9,712 research outputs found
Instability of combined gravity-inertial-Rossby waves in atmospheres and oceans
The properties of the instability of combined gravity-inertial-Rossby waves
on a β-plane are investigated. The wave-energy exchange equation shows
that there is an exchange of energy with the background stratified medium.
The energy source driving the instability lies in the background enthalpy
released by the gravitational buoyancy force.
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It is shown that if the phase speed of the westward propagating low
frequency-long wavelength Rossby wave exceeds the Poincaré-Kelvin (or
"equivalent" shallow water) wave speed, instability arises from the merging
of Rossby and Poincaré modes. There are two key parameters in this
instability condition; namely, the equatorial/rotational Mach (or Froude)
number <I>M</I> and the latitude θ<sub>0</sub> of the β-plane. In general waves
equatorward of a critical latitude for given <I>M</I> can be driven unstable, with
corresponding growth rates of the order of a day or so. Although these
conclusions may only be safely drawn for short wavelengths corresponding to a
JWKB wave packet propagating internally and located far from boundaries,
nevertheless such a local instability may play a significant role in
atmosphere-ocean dynamics
Trans-sonic cusped shaped, periodic waves and solitary waves of the electrostatic ion-cyclotron type
By adopting an essentially fluid dynamic viewpoint we derive the wave structure equation for stationary, fully nonlinear, electrostatic, ion-cyclotron waves. The existence of two fundamental constants of the motion, namely, conservation of momentum flux parallel to the ambient magnetic field, and energy flux parallel to the direction of wave propagation, enables the wave structure equation to be reduced to a first order differential equation, which has solutions that are physically transparent. The analysis shows that sufficiently oblique waves, propagating at sub-ion acoustic speeds, form soliton pulse-like solutions whose amplitudes are greatest for perpendicular propagation. Waves that propagate supersonically have periodic cnoidal waveforms, which are asymmetric about the compressive and rarefactive phases of the wave. It is also shown that there exist critical driver fields for which the end point of the compressive phase goes sonic (in the wave frame), with the consequence that the wave form develops a cusp. It is possible that this trans-sonic, choked flow feature provides a mechanism for the 'spiky' waveforms observed in auroral electric field measurements
Instabilities in decelerating supersonic flows with applications to cosmic ray shocks
The nature of instabilities in cosmic ray shocks is investigated by using two distinct models for the shock wave. For wavelengths which are short relative to the thickness of the shock wave, the shock is treated as a smoothly decelerating low, and an appropriate JWKB type expansion is used to describe the perturbations to the flow. In this, the short wavelength regime, the presence of squeezing and an effective g renders strong cosmic ray shocks unstable in a way which is similar to instabilities in other supersonic flows, such as in de Laval nozzle flow or a heat conduction dominated shock wave. In the long wavelength limit, where the shock is treated as a discontinuous transition, a stability function is derived which, if negative, corresponds to unstable disturbances growing exponentially in time. In this case, it was found that if the cosmic ray fluid is relativistic (gamma sub c = 4/3) and the background plasma ideal (gamma = 5/3), then strong shocks are unstable
Charge Distribution Near Oxygen Vacancies in Reduced Ceria
Understanding the electronic charge distribution around oxygen vacancies in
transition metal and rare earth oxides is a scientific challenge of
considerable technological importance. We show how significant information
about the charge distribution around vacancies in cerium oxide can be gained
from a study of high resolution crystal structures of higher order oxides which
exhibit ordering of oxygen vacancies. Specifically, we consider the
implications of a bond valence sum analysis of CeO and
CeO. To illuminate our analysis we show alternative
representations of the crystal structures in terms of orderly arrays of
co-ordination defects and in terms of flourite-type modules. We found that in
CeO, the excess charge resulting from removal of an oxygen atom
delocalizes among all three triclinic Ce sites closest to the O vacancy. In
CeO, the charge localizes on the next nearest neighbour Ce atoms.
Our main result is that the charge prefers to distribute itself so that it is
farthest away from the O vacancies. This contradicts \emph{the standard picture
of charge localisation} which assumes that each of the two excess electrons
localises on one of the cerium ions nearest to the vacancy. This standard
picture is assumed in most calculations based on density functional theory
(DFT). Based on the known crystal structure of PrO, we also
predict that the charge in CeO will be found in the second
coordination shell of the O vacancy. Although this review focuses on bulk
cerium oxides our approach to characterising electronic properties of oxygen
vacancies and the physical insights gained should also be relevant to surface
defects and to other rare earth and transition metal oxides.Comment: 20 pages, 23 figures. The replacement file has a new format for the
figures are the document layout but no change in content. v3 has the
following main changes: 1. The abstract and introduction were extensively
revised. 2. Sec. IV was removed. 3. The Conclusion was rewritte
Propagation properties of Rossby waves for latitudinal β-plane variations of <I>f</I> and zonal variations of the shallow water speed
Using the shallow water equations for a rotating layer of fluid, the wave and dispersion equations for Rossby waves
are developed for the cases of both the standard β-plane approximation for the latitudinal variation of the
Coriolis parameter <I>f</I> and a zonal variation of the shallow water speed. It is well known that the wave normal diagram for the
standard (mid-latitude) Rossby wave on a β-plane is a circle in wave number (<I>k</I><sub>y</sub>,<I>k</I><sub>x</sub>) space, whose
centre is displaced −β/2 ω units along the negative <I>k</I><sub>x</sub> axis, and whose radius is less than this displacement, which means that phase
propagation is entirely westward. This form of anisotropy (arising from the
latitudinal <I>y</I> variation of <I>f</I>), combined with the highly dispersive nature of the wave, gives rise to a group
velocity diagram which permits eastward as well as westward propagation. It is shown that the group velocity
diagram is an ellipse, whose centre is displaced westward, and whose major and minor axes give the
maximum westward, eastward and northward (southward) group speeds as functions of the frequency and a parameter
<I>m</I> which measures the ratio of the low frequency-long wavelength Rossby wave speed to the shallow water speed. We
believe these properties of group velocity diagram have not been elucidated in this way before. We present a
similar derivation of the wave normal diagram and its associated group velocity curve for the case of a zonal
(<I>x</I>) variation of the shallow water speed, which may arise when the depth of an ocean varies zonally from a
continental shelf
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