We analyze the evolution of hydrodynamic fluctuations in a heavy ion collision as the system passes close to the QCD critical point. We introduce two small dimensionless parameters λ and ∆ s to characterize the evolution. λ compares the microscopic relaxation time (away from the critical point) to the expansion rate λ ≡ τ 0 /τ Q , and ∆ s compares the baryon to entropy ratio, n/s, to its critical value, ∆ s ≡ (n/s − n c /s c )/(n c /s c ). We determine how the evolution of critical hydrodynamic fluctuations depends parametrically on λ and ∆ s . Finally, we use this parametric reasoning to estimate the critical fluctuations and correlation length for a heavy ion collision, and to give guidance to the experimental search for the QCD critical point.