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 \(\Rey \gsim 3 \times 10^{3}\), the laminar Stokes flow is unstable and helical, oscillating Taylor--G\"ortler vortices develop. The gravitational wave strain generated by the resulting kinetic-energy fluctuations is computed in both \(+\) and \(\times\) polarizations as a function of time. It is found that the signal-to-noise ratio for a coherent, \(10^{8}\)-{\rm s} integration with LIGO II scales as \( 6.5 (\Omega_*/10^{4} {\rm rad} {\rm s}^{-1})^{7/2}\) for a star at 1 {\rm kpc} with angular velocity \(\Omega_*\). This should be regarded as a lower limit: it excludes pressure fluctuations, herringbone flows, Stuart vortices, and fully developed turbulence (for \(\Rey \gsim 10^{6}\)).