Planetary and Gravity Waves in a Polar Basin

AbstractThe eigenfrequencies of freely propagating barotropic, divergent, planetary waves and gravity waves in a spherical polar cap are presented using an approximation in which full spherical geometry is retained in the derivation of the wave amplitude equation. Subsequently, the colatitude angle in the coefficients of the wave amplitude equation is fixed, thereby allowing the eigenvalue problem to be solved using analytical methods. The planetary wave frequencies are compared with published results that adopt the polar-plane approximation to solve the equivalent free-wave problem. Low-order planetary wave frequencies calculated in this study agree well with the polar-plane approximation results. The sensitivity of the wave frequencies to the choice of the fixed colatitude in the coefficients of the wave amplitude equation is discussed.

Download Full-text

Generalized function treatment of the Alfvén-gravity wave problem

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171283000344 ◽

1983 ◽

Vol 6 (2) ◽

pp. 395-402

Author(s):

L. Debnath ◽

K. Vajravelu

Keyword(s):

Steady State ◽

Gravity Waves ◽

Function Method ◽

Radiation Condition ◽

Physical Significance ◽

Generalized Function ◽

Wave Problem ◽

Physical Interest ◽

Electrically Conducting ◽

Electrically Conducting Fluid

A study is made of the steady-state Alfvén-gravity waves in an inviscid incompressible electrically conducting fluid with an interface due to a harmonically oscillating pressure distribution acting on the interface. The generalized function method is employed to solve the problem in the fluid of infinite, finite and shallow depth. A unique solution of physical interest is derived by imposing the Sommerfeld radiation condition at infinity. Several limiting cases of physical interest are obtained from the present analysis. The physical significance of the solutions and their limiting cases are discussed.

Download Full-text

INTERACTION OF WAVES AND A TURBULENT CURRENT

Coastal Engineering Proceedings ◽

10.9753/icce.v15.22 ◽

1976 ◽

Vol 1 (15) ◽

pp. 22 ◽

Cited By ~ 10

Author(s):

J.D.A. Van Hoften ◽

S. Karaki

Keyword(s):

Experimental Investigation ◽

Gravity Waves ◽

Wave Amplitude ◽

Current System ◽

Bottom Shear Stress ◽

Wave Dissipation ◽

Wave Channel ◽

Amplitude Attenuation ◽

Current Interaction ◽

The Waves

An experimental investigation was made to study wave-current interaction. Wave amplitude attenuation was measured along a laboratory wave channel to compare wave dissipation with and without flow. Mean, wave, and turbulent velocities were also measured to determine the modifications of the flow imposed by the gravity waves propogating with the current. The process of energy transfer in the wave current system was studied. Energy was found to be extracted from the waves, diffused downward and dissipated by an increase in bottom shear stress.

Download Full-text

Are polar cap gravity waves a heat source for the high-latitude thermosphere?

Geophysical Research Letters ◽

10.1029/98gl01026 ◽

1998 ◽

Vol 25 (9) ◽

pp. 1487-1490 ◽

Cited By ~ 7

Author(s):

J. L. Innis ◽

P. A. Greet ◽

P. L. Dyson

Keyword(s):

Heat Source ◽

Gravity Waves ◽

High Latitude ◽

Polar Cap

Download Full-text

Parametrically forced gravity waves in a circular cylinder and finite-time singularity

Journal of Fluid Mechanics ◽

10.1017/s0022112008000165 ◽

2008 ◽

Vol 599 ◽

pp. 205-228 ◽

Cited By ~ 23

Author(s):

S. P. DAS ◽

E. J. HOPFINGER

Keyword(s):

Surface Tension ◽

Circular Cylinder ◽

Gravity Waves ◽

Finite Time ◽

Wave Breaking ◽

Wave Amplitude ◽

Frequency Range ◽

Jet Formation ◽

Time Singularity ◽

Finite Time Singularity

In this paper we present results on parametrically forced gravity waves in a circular cylinder in the limit of large fluid-depth approximation. The phase diagram that shows the stability-forcing-amplitude threshold and the wave-breaking threshold has been determined in the frequency range of existence of the lowest axisymmetric wave mode. The instability is shown to be supercritical for forcing frequencies at and above the natural frequency and subcritical below in a frequency range where the instability and breaking thresholds do not coincide. Above the instability threshold, the growth in wave amplitude is exponential, but with an initial time delay. The wave-amplitude response curve of stationary wave motions exhibits steady-state wave motion, amplitude modulations and bifurcations to other wave modes at frequencies where the parametric instability boundary of the axisymmetric mode overlaps with the neighbouring modes. The amplitude modulations are either on a slow time scale or exhibit period tripling and intermittent period tripling, without wave breaking. In the wave-breaking regime, a finite-time singularity may occur with intense jet formation, a phenomenon demonstrated by others in fluids of high viscosity and large surface tension. Here, this singular behaviour with jet formation is demonstrated for a low viscosity and low kinematic surface tension liquid. The results indicate that the jet is driven by inertial collapse of the cavity created at the wave trough. Therefore, the jet velocity is determined by the wave fluid velocity but depends, in addition, on kinematic surface tension and viscosity as these affect the last stable wave crest shape and the cavity size.

Download Full-text

A note on the divergence effect and the Lagrangian-mean surface elevation in periodic water waves

Journal of Fluid Mechanics ◽

10.1017/s0022112088000989 ◽

1988 ◽

Vol 189 ◽

pp. 235-242 ◽

Cited By ~ 24

Author(s):

M. E. Mcintyre

Keyword(s):

Free Surface ◽

Velocity Field ◽

Gravity Waves ◽

Water Waves ◽

Wave Amplitude ◽

Exact Expression ◽

Mean Velocity ◽

Surface Gravity Waves ◽

Generalized Lagrangian ◽

Divergence Effect

Longuet-Higgins’ exact expression for the increase in the Lagrangian-mean elevation of the free surface due to the presence of periodic, irrotational surface gravity waves is rederived from generalized Lagrangian-mean theory. The raising of the Lagrangian-mean surface as wave amplitude builds up illustrates the non-zero divergence of the Lagrangian-mean velocity field in an incompressible fluid.

Download Full-text

A Model for the Periodic Water Wave Problem and Its Long Wave Amplitude Equations

Nonlinear Water Waves - Tutorials, Schools, and Workshops in the Mathematical Sciences ◽

10.1007/978-3-030-33536-6_8 ◽

2019 ◽

pp. 123-138

Author(s):

Roman Bauer ◽

Patrick Cummings ◽

Guido Schneider

Keyword(s):

Water Wave ◽

Wave Amplitude ◽

Amplitude Equations ◽

Wave Problem ◽

Water Wave Problem ◽

Long Wave

Download Full-text

Evidence for thermospheric gravity waves in the southern polar cap from ground-based vertical velocity and photometric observations

Annales Geophysicae ◽

10.5194/angeo-19-533-2001 ◽

2001 ◽

Vol 19 (5) ◽

pp. 533-543 ◽

Cited By ~ 6

Author(s):

J. L. Innis ◽

P. A. Greet ◽

P. L. Dyson

Keyword(s):

Gravity Waves ◽

Vertical Velocity ◽

Auroral Oval ◽

Local Times ◽

Polar Cap ◽

Photometric Observations ◽

Fabry Perot ◽

Waves And Tides ◽

Thermospheric Dynamics ◽

Vertical Winds

Abstract. Zenith-directed Fabry-Perot Spectrometer (FPS) and 3-Field Photometer (3FP) observations of the λ630 nm emission (~240 km altitude) were obtained at Davis station, Antarctica, during the austral winter of 1999. Eleven nights of suitable data were searched for significant periodicities common to vertical winds from the FPS and photo-metric variations from the 3FP. Three wave-like events were found, each of around one or more hours in duration, with periods around 15 minutes, vertical velocity amplitudes near 60 ms–1 , horizontal phase velocities around 300 ms–1 , and horizontal wavelengths from 240 to 400 km. These characteristics appear consistent with polar cap gravity waves seen by other workers, and we conclude this is a likely interpretation of our data. Assuming a source height near 125 km altitude, we determine the approximate source location by calculating back along the wave trajectory using the gravity wave property relating angle of ascent and frequency. The wave sources appear to be in the vicinity of the poleward border of the auroral oval, at magnetic local times up to 5 hours before local magnetic midnight.Key words. Meteorology and atmospheric dynamics (thermospheric dynamics; waves and tides)

Download Full-text