Nonlinear Evolution of Stationary Perturbations in a Spatially Evolving Round Submerged Jet

The non-modal spatial development of stationary three-dimensional perturbations in a round submerged jet at $$\operatorname{Re} = 2850$$ is numerically studied. The conditions of a laboratory experiment previously carried out in the Institute of Mechanics of Moscow State University are reproduced. A method for calculating optimal perturbations under conditions of the main flow developing downstream is proposed. Optimal perturbations corresponding to various azimuthal numbers are found. Their shape, nature of development, and growth rate are determined. The nonlinear development of optimal perturbations is studied for various values of their initial amplitude. It is shown that nonlinear effects lead to a slowdown in the growth rate during their development downstream. Flows deformed by stationary perturbations in the angular direction are studied for stability under small non-stationary perturbations. It is found that with an increase in the degree of deformation, the maximum growth rate of perturbations increases noticeably due to the emergence of a specific short-wave instability mode.