The starting processes of under-expanded free jets with nozzle pressure ratios of 2.15, 2.7, and 3.4 are systematically analyzed by large-eddy simulations, and the unified laws of the evolution of the screech frequency and the screech mode in the starting jet are given. Through the development of vortices, the critical time points of the generations of screech tones are investigated. The wavenumber spectra and dispersion relations are employed, showing that the screech feedback loops in the different starting jets are all closed by the neutral waves excited by the interaction between the Kelvin–Helmholtz wavepacket and shock cells of different wavenumbers. The screech frequency prediction during the starting process is put forward for the first time, which is achieved by combining the neutral acoustic wave mode with wavenumber differences between shock cells and the Kelvin–Helmholtz wavepacket. Spectral proper orthogonal decomposition is applied to explain the reason for the change in the interaction mechanism during the starting process.
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