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In the near field of a subsonic jet, complex energy transport and transformation processes occur among kinetic, thermal, and acoustic energies, which play crucial roles in jet instability and noise radiation. Accurately characterizing the transport features of each energy component is essential for developing effective noise suppression technologies. Building upon Myers' [1991 J. Fluid Mech. 226 383] exact energy equation for total disturbances in arbitrary steady flow, the present study develops a modified energy equation based on hydro-acoustic mode decomposition to separate the contributions of vortical, entropic, and acoustic modes to the total disturbance energy. The methodology begins with the decomposition formulas for velocity, pressure, and density, following the hydro-acoustic mode decomposition method proposed by Han et al. [2023 Phys. Fluids 35 076107]. In Myers' energy equation framework, the disturbances of primitive variables (velocity, pressure, and density) are expressed as linear combinations of their vortical, entropic, and acoustic components. Through this formulation, vortical (entropic, acoustic) energy is defined as exclusively contributed by the corresponding mode's disturbances, while nonlinear energy is attributed to interactions among vortical, entropic, and acoustic components. This approach yields a modified energy equation capable of distinguishing the individual contributions of vortical, entropic, and acoustic modes to both total disturbance energy and energy flux, making it particularly suitable for analyzing energy transport characteristics in the near flow field. The developed equation is applied to analyze a Mach number 0.9 subsonic jet, revealing distinct spatial distributions and transport mechanisms of hydrodynamic and acoustic energies. The results demonstrate that vortical and entropic energies are predominantly concentrated in the near field, convecting downstream at approximately 0.8 times the jet velocity. In contrast, acoustic energy exhibits dual propagation characteristics: radiating outward to the far field through acoustic waves outside the potential core while propagating upstream via trapped waves within the potential core. The energy associated with multi-mode nonlinear interactions primarily concentrates in the jet wake, propagating without significant directivity. The total disturbance energy is predominantly contributed by vortical energy, while the acoustic energy accounting for only a minuscule fraction of the total disturbance energy, approximately on the order of 10-3 of the total. This refined analysis provides deeper insights into the complex energy dynamics in subsonic jets, offering valuable information for jet noise prediction and control strategies. The modified energy equation presents a robust framework for understanding and quantifying the intricate energy transport processes in jet flows.
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