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 $\text{Rey}\text{gsim}3\times {10}^3$, 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}$forastarat1\mathrm{k}\mathrm{p}\mathrm{c}withangularvelocity$\Omega_$. This should be regarded as a lower limit: it excludes pressure fluctuations, herringbone flows, Stuart vortices, and fully developed turbulence (for $\text{Rey}\text{gsim}{10}^6$).