The velocity autocorrelation function (VACF) of a disk moving in a two-dimensional viscous fluid is calculated under the condition that the momentum leaks out of the fluid with a relaxation time τ. In the absence of any memory effects, VACF decays exponentially. Even in the presence of memory effects, VACF essentially decays exponentially being accompanied by the correction of algebraic decay. This correction depends on the coupling strength between the sheet and the outer fluid, i.e., ∼${\mathit{e}}^{\mathrm{-}\mathit{t}/\mathrm{\tau }}$${\mathit{t}}^{\mathrm{-}3/2}$ and ∼${\mathit{e}}^{\mathrm{-}\mathit{t}/\mathrm{\tau }}$${\mathit{t}}^{\mathrm{-}1}$ for strong- and weak-coupling limits, respectively. The correction of ${\mathit{t}}^{\mathrm{-}1}$ reflects the two-dimensional character of the fluid sheet.

• Received 14 July 1992

DOI:https://doi.org/10.1103/PhysRevE.47.2377