Rayleigh - Taylor Gravity Waves and Quasiperiodic Oscillation Phenomenon in X-ray Binaries

Accretion onto compact objects in X-ray binaries [black hole, neutron star (NS), white dwarf] is characterized by non-uniform flow density profiles. Such an effect of heterogeneity in presence of gravitational forces and pressure gradients exhibits Raylegh-Taylor gravity waves (RTGW). They should be seen as quasioperiodic wave oscillations (QPO). In this paper I show that the main QPO frequency, which is very close to the Keplerian frequency, is split into separate frequencies (hybrid and low branch) under the influence of the gravitational forces in the rotational frame of reference. The observed low and high QPO frequencies are an intrinsic signature of the RTGW. I elaborate the conditions for the density profile when the RTGW oscillations are stable. A comparison of the inferred QPO frequencies with QPO observations is presented. I find that hectohertz frequencies detected from NS binaries can be identified as the RTGW low branch frequencies. I also predict that an observer can see the double NS spin frequency during the NS long (super) burst events when the pressure gradients and buoyant forces are suppressed. The Coriolis force is the only force which acts in the rotational frame of reference and its presence causes perfect coherent pulsations with a frequency twice of the NS spin.Comment: 14 pages and 2 figures, ApJ in pres

Effect of Rossby and Alfv\'{e}n waves on the dynamics of the tachocline

To understand magnetic diffusion, momentum transport, and mixing in the interior of the sun, we consider an idealized model of the tachocline, namely magnetohydrodynamics (MHD) turbulence on a $\beta$ plane subject to a large scale shear (provided by the latitudinal differential rotation). This model enables us to self-consistently derive the influence of shear, Rossby and Alfv\'{e}n waves on the transport properties of turbulence. In the strong magnetic field regime, we find that the turbulent viscosity and diffusivity are reduced by magnetic fields only, similarly to the two-dimensional MHD case (without Rossby waves). In the weak magnetic field regime, we find a crossover scale ($L\_R$) from a Alfv\'{e}n dominated regime (on small scales) to a Rossby dominated regime (on large scales). For parameter values typical of the tachocline, $L\_R$ is larger that the solar radius so that Rossby waves are unlikely to play an important role in the transport of magnetic field and angular momentum. This is mainly due to the enhancement of magnetic back-reaction by shearing which efficiently generates small scales, thus strong currents

Rossby waves in rapidly rotating Bose-Einstein condensates

We predict and describe a new collective mode in rotating Bose-Einstein condensates, which is very similar to the Rossby waves in geophysics. In the regime of fast rotation, the Coriolis force dominates the dynamics and acts as a restoring force for acoustic-drift waves along the condensate. We derive a nonlinear equation that includes the effects of both the zero-point pressure and the anharmonicity of the trap. It is shown that such waves have negative phase speed, propagating in the opposite sense of the rotation. We discuss different equilibrium configurations and compare with those resulting from the Thomas-Fermi approximation.Comment: 4 pages, 2 figures (submitted to PRL

Coriolis force in Geophysics: an elementary introduction and examples

We show how Geophysics may illustrate and thus improve classical Mechanics lectures concerning the study of Coriolis force effects. We are then interested in atmospheric as well as oceanic phenomena we are familiar with, and are for that reason of pedagogical and practical interest. Our aim is to model them in a very simple way to bring out the physical phenomena that are involved.Comment: Accepted for publication in European Journal of Physic

On the mutual adjustment of pressure and velocity distributions in certain simple current systems, II

In a previous report (Rossby, 1937) the author investigated certain changes in the mass distribution which accompany t he slow lateral diffusion of momentum in a straight parallel current in an unlimited ocean of constant depth. The principal results of this investigation may be st ated as follows:..

Editor\u27s Commentary: On the mutual adjustment of pressure and velocity distributions in certain simple current systems

These are the original geostrophic adjustment papers. Rossby starts out by asking what,if anything, limits the ability for a flow to be in geostrophic balance (to precisely follow pressure contours on a rotating planet). This topic is now a classroom standard, but we often forget how insightful the original articles are..

Editor\u27s Commentary: Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi permanent centers of action

Rossby waves! Beta-plane! Here Carl-Gustav Rossby, motivated by observations of weather patterns that move upstream relative to the dominant mid-latitude eastward wind flow, formulates a com-pletely novel linearized theory to account for the tendency for large-scale disturbances to move westward and smaller-scale disturbances to move eastward relative to the winds

On displacements and intensity changes of atmospheric vortices

Aerological investigations conducted during the last few years have revealed that the long, meandering disturbances characteristic of the middle latitude belt of westerlies in the upper troposphere frequently increase in amplitude until troughs and ridges finally are cut off from the main current, thus forming cold cyclonic vortices on the equatorial side of the west-wind belt and warm anticyclonic vortices on the north side thereof. True vortices, with nearly vertical axes, are thus characteristic phenomena not only of equatorial regions where they appear as tropical cyclones but also of middle latitudes. The middle latitude vortices seem to be phenomena of great stability which have sometimes been observed to persist for several weeks

On the mutual adjustment of pressure and velocity distributions in certain simple current systems

The writer (J) recently advanced the hypothesis that the horizontal pressure gradients observed in the current systems of the atmosphere and the ocean to a large extent must be interpreted as reactions to the Coriolis\u27 forces impressed upon these systems by the rotation of the earth. Observational support for this point of view was found in the fact that both the temperature-salinity and oxygen-salinity correlation curves obtained from stations on both sides of the Gulf Stream in the region between Nova Scotia and Bermuda are very nearly identical, even though the individual isotherms may drop as much as 700 meters between the slope water basin and the Sargasso Sea. This mass distribution and the resulting pressure distribution are most readily interpreted as the result of a continuous banking process caused by the action of the Coriolis\u27 forces on the moving masses of the Gulf Stream system. Theoretical support was found in a theorem by Taylor (2) ...

On the mutual adjustment of pressure and velocity distributions in certain simple current systems, II

In a previous report (Rossby 1937) the author investigated certain changes in the mass distribution which accompany the slow lateral diffusion of momentum in a straight parallel current in an unlimited ocean of constant depth