On the dynamics of unsteady gravity waves of finite amplitude Part 2. Local properties of a random wave field
On the dynamics of unsteady gravity waves of finite amplitude Part 2. Local properties of a random wave field
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DOI：
10.1017/s0022112061000913
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发表时间：
1961-08
影响因子：
3.7
通讯作者：
O. Phillips
中科院分区：
文献类型：
--
作者：
O. Phillips
封闭形式的表达式推导出一些随机的，无旋波场的局部性质。它们是：（i）每单位投影面积的平均位能和动能;（ii）来自地面气压波动的能量输入过程、位能和动能的增长率以及水平能通量之间的能量平衡;以及（iii）位能和动能之间的分配。这些表达式主要是在自由表面测量的量，因此，它们仅是两个空间变量（x，y）和时间t的函数。这些表达式的近似值可以简单地通过随后的展开方法找到;四阶是最高阶，在真实的流体中，无旋运动的假设是适当的。结果表明，任意三个一阶量的平均乘积在均方根波斜率上是四阶或更高阶的，并将这一结果应用于估计某些高阶效应的大小。特别地，表面位移的偏斜度是均方根表面斜率的数量级，这已经由Kinsman（1960）通过观测证实。
Expressions in closed form are derived for a number of local properties of a random, irrotational wave field. They are: (i) the mean potential and kinetic energies per unit projected area; (ii) the energy balance among the processes of energy input from the surface pressure fluctuations, rate of growth of potential and kinetic energy and horizontal energy flux; and (iii) the partition between potential and kinetic energy. These expressions are mainly in terms of quantities measured at the free surface, which are therefore functions of only two spatial variables (x, y) and of time t. Approximations for these expressions can be found simply by subsequent expansion methods; the fourth order being the highest for which the assumption of irrotational motion is appropriate in a real fluid. It is shown that the mean product of any three first-order quantities is of fourth or higher order in the root-mean-square wave slope, and this result is applied in estimating the magnitude of some higher order effects. In particular, the skewness of the surface displacement is of the order of the root-mean-square surface slope, which has been confirmed observationally by Kinsman (1960).