AI 中文总结
该研究将可压缩流动的受扰对流波方程（cPCWE）推广至空间变平均密度场，通过数值验证表明其在宽马赫数范围的声辐射预测精度优于Lighthill类比，可解析剪切层内的声场。
AI 中文摘要
针对可压缩流动的受扰对流波方程理论（cPCWE）被推广到空间变化的平均密度场。所得方程是声学扰动方程的精确标量重构，利用单一未知量描述运动非均匀介质中的声音产生与传播。相关工作流程需依次求解亥姆霍兹分解问题、泊松方程和cPCWE，其中间变量与Kovasznay的涡模式、熵模式和声学模式相关，为每个处理步骤提供了物理解释。通过对二维等温混合层的完全可压缩直接数值模拟（DNS）及同一框架下计算的Lighthill类比进行定量精度评估，马赫数范围为M=0.2至M=0.4，基于层间速度差和环境声速。在该马赫数范围内，辐射功率跨越数个数量级。对于M≥0.25，三种方法得到的声功率水平偏差在0.9dB以内；对于M≥0.3，偏差在0.5dB以内。在M=0.2时，声学波动相对于流体动力学波动最弱，Lighthill类比对辐射功率的预测偏高2.8dB，而cPCWE与DNS参考值的偏差仅为-1.2dB。这种更紧密的一致性源于cPCWE源项被限制在涡配对区域，且其对流波算子可表征对流与折射。除重现远场声音外，cPCWE还能解析剪切层内的声场，而DNS的该区域场被涡波动掩盖。
英文摘要
The theory of the perturbed convective wave equation for compressible flows (cPCWE) is generalised to spatially varying mean-density fields. The resulting equation is an exact scalar reformulation of the acoustic perturbation equations and describes sound generation and propagation in moving inhomogeneous media using a single unknown. The intermediate variables of the associated workflow, in which a Helmholtz decomposition problem, a Poisson equation and the cPCWE are solved successively, are related to the vortical, entropy and acoustic modes of Kovasznay, providing a physical interpretation of each processing step. The quantitative accuracy is assessed against fully compressible direct numerical simulations (DNS) of two-dimensional isothermal mixing layer and Lighthill's analogy computed in the same framework at Mach numbers between M=0.2 and M=0.4, based on the velocity difference across the layer and the ambient speed of sound. Over this range of Mach numbers, the radiated power spans several orders of magnitude. For M>=0.25, the sound power levels obtained using the three methods agree within 0.9dB, and within 0.5dB for M>=0.3. At M=0.2, where the acoustic fluctuations are weakest relative to the hydrodynamic ones, Lighthill's analogy over-predicts the radiated power by 2.8dB. In contrast, the cPCWE deviates from the DNS reference by only -1.2dB. This closer agreement is because the cPCWE source term is confined to the vortex-pairing region, while convection and refraction are represented by its convective wave operator. Beyond reproducing the far-field sound, the cPCWE resolves the acoustic field within the shear zone itself, where the DNS' fields are masked by vortical fluctuations.
Comments10 pages, 4 figures
