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. <br><br> 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 &theta;₀ 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

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>_y,<I>k</I>_x) space, whose centre is displaced &minus;&beta;/2 &omega; units along the negative <I>k</I>_x 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

The role of cosmic rays and Alfven waves in the structure of the galactic halo

The effect that cosmic rays and the Alfven waves they generate have on the structure of the plasma distribution perpendicular to the galactic disk is examined. It is shown that the plasma distribution exhibits two length scales and the predicted values of gas density far from the galactic plane indicate that models involving hydrostatic equilibrium should be replaced by those allowing for a galactic wind

Use of thermal infrared and colour infrared imagery to detect crop moisture stress

The author has identified the following significant results. In the presence of variable plant cover (primarily percent cover) and variable available water content, the remotely sensed apparent temperatures correlate closely with plant cover and poorly with soil water. To the extent that plant cover is not systematically related to available soil water, available water in the root zone values may not be reliably predicted from the thermal infrared data. On the other hand, if plant cover is uniform and the soil surface is shown in a minor way, the thermal data indicate plant stress and consequently available water in the soil profile

Comment on "Plasma ionization by annularly bounded helicon waves" [Phys . Plasmas 13, 063501 (2006)]

The neoclassical calculation of the helicon wave theory contains a fundamental flaw. Use is made of a proportional relationship between the magnetic field and its curl to derive the Helmholtz equation describing helicon wave propagation; however, by the fundamental theorem of Stokes, the curl of the magnetic field must be perpendicular to that portion of the field contributing to the local curl. Reexamination of the equations of motion indicates that only electromagnetic waves propagate through a stationary region of constant pressure in a fully ionized, neutral medium.Comment: 7 pages, 1 figure, to be published in Phys. Plasmas, http://link.aip.org/link/?PHPAEN/16/054701/