ON VELOCITY POTENTIALS DUE TO PULSATING PRESSURE DISTRIBUTIONS ON THE FREE SURFACE OF INFINITE-DEPTH WATERS AND THE RADIATION CONDITIONS FOR SECOND-ORDER DIFFRACTION PROBLEMS

In the present paper,two-and three-dimensional velocity potentials generated by pulsating pressure distributions of infinite extent on the free surface of infinite-depth waters are strictly derived based on special cases of concentrated pulsating pressure.The far-field asymptotic behaviour of the potentials and the radiation conditions to be satisfied by them are discussed. It is proved in a general sense that the potentials should be composed of a forced wave component,a free wave component and a local disturbance component.The radiation condition of the forced wave component should correspond to the far-field asymptotic behaviour of the pressure distribution,Hence,the formulation of radiation conditions for the second-order diffraction potentials has theoretically become clear,The radiation conditions for two-and three-dimensional problems are explicitly given in the paper.

AN ANALYTICAL SOLUTION OF SECOND－ORDER WAVE FORCE ON A VERTICAL CIRCULAR CYLINDER

So far many investigations have been made on nonlinear wave diffraction problemfor a large-diameter vertical circular cylinder. However,there are still some problemsworthy to be further discussed. It includes that the second order radiation condition isnot very clear and the inhomogeneous term of second order free surface boundarycondition makes the calculation of second order wave force either not easier to beperformed accurately due to its slowly decaying with radial distance or toocomplicated for practical application. In this paper, the second order radiationcondition is posed of the circumferential Fourier components of second orderpotential, instead of the second order potential. It is found that the circumferenatialFourier cormponents of second order potential have to satisfy Sommerfeld radiationcondition. By means of the mathematical formulae derived in this paper, theinhomogeneous term of second order free surface boundary condition were simplifiedand then an exact expression of second order wave force was obtained, which issimpler in form and easier to be used in practical calculation. The calculation resultsagree well with some experimental data.

直立圆柱二阶波浪力解析解

大直径直立圆柱体上的二阶波浪力目前已有一些研究结果，但仍存在一些值得进一步探讨之处。这一方面在于二阶辐射条件还不甚清楚：另一方面在于已有的二阶力公式或是所含积分的收敛精度不易保证，或是表达式繁杂，不利于实际计算。本文在求解这一问题时，不是对二阶势提出辐射条件，而是对二阶势的周向富里叶分量提出辐射条件──Ｓｏｍｍｅｒｆｅｌｄ辐射条件。求解中，利用本文推导出的数学公式，简化了二阶自由面条件非齐次项的表达式，得到了形式简单，易于计算的二阶波浪力精确公式。二阶力计算结果与实验结果吻合良好。