风浪场波生横向彻体切应力的分析

ANALYSIS OF WAVE-INDUCED LATERAL BODY FORCE

使用风浪经验公式和风浪传入近岸的小振幅波动理论计算并分析了地转条件下波生横向彻体切应力随风速、风区、水深等因素的变化规律。结果表明,彻体切应力随风速、风区的增大而增大,直到波浪达到完全成长状态,但增长速度并不规则;为更加直观的显示彻体切应力的海流驱动作用,将其与定常Ekman漂流中的风生湍粘性力进行了有意义的比较,结果表明,在中、高纬度的通常海况下两者具有相同量级,因此,在有波浪场存在的条件下,由风、浪共生海流的总体强度将比理论Ekman漂流大,并且不会完全符合Ekman漂流理论的转向规律,在表层尤其明显。由此说明,在一定情况下在风生漂流研究中考虑由地转引起的波生横向彻体切应力是非常必要的。

The wave-induced lateral body force is a newfound wave-driven force on ocean current. In order to understand the vertical structure of the wave-induced lateral body force, its variations in deep water with some factors such as wind speed, wind fetch and water depth are analyzed respectively according to the Wilson IV wind waves empirical formulae and the P-M nondimensional fully developed wind waves frequency spectrum. The results indicate that the body force will augment continuously with the increases of wind speed and wind fetch till the waves become fully developed; however this kind of augment is irregular since the wave height and the wave number usually change oppositely with the increase of wind speed and wind fetch. Furthermore, the vertical variation of the wave-induced lateral body force with bottom depth in shallow water is also calculated using the small amplitude theory of waves propagating to the offshore, and the numerical solutions of wave number and wave height in shallow water. The result shows that when the waves propagate to the shallow water from deep sea, the body force will be magnified, but the magnification is not very evident until the product of bottom depth and wave number is less than1.6, at that time, the body force would be amplified drastically along with the fast increase of a shallow water factor defined in this paper. In order to explicitly evaluate the driven effect of the wave-induced lateral body force on ocean current relative to the wind effect, a comparison between the body force and wind-induced viscosity force in constant Ekman drift was made. By use of the classical Ekman drift theory and Wu Jing’s ocean surface wind stress formula, the module of wind-induced viscosity force was calculated, and then we compared it with the magnitude of the wave-induced lateral body force of fully developed wind wave at the same wind speed. The result shows that the surface magnitude of wave-induced lateral body force was 70% larger than the wind-induced viscosity force in normal sea of the mid-high latitude, while the depth with corresponding effect was less than 30 of wind-induced viscosity force. In rough sea, although the surface magnitude ratio of wave-induced lateral body force to wind induced viscosity force is less than that of normal sea, their ratio of the effect depth becomes larger than in normal sea. It can be seen from the results that, relative to the wind effect, the effect of wave-induced lateral body force is concentrated on surface layer, and is less than the wind effect, but they indubitably have the same order. That is, when there exist waves, the magnitude of drift driven by wind and wave together would be larger than the theoretical Ekman drift that driven only by wind. Besides, the direction of wind-wave driven drift is not completely accord with the Ekman drift theory, especially on the upper layer of ocean. In particular, there is the status of surge with breeze in real sea. On that condition, the relative effect of lateral body force is more important. Therefore, in one word, the effect of wave-induced lateral body force should be counted in wind-induced currents in certain conditions.