Two types of existing iterative methods for solving the nonlinear balance equation (NBE) are revisited. In the first type, the NBE is rearranged into a linearized equation for a presumably small correction to the initial guess or the subsequent updated solution. In the second type, the NBE is rearranged into a quadratic form of the absolute vorticity with the positive root of this quadratic form used in the form of a Poisson equation to solve NBE iteratively. The two methods are rederived by expanding the solution asymptotically upon a small Rossby number, and a criterion for optimally truncating the asymptotic expansion is proposed to obtain the super-asymptotic approximation of the solution. For each rederived method, two iterative procedures are designed using the integral-form Poisson solver versus the over-relaxation scheme to solve the boundary value problem in each iteration. Upon testing with analytically formulated wavering jet flows on the synoptic, sub-synoptic and meso-α scales, the iterative procedure designed for the first method with the Poisson solver, named M1a, is found to be the most accurate and efficient. For the synoptic wavering jet flow in which the NBE is entirely elliptic, M1a is extremely accurate. For the sub-synoptic wavering jet flow in which the NBE is mostly elliptic, M1a is sufficiently accurate. For the meso-α wavering jet flow in which the NBE is partially hyperbolic so its boundary value problem becomes seriously ill-posed, M1a can effectively reduce the solution error for the cyclonically curved part of the wavering jet flow, but not for the anti-cyclonically curved part.

讨论了两种现有的求解非线性平衡方程（NBE）的迭代方法。在第一种类型中，将NBE重新排列为线性方程式，以便对初始猜测或后续更新的解决方案进行较小的校正。在第二种类型中，NBE被重新排列为绝对涡度的二次形式，该二次形式的正根以泊松方程的形式用于迭代地求解NBE。通过在较小的Rossby数上渐近展开解来重新尝试这两种方法，并提出了一种最佳截断渐近展开的准则，以获得该解的超渐近逼近。对于每种重新尝试的方法，使用积分形式的Poisson求解器和过松弛方案设计了两个迭代过程，以解决每次迭代中的边值问题。经过分析公式化的摇摆射流测试后，天气，次天气和中观发现使用第一个方法，即名为M1a的Poisson求解器设计的迭代程序α标尺是最准确，最有效的。对于NBE完全呈椭圆形的天气成波状射流，M1a非常精确。对于NBE大部分为椭圆形的次天气成波状射流，M1a足够精确。对于NBE是部分双曲的中α摇摆射流，其边界值问题变得严重不适，M1a可以有效地减少摇摆射流的旋弯部分的求解误差，而对于反射流则不能。气旋弯曲的部分。