Abstract: The unsteady force can affect the noise performance and service life greatly both to rudder and aerofoil，so it is necessary to study the exciting force in turbulence. Two different wavenumber functions with dif.ferent flow coefficient are presented to describe the three dimensional turbulent field in the analysis of unsteadybehaviour of a finite-span hydrofoil in a turbulent field. The aerodynamic admittance of finite-span hydrofoil isdeduced and validated by comparing with the experimental results. The present work investigates the correctnessof strip theory under different conditions. The analysis shows that the influence of spanwise wavenumber becomesnegligible for large enough aspect-ratios. And it also shows that the turbulence scale can exert effects on the cor.rectness of strip theory only when reduced frequency is small. The coherences of lift coefficient and vertical veloci.ty are discussed in the last passage，as well as the real cause of deviation of the strip theory. The following conclu. sions are obtained. First，when the reduced frequency is small(<1)the error of strip theory is decreasing with theincrease of scale length of turbulence. When the reduced frequency is large(>5)，the scale length of turbulence has no influence on the error of strip theory. Second，the error of strip theory decrease with the increase of span of hydrofoil，and this relationship is not affected by other factors. Third，the coherence of lift coefficient is greaterthan that of vertical fluctuating velocity. Strip theory is unsuitable under most of conditions because it ignores the difference between the coherence of vertical fluctuating velocity and lift force.

Key words: Aerodynamic admittance；Wavenumber function；Strip theory

摘要： 无论船舵还是机翼，激振力的产生都会严重地影响其噪声性能和使用寿命，因此深入研究湍流中激振力是很有必要的。针对有限长水翼在湍流中的非定常激振力问题，分别建立流动系数不同的两向波谱函数描述三维湍流场，并推导了有限长水翼的响应函数。将计算结果分别与实验值进行对比，发现与实验结果吻合较好。在此基础上分别在不同情况下对薄片理论的适用性进行了研究，发现水翼展长比较大时，可忽略展向波数的影响；而湍流尺度只在无因次频率 κ较小时对薄片假设产生的误差有影响。对水翼升力系数和下洗速度的自相关性进行了研究，深入探究薄片假设产生误差的原因。结果表明:当无因次频率较小( <1时)，湍流尺度越大，薄片理论的误差越小；当无因次频率较大时( >5时)，湍流尺度的大小不能影响薄片理论的误差。随着水翼展长 b增大，薄片理论的误差减小，该参数对薄片理论的影响不受其他条件影响。升力系数的相关性比下洗速度更强，而薄片假设忽略了升力和下洗速度分量 w展向方向相关性的差异，这是薄片假设在大多数情况下不适用的原因。

关键词: 响应函数；波谱函数；薄片理论