Evaluation of Hydrodynamic Forces with Nonlinear Wave Equations for a Compressible Fluid

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A nonlinear wave equation for a compressible fluid was derived to investigate effects of nonlinearlity of a motion on hydrodynamic forces. The nonlinear equation was solved by a perturbation method in case of harmonic motion. The magnitude of nonlinear term was evaluated in term of first order solution and compared with those of linear term. It was found that the nonlinearity of hydrodynamic forces was significant in the vicinity of a free surface, while it is negligibly small in other region.Lavoratory experiments were conducted to investigate characteristics of wave impact pressure on a vertical wall. The impact pressure oscillation was damped when air bubbles were contained in a water body in front of a vertical wall. To simulate this phenomenon, nonlinear equations of motion for mixtures of liquid and gas bubbles were used. The equations includes the effects of dispersion and dissipation as well as nonlinearity, similar to the Boussinesq Equations for water waves, and were solved numerically. The numerical results indicated that the larger the air content, the lower the magnitude of the impact pressure.