  We study the entanglement evolution of photonic orbital angular momentum
qubit states with opposite azimuthal indices $l_0$, in a weakly turbulent
atmosphere. Using asymptotic methods, we deduce analytical expressions for the
amplitude of turbulence-induced crosstalk between the modes $l_0$ and $-l_0$.
Furthermore, we analytically establish distinct, universal entanglement decay
laws for Kolmogorov's turbulence model and for two approximations thereof.
