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