Under the' assumption of linearization of the free-surface condition, making use of Green's function method and the convolution theorem, analytic solutions of perturbation velocity potentials which correspond ...Under the' assumption of linearization of the free-surface condition, making use of Green's function method and the convolution theorem, analytic solutions of perturbation velocity potentials which correspond to three dimensional unsteady thickness problem and lifting problem caused respectively by arbitrary motions of a body and a hydrofoil beneath the water surface can be achieved in the closed form, In general, the whole perturbation velocity potential consists of three terms, namely φ=φ1+φ2+φ3 , where φ1 denotes the induced velocity potential of the surface singularity distribution in an unbounded fluid, φ2 denotes its mirror image and φ3 denotes that of wave formation which includes the memory effect of the action of the singularity distribution. Utilizing the polynomial expansion of sin[(t-τ)] , the similarity between φ2 and φ3 is discovered and thus a simpler differential relation between them is obtained. Applying this relation, the amount of work in calculation of φ3 which is the most time-consuming one will be reduced significantly. It is favorable not only for dealing with unsteady wave- making problems but also for solving the steady ones in virtue of evading a major difficulty which has to be encountered during the evaluation of an improper inte- gral containing a singularity in the Green's function. The limitation of this new technique turns out to be its slower convergence as the Froude number is lower.展开更多
文摘Under the' assumption of linearization of the free-surface condition, making use of Green's function method and the convolution theorem, analytic solutions of perturbation velocity potentials which correspond to three dimensional unsteady thickness problem and lifting problem caused respectively by arbitrary motions of a body and a hydrofoil beneath the water surface can be achieved in the closed form, In general, the whole perturbation velocity potential consists of three terms, namely φ=φ1+φ2+φ3 , where φ1 denotes the induced velocity potential of the surface singularity distribution in an unbounded fluid, φ2 denotes its mirror image and φ3 denotes that of wave formation which includes the memory effect of the action of the singularity distribution. Utilizing the polynomial expansion of sin[(t-τ)] , the similarity between φ2 and φ3 is discovered and thus a simpler differential relation between them is obtained. Applying this relation, the amount of work in calculation of φ3 which is the most time-consuming one will be reduced significantly. It is favorable not only for dealing with unsteady wave- making problems but also for solving the steady ones in virtue of evading a major difficulty which has to be encountered during the evaluation of an improper inte- gral containing a singularity in the Green's function. The limitation of this new technique turns out to be its slower convergence as the Froude number is lower.
