With increased computing power, the horizontal grid-spacing of regional ocean models is decreasing to the point where they can directly simulate lee waves. Although oceanic lee waves can be inherently nonhydrostatic, such as in the abyssal ocean or in the Gulf Stream, regional ocean models are frequently run in hydrostatic mode to avoid the computational expense of solving the nonhydrostatic pressure. However, the effects of the nonhydrostatic pressure and the numerical error on the accuracy of the simulated lee waves is not immediately obvious. To quantify these effects, this paper presents hydrostatic and nonhydrostatic simulations of an idealized lee wave over both linear and nonlinear height and varying length bathymetry utilizing a range of horizontal grid-spacings. We present an analysis of the numerical error arising from the discrete linear, stratified Euler equations to identify the numerically induced physics in lee wave simulations. As expected for the second-order accurate model, the numerical error in the lee wave drag decreases quadratically with respect to horizontal grid refinement, although the error arises from two primary sources. The first is related to discretization of the kinematic bottom boundary condition, which acts to decrease the lee wave drag. The second is related to discretization of the nonhydrostatic pressure, which acts to increase the drag. Together, the results offer a regional ocean modeler several cautionary notes for calculating and interpreting properties of simulated lee waves, namely, that a hydrostatic model can produce the correct form drag due simply to numerical error, and attempting to employ a nonhydrostatic model to correct for this error can require prohibitively fine grid resolution.

随着计算能力的提高，区域海洋模型的水平网格间距逐渐减小到可以直接模拟回风的程度。尽管大风里风在本质上可能是非静水的，例如在深海或墨西哥湾流中，但是区域性海洋模型通常以静水模式运行，以避免解决非静水压力的计算费用。但是，非静水压力和数值误差对模拟背风精度的影响尚不明显。为了量化这些影响，本文介绍了利用线性水平和水平网格间距在线性和非线性高度以及变长测深法上对理想回风的静水和非静水模拟。我们提出了对由离散线性，分层欧拉方程式引起的数值误差的分析，以识别回风模拟中的数值诱导物理。正如二阶精确模型所预期的那样，尽管风速阻力的数值误差来自两个主要来源，但相对于水平网格细化，回风阻力的数值误差呈二次方减小。第一个与运动学底边界条件的离散化有关，这可以减小回风阻力。第二个问题涉及非静水压力的离散化，这会增加阻力。这些结果共同为区域海洋建模者提供了一些警告提示，用于计算和解释模拟的风速波特性，即静水压力模型可以简单地由于数值误差而产生正确的形式阻力，