Well-resolved galaxy clusters often show a large-scale quasi-spiral structure
in deprojected density $\rho $ and temperature $T$ fields, delineated by a
tangential discontinuity known as a cold front, superimposed on a universal
radial entropy profile with a linear $K(r)\propto T{\rho}^{-2/3}\propto r$
adiabat. We show that a spiral structure provides a natural quasi-stationary
solution for the mixed intracluster medium (ICM), introducing a modest pressure
spiral that confines the locally buoyant or heavy plasma phases. The solution
persists in the presence of uniform or differential rotation, and can
accommodate both an inflow and an outflow. Hydrodynamic adiabatic simulations
with perturbations that deposit angular momentum and mix the plasma thus
asymptote to a self-similar spiral structure. We find similar spirals in
Eulerian and Lagrangian simulations of 2D and 3D, merger and offset, clusters.
The discontinuity surface is given in spherical coordinates $\{r,\theta ,\varphi \}$
by $\varphi \propto \mathrm{\Phi}(r)$ , where $\mathrm{\Phi}$ is the gravitational potential,
combining a trailing spiral in the equatorial ($\theta =\pi /2$ ) plane and
semicircles perpendicular to the plane, in resemblance of a snail shell. A
local convective instability can develop between spiral windings, driving a
modified global instability in sublinear $K(r)$ regions; evolved spirals thus
imprint the observed $K\propto r$ onto the ICM even after they dissipate. The
spiral structure brings hot and cold phases to close proximity, suggesting that
the observed fast outflows could sustain the structure even in the presence of
radiative cooling.