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<p>This paper investigates the geometry of the free boundary for a three-dimensional axially symmetric, steady, subsonic, non-isentropic jet with nonzero vorticity. Motivated by discharge processes in hydraulic engineering, such as regulated river flushing, we formulate the mathematical model for the interface between the jet issuing from a nozzle and the ambient air. Under a concavity assumption on the nozzle wall, the main results establish the strict convexity of the free boundary and the positivity of the axial velocity throughout the fluid domain. The findings provide a mathematical foundation for predicting the interfacial geometry of such jets and for ensuring stable, unidirectional discharge in practical hydraulic designs.</p>

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On the Geometric Shape of Axially Symmetric Subsonic Non-isentropic Jets with Application to Regulated River Flushing

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  • 发表日期：

    2026年6月2日

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  • Lang Zhou

摘要

This paper investigates the geometry of the free boundary for a three-dimensional axially symmetric, steady, subsonic, non-isentropic jet with nonzero vorticity. Motivated by discharge processes in hydraulic engineering, such as regulated river flushing, we formulate the mathematical model for the interface between the jet issuing from a nozzle and the ambient air. Under a concavity assumption on the nozzle wall, the main results establish the strict convexity of the free boundary and the positivity of the axial velocity throughout the fluid domain. The findings provide a mathematical foundation for predicting the interfacial geometry of such jets and for ensuring stable, unidirectional discharge in practical hydraulic designs.