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A potential-flow theory for the dynamics of cylinder arrays in cross-flow

The full linear unsteady potential-flow solution for fluid flowing across a bank of cylinders has been obtained. The potential function is expanded into a Fourier series and the boundary condition of impermeability is applied at the moving cylinder surfaces. Mutual contradictions among the various potential-flow solutions available in the literature are exposed, and it is shown that the present solution is consistent with certain basic physical checks, which some of the previous solutions could not meet. The effect of fluid viscosity is incorporated solely as a phase lag between the steady-state lift and drag coefficients on each cylinder and its respective motions. By incorporating the fluid-dynamic forces obtained from this modified potential-flow theory in a stability analysis, the threshold for fluid-elastic instability is predicted. Comparison with experimentally observed thresholds is encouraging, given the high level of idealization of the theory and the accuracy of present-day semi-empirical prediction methods.