论狭窄潮汐水道中sigma坐标下的余流

在受波动影响的近岸浅水区域，运用sigma坐标是计算平均水位附近的余流的有效途径。本项研究在理论上分析了在狭窄潮汐水道中sigma坐标下的余流的物理意义，并运用一系列的理想化数值模型对分析结果进行了验证。对于浅水波，sigma层和水体中的波动面相一致，因而斯托克斯速度及其分量可以用sigma坐标上的速度来表达。一个sigma层上的余流（即sigma余流）是位于这一sigma层平均深度上的欧拉余流和斯托克斯速度垂向分量的和，可以被看做是半拉格朗日余流。因为斯托克斯速度的垂向分量比其水平分量小一个量级，sigma余流可看做为欧拉余流的近似。在sigma层上的物质输运余流是sigma余流和斯托克斯速度水平分量的和，在大小和方向上和拉格朗日余流近似。

On residual velocities in sigma coordinates in narrow tidal channels

In shallow coastal regions where water surface fluctuations are non-negligible compared to the mean water depth, the use of sigma coordinates allows the calculation of residual velocity around the mean water surface level. Theoretical analysis and generic numerical experiments were conducted to understand the physical meaning of the residual velocities at sigma layers in breadth-averaged tidal channels. For shallow water waves, the sigma layers coincide with the water wave surfaces within the water column such that the Stokes velocity and its vertical and horizontal components can be expressed in discrete forms using the sigma velocity. The residual velocity at a sigma layer is the sum of the Eulerian velocity and the vertical component of the Stokes velocity at the mean depth of the sigma layer and, therefore, can be referred to as a semi-Lagrangian residual velocity. Because the vertical component of the Stokes velocity is one order of magnitude smaller than the horizontal component, the sigma residual velocity approximates the Eulerian residual velocity. The residual transport velocity at a sigma layer is the sum of the sigma residual velocity and the horizontal component of the Stokes velocity and approximates the Lagrangian residual velocity in magnitude and direction, but the two residual velocities are not conceptually the same.