Second-order interaction of irregular waves with a truncated column

A complete semi-analytical solution is obtained for second-order diffraction of plane bichromatic waves by a fixed truncated circular column. The fluid domain is divided into interior and exterior regions. In the exterior region, the second-order velocity potential is expressed in terms of ‘locked-wave’ and ‘free-wave’ components, both are solved using Fourier and eigenfunction expansions. The resulting ‘locked wave’ potential is expressed by one-dimensional Green's integrals with oscillating integrands. In order to increase computational efficiency, the far-field part of the integrals are carried out analytically. Solutions in both regions are matched on the interface by the potential and its normal derivative continuity conditions. Based on the present approach, the sum-and difference-frequency potentials are efficiently evaluated and are used to generate the quadratic transfer functions which correlates sum-frequency QTFs for a TLP column are present, which are compared for some frequency pairs with those from a fully numerical procedure. Satisfactory agreement has been obtained. QTF spectra for a case study TLP column, generated using the semi-analytical solution are presented. Also given are the results for nonlinear wave field around the column.     

A second order stationary solution of the three dimensional wave diffraction potential

A theory on the second order wave diffraction by a three dimensional body fixed in a regular sea has been developed in the present paper. By regarding the sinusoidal disturb potential as a stationary solution of an initial value problem, and using Laplace transformation method and Tauberian theorem, the boundary value problems of stationary solution of the first and second order diffraction potential have been derived in this paper. Furthermore, the explicit solution of the second order stationary diffraction potential has been obtained with the method of the double Fourier transformation. It is found that the asymptotic behaviour of the second order stationary solution at far field is dependent on two wave systems, the first is “free wave”, travelling independently of the first order wave system, the other is “phase locked waves”, which accompany the first order waves. At the same time, the radiation conditions of the second order diffraction problems are derived. We also find that one can still pursue a steady state formulation with the inclusion of Rayleigh damping. Finally, as an example, the second order wave forces upon a fixed vertical circular cylinder have been calculated, and the numerical results agree well with the experimental data.     

波浪与外壁开孔双筒柱群的相互作用

应用速度势的特征函数展开和透空壁内两壁间压力差和流体速度成正比的线性模型,建立了波浪与外壁开孔同轴双筒桩柱群相互作用的线性解析解. 应用这一模型进行了数值计算,用以检验孔隙系数对双筒柱上的波浪力和波面高度的影响. 结果表明,外壁孔隙系数的增加对减小波浪力和柱外波面高度有很大影响.     

横浪中的波浪二阶力计算

本文提出了用基于多极展开的切片法来计算横浪规则波中的波浪二阶力。把本文的计算方法和实验与其它方法相比较结果是令人满意的，并且计算量不大。因而这是一种实用的数值计算方法。     

Effect of acoustic radiation on a spherical drop of liquid

The effect of radiation force on a drop of liquid in an acoustic field is examined. It is established that the force depends on the ratio of the densities of the liquid and the drop and on their adiabatic elastic moduli __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 26–34, July 2007.     

Minimum drag shape in two-dimensional viscous flow

The problem of finding the shape of a body with smallest drag in a flow governed by the two-dimensional steady Navier-Stokes equations is considered. The flow is expressed in terms of a streamfunction which satisfies a fourth-order partial differential equation with the biharmonic operator as principal part. Using the adjoint variable approach, both the first- and second-order necessary conditions for the shape with smallest drag are obtained. An algorithm for the calculation of the optimal shape is proposed in which the first variations of solutions of the direct and adjoint problems are incorporated. Numerical examples show that the algorithm can produce the optimal shape successfully.     

Turbulence in broken lee waves

In this paper, the waves' breaking in the lee waves in successfully simulated by the atmospheric mesoscale numerical model with a second-order turbulent closure. It is further proved that the turbulence in the wave-breaking region plays the role of intense mixing for the average field, which leads to the trapping of upward propagating waves and thus promotes the development of the downslope wind. The turbulent structure in the wave-breaking region is discussed and the following conclusions are obtained: (1) In the wave-breaking region, the turbulent heat fluxes transfer from inside to outside and the turbulent momentum fluxes transfer from outside to inside. (2) In the wave-breaking region, the turbulent energy mainly comes from the wind shear and the buoyancy promotes the turbulent development only in part of the region. (3) In the upper part of the wave-breaking region, the turbulent momentum fluxes behave as a counter-gradient transfer. (4) The turbulent mixing in the wave-breaking region is non-local. recommended by Professor Li Jiachun.     

Nonlinear free surface action with an array of vertical cylinders

Nonlinear diffraction of regular waves by an array of bottom-seated circular cylinders is investigated in frequency domain, based on a Stokes expansion approach. A complete semi-analytical solution is developed which allows an efficient evaluation of the second-order potentials in the entire fluid domain, and the wave forces on the structure. Expressions are derived for the second-order potential in the vicinity of individual cylinders. These expressions have a simple form, thus providing an effective means for investigating the wave enhancement due to nonlinear interactions with multiple cylinders. Based on the present method, the wave run-up and free-surface elevations around an array of two, three and four cylinders are investigated numerically.