  For asymmetric sinh-Poisson type problems with Dirichlet boundary condition
arising as a mean field equation of equilibrium turbulence vortices with
variable intensities of interest in hydrodynamic turbulence, we address the
existence of sign-changing bubble tower solutions on a pierced domain
$\Omega_\epsilon:=\Omega\setminus \displaystyle \overline{B(\xi,\epsilon)}$,
where $\Omega$ is a smooth bounded domain in $\mathbb{R}^2$ and
$B(\xi,\epsilon)$ is a ball centered at $\xi\in \Omega$ with radius
$\epsilon>0$. Precisely, given a small parameter $\rho>0$ and any integer $m\ge
2$, there exist a radius $\epsilon=\epsilon(\rho)>0$ small enough such that
each sinh-Poisson type equation, either in Liouville form or mean field form,
has a solution $u_\rho$ with an asymptotic profile as a sign-changing tower of
$m$ singular Liouville bubbles centered at the same $\xi$ and with
$\epsilon(\rho)\to 0^+$ as $\rho$ approaches to zero.
