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 $\Rey \gsim 10^{6}$).