The instability of propagating internal gravity waves (IGWs) is of long-standing interest in geophysical fluid dynamics since breaking IGWs exchange energy and momentum with the large-scale flow and hence they support the large-scale circulation. In this study a low-order IGW beam model is used to delineate both linear and so called non-modal transient instability. In the first part of the study, linear normal mode instability of a wave beam consisting of two finite-amplitude plane monochromatic IGWs with the same frequency and parallel wave vectors of different magnitude is investigated using the Galerkin method. It is concluded that the wave beam is linearly more unstable than its constituent plane waves, taken separately. The degree of instability increases with the separation of the constituent waves in the wave number space, that is, with the wave beam concentration in the physical space. The narrower a wave beam is, the more linearly unstable it is. In its turn, transient instability typically occurs for linearly stable flows or before linear instability can set in (subcritical instability) if the governing system matrix is non-normal. In the second part of the paper, first the non-normality of the linear system matrix of the wave beam model is examined by computing measures like the Henrici number, the pseudospectrum, and the range of the matrix. Subsequently, the robustness of the transient growth is studied when the initial condition for optimal growth is randomly perturbed. It is concluded that for full randomisation, in particular, shallow wave beams can show subcritical growth when entering a turbulent background field. Such growing and eventually breaking wave beams might add turbulence to existing background turbulence that originates from other sources of instability. However, the robustness of transient growth for wave beam perturbations depends strongly on the strength of randomisation of the initial conditions, the beam angle and the perturbation wavelength.

传播的内部重力波（IGW）的不稳定性长期以来一直是地球物理流体动力学的关注点，因为破碎的IGW与大规模流动交换能量和动量，因此它们支持大规模循环。在这项研究中，低阶 IGW 梁模型用于描述线性和所谓的非模态瞬态不稳定性。在研究的第一部分，使用Galerkin方法研究了由两个具有相同频率的有限幅度平面单色IGW和不同幅度的平行波矢量组成的光束的线性法向模不稳定性。得出的结论是，光束比其组成的平面波在线性上更不稳定，分别取。不稳定程度随着波数空间中成分波的分离而增加，即 与物理空间中的光束集中。光束越窄，它的线性越不稳定。反过来，瞬态不稳定通常发生在线性稳定的流动中，或者如果控制系统矩阵是非正态的，则在线性不稳定（亚临界不稳定）可能出现之前。在论文的第二部分，首先通过计算Henrici数、伪谱和矩阵的范围等度量来检验光束模型线性系统矩阵的非正态性。随后，研究了当最优增长的初始条件被随机扰动时瞬态增长的鲁棒性。得出的结论是，对于完全随机化，特别是浅光束在进入湍流背景场时会显示出亚临界增长。这种不断增长并最终破坏的光束可能会给源自其他不稳定源的现有背景湍流增加湍流。然而，光束扰动的瞬态增长的稳健性在很大程度上取决于初始条件、光束角和扰动波长的随机化强度。