Growth rate of the tidal p-mode g-mode instability in coalescing binary neutron stars

We recently described an instability due to the nonlinear coupling of p-modes to g-modes and, as an application, we studied the stability of the tide in coalescing binary neutron stars. Although we found that the tide is p-g unstable early in the inspiral and rapidly drives modes to large energies, our analysis only accounted for three-mode interactions. Venumadhav, Zimmerman, and Hirata showed that four-mode interactions must also be accounted for as they enter into the analysis at the same order. They found a near-exact cancellation between three- and four-mode interactions and concluded that while the tide in binary neutron stars can be p-g unstable, the growth rates are not fast enough to impact the gravitational wave signal. Their analysis assumes that the linear tide is incompressible, which is true of the static linear tide (the m=0 harmonic) but not the non-static linear tide (m=+/- 2). Here we account for the compressibility of the non-static linear tide and find that the three- and four-mode interactions no longer cancel. As a result, we find that the instability can rapidly drive modes to significant energies (there is time for several dozen e-foldings of growth before the binary merges). We also show that linear damping interferes with the cancellation and may further enhance the p-g growth rates. The early onset of the instability (at gravitational wave frequencies near 50 Hz), the rapid growth rates, and the large number of unstable modes (> 10^3), suggest that the instability could impact the phase evolution of gravitational waves from binary neutron stars. Assessing its impact will require an understanding of how the instability saturates and is left to future work.Comment: 28 pages, 14 figures, matches version published in Ap

Effects of the oceans on polar motion: Extended investigations

Matrix formulation of the tide equations (pole tide in nonglobal oceans); matrix formulation of the associated boundary conditions (constraints on the tide velocity at coastlines); and FORTRAN encoding of the tide equations excluding boundary conditions were completed. The need for supercomputer facilities was evident. Large versions of the programs were successfully run on the CYBER, submitting the jobs from SUNY through the BITNET network. The code was also restructured to include boundary constraints

Monitoring of the water particle velocity field near the seabed under different wave and tidal scenarios: a real case

Monitoring of water particle velocity on the sea bed is crucial to study morphological shore changes in a coast at intermediate and shallow water depth under progressive surface waves and tidal flow current. Therefore, 3-D particle velocity was monitored continuously at the bottom of Santa Maria del Mar (SMM) beach (SW Spain) by means of a single point current meter during 3 weeks in 2007 since August 28. The current meter was placed at 0.45m above the seabed in order to acquire instantaneous velocity. Wave properties (height and period) were taken from the nearby wave buoy and tidal data were taken from a tidal gauge station. Wave-induced bottom particle velocities were obtained during spring and neap tides at a d/L (depth over wave length) parameter ranging from 0.06 to 0.3. Bottom water particle velocity near the seabed ranges from 0 to ± 0.5 m/sec of which about 82% does not exceed 0.2 m/sec during monitoring. Therefore, only 18% of the surveyed water particle velocities exceed the critical Shield parameter of the beach sand (d50 = 0.23mm) which is about 0.05-0.2 depending on Reynolds number. Results show that maximum horizontal speed is obviously lower during the slack tide (high or low tide) in comparison with flood tide and ebb tide. Moreover, speed is higher during ebb tide in comparison to adjacent flood tide, with steady wave climate. Finally and among other conclusions, the maximum real values of the bottom current surveyed in SMM, as well as the Shield parameter, substantially coincide with the theoretical estimates calculated for a given wave and tidal climate

Effects of the oceans on polar motion: Extended investigations

A method was found for expressing the tide current velocities in terms of the tide height (with all variables expanded in spherical harmonics). All time equations were then combined into a single, nondifferential matrix equation involving only the unknown tide height. The pole tide was constrained so that no tidewater flows across continental boundaries. The constraint was derived for the case of turbulent oceans; with the tide velocities expressed in terms of the tide height. The two matrix equations were combined. Simple matrix inversion then yielded the constrained solution. Programs to construct and invert the matrix equations were written. Preliminary results were obtained and are discussed

A comparison of optical and radar measurements of mesospheric winds and tides

Optical measurements of mesospheric winds by Fabry‐Perot spectrometers, FPSs, at Mawson, 67.6°S 62.9°E, and Davis, 68.6°S 78.0°E, Antarctica are compared with similar measurements obtained using a spaced‐antenna MF radar at Davis. The FPSs observed the OH emission. Different analysis procedures, used to determine the mean wind, and amplitude and phase of the semidiurnal tide, have been compared. At these latitudes the diurnal tide is weak and the semi‐diurnal tide, although highly variable in amplitude, is usually the dominant periodicity. When comparing the amplitude and phase of the semidiurnal tide good agreement is obtained between measurements by the two instruments

Tidal perturbations on the satellite 1967-92A

The orbit of the 1967-92A satellite was studied to ascertain the extent to which tidal forces contribute to orbital perturbations. Parameters describing the ocean tide potential-in particular for the M2 and S2 constituents-were estimated. Since the ocean tide potential is less well known than the solid Earth tide, the ocean tide parameter estimation is based upon the use of a value of 0.3 for the solid Earth tide Love number in the orbit determination procedure. These tidal parameter values are in good agreement with those appearing in numerical models of the M2 and S2 tides derived from surface data