Abstract
Motivated by the statistical mechanics description of stationary 2D-turbulence, for a sinh-Poisson type equation with asymmetric nonlinearity, we construct a concentrating solution sequence in the form of a tower of singular Liouville bubbles, each of which has a different degeneracy exponent. The asymmetry parameter \begin{document} $γ∈(0, 1]$ \end{document} corresponds to the ratio between the intensity of the negatively rotating vortices and the intensity of the positively rotating vortices. Our solutions correspond to a superposition of highly concentrated vortex configurations of alternating orientation; they extend in a nontrivial way some known results for \begin{document} $\gamma=1$ \end{document} . Thus, by analyzing the case \begin{document} $\gamma≠1$ \end{document} we emphasize specific properties of the physically relevant parameter \begin{document} $\gamma$ \end{document} in the vortex concentration phenomena.
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