Various strategies are proposed for enforcing stress-free boundary conditions on deformed domains using a weak-form-based discretization in a Cartesian frame of reference. Due to the irregularity of the computational domain and the particular type of boundary condition, a coupling between the Cartesian velocity components is introduced. As such, a different computational kernel is required for the numerical solution of the associated vector Helmholtz equation, as contrasted to what is used for the scalar unknowns of the equations. Three approaches are presented, aimed towards the exact or approximate implementation of zero tangential stress (traction) at the deformed boundary while ensuring a decoupling of the velocity components in the solution of the vector Helmholtz equation. Two of these strategies, those which approximate the free slip boundary condition, are applied to the propagation of an internal solitary wave (ISW) of depression over a deformed bathymetry. The spatial structure and amplitude of the resultant pseudo-traction, which is accurately predicted by a simple scaling estimate, are explored as a function of the ISW-based Reynolds number, $Re$. For the $Re$ values considered, the pseudo-traction is negligible with respect to the corresponding no-slip tangential shear stress. The pseudo-traction-induced, time-integrated loss of ISW energy is found to be significantly weaker than the associated viscous dissipation in the interior water column. Although, at laboratory-scale or oceanic $Re$, an approximate free-slip boundary condition is found to yield negligible pseudo-traction, this might not be the case when an elevated eddy viscosity is used in this context as a surrogate for no-slip turbulent bottom boundary layer dynamics.

提出了各种策略，用于在笛卡尔参考系中使用基于弱形式的离散化在变形域上强制执行无应力边界条件。由于计算域的不规则性和特定类型的边界条件，笛卡尔速度分量之间的耦合被引入。因此，与用于方程的标量未知数的计算内核相比，关联向量亥姆霍兹方程的数值解需要不同的计算内核。提出了三种方法，旨在在变形边界处精确或近似实现零切向应力（牵引力），同时确保矢量亥姆霍兹方程解中速度分量的解耦。其中两个策略，那些近似于自由滑移边界条件的条件被应用于在变形的水深测量上的凹陷内部孤立波 (ISW) 的传播。作为基于 ISW 的雷诺数的函数，探索了通过简单的缩放估计准确预测的合成伪牵引的空间结构和幅度， $\mathrm{电阻}\mathrm{电子}$. 为了 $\mathrm{电阻}\mathrm{电子}$考虑到的值，相对于相应的无滑移切向剪切应力，伪牵引可以忽略不计。发现 ISW 能量的伪牵引引起的时间积分损失明显弱于内部水体中相关的粘性耗散。虽然，在实验室规模或海洋 $\mathrm{电阻}\mathrm{电子}$，发现近似的自由滑移边界条件产生可忽略不计的伪牵引力，当在这种情况下使用升高的涡流粘度作为无滑移湍流底部边界层动力学的替代物时，情况可能并非如此。