  It is shown that the logarithmic derivative of the characteristic polynomial
of a Wilson loop in two dimensional pure Yang Mills theory with gauge group
SU(N) exactly satisfies Burgers' equation, with viscosity given by 1/(2N). The
Wilson loop does not intersect itself and Euclidean space-time is assumed flat
and infinite. This result provides a precise framework in 2D YM for recent
observations of Blaizot and Nowak and was inspired by their work.
