Energy transport analysis of subsonic jet based on hydro-acoustic mode decomposition

In the near-field of a subsonic jet, complex energy transport and transformation processes occur between kinetic energy, thermal energy, and acoustic energy, which play a crucial role in jet instability and noise radiation. Accurately characterizing the transport features of each energy component is essential for developing effective noise suppression technologies. According to Myers’ exact energy equation for total disturbances in arbitrary steady flow [<ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1017/S0022112091002434">1991 <i>J. Fluid Mech.</i> <b>226</b> 383</ext-link>], 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 method begins with the decomposition formulas for velocity, pressure, and density, following the hydro-acoustic mode decomposition method proposed by Han et al. [<ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1063/5.0157377">2023 <i>Phys. Fluids</i> <b>35</b> 076107</ext-link>]. 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. With this formula, the vortical (entropic, acoustic) energy is defined as being contributed only by the disturbance of the corresponding mode, while the nonlinear energy is attributed to interaction between 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, thus making it particularly suitable for analyzing energy transport characteristics in the near flow field. The developed equation is used to analyze a subsonic jet with a Mach number of 0.9, revealing different spatial distributions and transport mechanisms of hydrodynamic energy and acoustic energy. The results indicate that vortical energy and entropic energy are mainly concentrated in the near-field, convecting downstream at a velocity about 0.8 times the jet velocity. In contrast, acoustic energy exhibits dual propagation characteristics: it radiates outward to the far field through acoustic waves outside the potential core, while propagating upstream through trapped waves inside the potential core. The energy related to multi-mode nonlinear interactions is mainly concentrated in the jet wake and propagates without obvious directionality. The total disturbance energy is mainly contributed by vortical energy, while the acoustic energy only accounts for a small part of the total disturbance energy, approximately 10<sup>–3</sup> of the total. This refined analysis provides deeper insights into the complex energy dynamics in subsonic jets and valuable information for predicting and controlling jet noise strategies. The modified energy equation provides a robust framework for understanding and quantifying the intricate energy transport processes in jet flows.