Gravitational radiation from nonaxisymmetric spherical Couette flow in a neutron star
Abstract
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--Görtler vortices develop. The gravitational wave strain generated by the resulting kinetic-energy fluctuations is computed in both
+
and
×
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(
Ω
∗
/
10
4
rad
s
−1
)
7/2
for a star at 1 {\rm 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 $\Rey \gsim 10^{6}$).