Planet formation scenarios and the observed planetary dynamics in binaries pose a number of theoretical challenges, especially concerning circumbinary planetary systems. We explore the dynamical stirring of a planetesimal circumbinary disk in the epoch when the gas component disappears. For this purpose, following theoretical approaches by Heppenheimer and Moriwaki & Nakagawa, we develop a secular theory of the dynamics of planetesimals in circumbinary disks. If a binary is eccentric and its components have unequal masses, a spiral density wave is generated, engulfing the disk on a secular timescale, which may exceed 10⁷ yr, depending on the problem parameters. The spiral pattern is transient; thus, its observed presence may betray a system's young age. We explore the pattern both analytically and in numerical experiments. The derived analytical spiral is a modified lituus; it matches the numerical density wave in the gas-free case perfectly. Using the smoothed particle hydrodynamics scheme, we explore the effect of residual gas on the wave propagation.