Euler Singularities II: Interior Quadrupole Blow-Up for Smooth Axisymmetric Euler with Swirl in \texorpdfstring{${\mathbb{R}}^3$}

We present a self-contained interior quadrupole mechanism for finite-time singularity formation in the axisymmetric three-dimensional incompressible Euler equations with swirl in the whole space. The construction is localized away from the axis. In local variables $$x=r-r_{\ast }(t),y=z,$$ centered at a tracked radial point, the active vorticity and swirl profiles are $$G(x,y,t)\approx a(t)xy,\mathrm{\Gamma }(x,y,t)\approx {\mathrm{\Gamma }}_{\ast }(t)+\frac{1}{2}b(t)x{y}^2,{\mathrm{\Gamma }}_{\ast }(t)>0.$$ The first profile produces a positive interior Biot–Savart hyperbolic strain; the second profile makes the Euler source term in the equation for $G={\omega }^{\theta }\mathrm{/}r$ regenerate the same quadrupole shape. The active quantity is the full four-quadrant quadrupole score, while a narrow diagonal sector is used only as a coercive subscore. We give the notation and the 5D recovery formula connecting the 3D axisymmetric variables to the lifted elliptic problem, construct explicit smooth decaying divergence-free data, verify their initial entry into the quadrupole bootstrap, prove the master propagation estimates, and derive the comparison system $$Q^{\mathrm{\prime }}(t)\ge cC(t),C^{\mathrm{\prime }}(t)\ge cQ(t)C(t),C(t)\ge \kappa Q(t{)}^2\mathrm{.}$$ Consequently the tracked quadrupole score blows up in finite comparison time, and the strain lower bound gives blow-up of $\text{norm}{\mathrm{\nabla }u(t)}_{L^{\mathrm{\infty }}}$. All geometric and analytic constraints used by the construction are stated as named estimates: the interior quadrupole kernel sign expansion, source compatibility, swirl-jet amplification, full-score/coercive-subscore comparison, angular-profile defect persistence, radial-center tracking, neutral-jet hierarchy, and two-sided Dini bounds. This is Part II of a two-paper Euler series; Part I treats boundary blow-up in a periodic cylinder.