  We investigate the complex-time analytic structure of solutions of the
3D-axisymmetric, wall-bounded, incompressible Euler equations, by starting with
the initial data proposed in Luo and Hou (2014), to study a possible
finite-time singularity. We use our pseudospectral Fourier-Chebyshev method,
with quadruple-precision arithmetic, to compute the time-Taylor series
coefficients of the flow fields, up to a high order. We show that the resulting
approximations display early-time resonances; the initial spatial location of
these structures is different from that for the tygers, which we have obtained
in Kolluru et al. (2022). We then perform asymptotic analysis of the
Taylor-series coefficients, by using generalised ratio methods, to extract the
location and nature of the convergence-limiting singularities and demonstrate
that these singularities are distributed around the origin, in the complex-t2
plane, along two curves that resemble the shape of an eye. We obtain similar
results for the 1D wall-approximation (of the full 3D-axisymmetric Euler
equation) called the 1D HL model, for which we use Fourier-pseudospectral
methods to compute the time-Taylor series coefficients of the flow fields. Our
work examines the link between tygers, in Galerkin-truncated pseudospectral
studies, and early-time resonances, in truncated time-Taylor expansions of
solutions of PDEs, such as those we consider.
