfacial tension is independent of the curvature of the interface. Nov 21, 2019 we consider the wave equation with kelvinvoigt damping in a bounded domain. As noted above surface wave systems of general form always consist of combinations of plane progressive waves of different frequencies and directions. Local view of kelvin wake consists approximately of a plane progressive wave group propagating in direction math \theta\,\. A solid wall makes possible a rather special wave trapped at the wall, a gravity wave modified by rotation. Effect of kelvin voigt damping on spectrum analysis of a wave equation liqing lu, liyan zhao, jing hu communicated by goong chen abstract. For midlatitude kelvin waves traveling on the ocean. Firstorder kelvin wave solution we take the initial data of the system 2.
A kelvin wave is a wave in the ocean or atmosphere that balances the earths coriolis force against a topographic boundary such as a coastline, or a waveguide such as the equator. Equation 5 is the kinematic boundary condition which states that the interface moves up and down with a velocity. An alternative form, which we will discuss later, is the equatorial kelvin wave. The quantity lr is called the equatorial rossby radius. The ab equations fell out of another class of geophysical waves boyd 2001. Frequency analysis of a wave equation with kelvin voigt damping. Chapter 4 the wave equation another classical example of a hyperbolic pde is a wave equation. Let us take the linearized shallow water equation on a f plane with d constant. Let us take the linearized shallow water equation on a fplane with d constant. This establishes a coastal kelvin wave current that. March 2, 2018 ultracold quantum turbulence is expected to. Several eigenvalue problems for each method were solved and compared.
Kk kmay be added to the nonspurious solutions of eq. The exponential stability result proposed by liu and rao z angew math phys zamp 57. A solid wall makes possible a rather special wave trapped. This is a wave equation for which we can obtain a solution of the form h. Primer notes and associated figures are available waves. The value of for the kelvin wave can be obtained from the first law of thermodynamics in the same manner as in maruyama 1968b. On the relation between kelvin waves and the quasi.
Kelvin wave amplitude is negligible at a distance offshore given by the rossby radius of. The waves that most of us are familiar with are the waves at the beachwaves that endlessly curl and crash on the shore. Stabilization of the wave equation with localized kelvinvoigt damping louis tebou florida international university miami searcde university of memphis october 1112, 2014 louis tebou fiu, miami stabilization. Then the wave will travel about 5000km in about 2 months. The m2 tide travels as a kelvin wave up the west coast of canada and around alaska to the tip of the alaskan islands. On kelvin waves in balance models semantic scholar. Lindzen 385 a note on kelvin waves in the atmosphere jams r. Pdf the nonlinear equatorial kelvin wave researchgate.
Equatorial waves forced by brief wind perturbations of the order of a few weeks. Effect of kelvinvoigt damping on spectrum analysis of a wave equation liqing lu, liyan zhao, jing hu communicated by goong chen abstract. The mathematical derivation for kelvin waves can be found in knauss. Introduction and statement of main results the stabilization of the wave equation with localized damping has received a.
Waves in the atmosphere and oceanswaves in the atmosphere and. A kelvin wave is a wave in the ocean or atmosphere that balances the earths coriolis force. But the ocean and atmosphere also have what are called planetary waveswaves of immense scale. The equations of motion in a homogeneous, inviscid ocean by ignoring the. Kelvin wave propagation along an irregular coastline. Waves in the atmosphere and oceanswaves in the atmosphere. For the kelvin wave, how equation of celestial mechanics for which an analytic. In this article, we analyze the dynamics of a nonlinear kelvin wave packet whose structure in longitude is illustrated schematically.
Depending on the medium and type of wave, the velocity v v v can mean many different things, e. Reflects off south america as westward moving rossby wave at 1 ms, 210 days across pacific 3. Free equatorial waves which arise as solutions of unforced equations of motion e. Nonhamiltonian kelvin wave generation on vortices in boseeinstein condensates scott a. Sep 08, 20 a kelvin wave is a wave in the ocean or atmosphere that balances the earths coriolis force against a topographic boundary such as a coastline, or a waveguide such as the equator. The peculiar property of the wave is that the velocity normal to the wall is identically zero. Discrete and continuous dynamical systems series s 9. In view of the similarity of the present solution to kelvin waves, it seems reasonable to call the wave of the solution 2 an atmospheric kelvin wave, noting that the equator plays the same role as a coastal boundary. This article concerns a onedimensional wave equation with a small amount of kelvinvoigt damping. We consider the wave equation with kelvinvoigt damping in a bounded domain. Derived the fixed depth, barotropic, inviscid vorticity equation starting from kelvins circulation theorem.
Awavemoderelatedtoinertiagravitywavesisthe kelvin wave. A conceptually simple derivation of the kelvin equation. To follow the kelvin wave, shown is a longitudetime plot. The kelvin wave is the gravest and most energetic latitudinal mode in the tropical ocean. This article concerns a onedimensional wave equation with a small amount of kelvin voigt damping. We had a wave with no crossshore velocity u 0, an alongshore velocity given by v vo exp. This wave propagates toward the east on the equator, with rapid decay in the wave. Eigenvalue approximations of the wave equation with local kelvinvoigt damping are presented using the well known chebyshevtau spectral method. The basic dynamics of kelvin waves the same as for. The nonlinear equatorial kelvin wave ams journals american. Eigenvalue approximations of the wave equation with local. It is a wave in the ocean or atmosphere that balances the cilif i t t hi b d h tli ess228 prof. Stability of abstractwave equation with delay and a kelvinvoigt damping article pdf available in asymptotic analysis 9512 august 2014 with 286 reads how we measure reads.