Gravitational Radiation from Nonaxisymmetric Spherical Couette Flow in a Neutron Star

The gravitational-wave signal generated by global, nonaxisymmetric shear flows in a neutron star is calculated numerically by integrating the incompressible Navier-Stokes equation in a spherical, differentially rotating shell. At Reynolds numbers Re ≳ 3 × 10 3 the laminar Stokes flow is unstable, and helical, oscillating Taylor-Görtler vortices develop. The gravitational-wave strain generated by the resulting kinetic energy fluctuations is computed in both plus and cross polarizations as a function of time. It is found that the signal-to-noise ratio for a coherent, 10 8 s integration with LIGO II scales as 6.5[Ω * /(10 4 rad s -1 )] 7/2 for a star at 1 kpc with angular velocity Ω * . This should be regarded as a lower limit: it excludes pressure fluctuations, herringbone flows, Stuart vortices, and fully developed turbulence (for Re ≳ 10 6 ).