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

Onset of unsteady horizontal convection in rectangle tank at Pr=1Pr=1

The horizontal convection within a rectangle tank is numerically simulated. The flow is found to be unsteady at high Rayleigh numbers. There is a Hopf bifurcation of $Ra$ from steady solutions to periodic solutions, and the critical Rayleigh number $Ra_c$ is obtained as $Ra_c=5.5377\times 10^8$ for the middle plume forcing at $Pr=1$, which is much larger than the formerly obtained value. Besides, the unstable perturbations are always generated from the central jet, which implies that the onset of instability is due to velocity shear (shear instability) other than thermally dynamics (thermal instability). Finally, Paparella and Young's [J. Fluid Mech. 466 (2002) 205] first hypotheses about the destabilization of the flow is numerically proved, i.e. the middle plume forcing can lead to a destabilization of the flow.Comment: 4pages, 6 figures, extension of Chin. Phys. Lett. 2008, 25(6), in pres

On the energetics of the Gulf Stream at 73W

From September 1980 through May 1983 a series of nineteen sections of velocity profiles were obtained across the Gulf Stream 200 km northeast of Cape Hatteras. By decomposing the velocity and temperature observations into mean and fluctuating fields in two coordinate systems, geographic (or Eulerian) and \u27stream\u27 coordinates, it is shown that at least ⅔ of the eddy kinetic and potential energy is caused by the meandering of a well defined baroclinic front with a structure that is nearly independent of space and time. It is also shown that more than 95% of the kinetic energy of the front can be accounted for by a barotropic and a baroclinic mode with near equipartition between the two.The cross-stream baroclinic, barotropic, and pressure-work terms in the eddy energy production equation are estimated to determine what processes contribute to the rapid growth of meandering after the current leaves the coast. In order of importance, the cross-stream average of the baroclinic conversion term is a factor three larger than the other two. The cross-stream averaged production of eddy energy is, however, clearly too large to be consistent with the observed rate of growth of the meander envelope since it would lead to a doubling of eddy kinetic and potential energy in only 2.1 days or 50 km following the mean flow. It is shown that in the case of the baroclinic conversion term the large cross-stream covariances 〈u′T′〉 have a simple geometric interpretation in terms of meander growth (and decay). They represent a down (or up) gradient heat flux that is not actually participating in the conversion processes suggesting that the baroclinic production terms are nearly horizontally nondivergent. Similarly, the pressure-work terms must be very nearly horizontally nondivergent (geostrophy). Thus, estimates of energy conversion rates are bound to be greatly exaggerated unless both horizontal components are included. Furthermore, conclusions about the relative importance of the cross-stream conversion terms to the production of eddy energy depend upon their horizontal divergence being in the same proportions, a very unsatisfactory assumption.A simple kinematic model is used to show that the amount of energy needed to support meander growth is quite small. It is clear that to determine these rates experimentally puts great stress on conventional measurement procedures and suggests that alternative approaches such as paying more attention to boundary or flux conditions might be more rewarding in future studies

An oceanic vorticity meter

An acoustical method of determining the relative vorticity of oceanic motions is advanced. By transmitting signals in opposite directions around a closed loop, for example a 3 km triangle, one can obtain directly the circulation, which by virtue of Stoke\u27s theorem is equivalent to the average vorticity of the enclosed fluid times the area...

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..

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:..

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

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