We study the cyclic dynamics of a single polymer tethered to a hard wall in shear flow using Brownian dynamics, the lattice Boltzmann method, and a recent stochastic event-driven molecular dynamics algorithm. We focus on the dynamics of the free end (last bead) of the tethered chain and we examine the cross-correlation function and power spectral density of the chain extensions in the flow and gradient directions as a function of chain length N and dimensionless shear rate Wi. Extensive simulation results suggest a classical fluctuation-dissipation stochastic process and question the existence of periodicity of the cyclic dynamics, as previously claimed. We support our numerical findings with a simple analytical calculation for a harmonic dimer in shear flow.
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