A two-dimensional model of the edge tone is studied by a highly accurate and reliable method of direct numerical simulation of the compressible Navier-Stokes equations, and used to verify key features observed in previous experimental and numerical studies, and to discover new features related to the jet motion and the edge tone generation mechanism. The first and second modes of the edge tone that are numerically reproduced agree well with Brown’s equation. In the mode transition region, dynamical mode transition is observed at a fixed jet velocity. For both first and second modes, the pressure distributions are antisymmetric with respect to the edge plate, and the sound intensity is proportional to the fifth power of the jet velocity. These results are consistent with the edge tone being radiated from a dipole-like source. Spatial profiles of the velocity and the velocity variance of the oscillating jet are also investigated for each mode over a range of the jet velocity including the mode transition regime. The amplitude of the velocity oscillation becomes constant with increasing jet velocity, while a measure of the amplitude of the velocity variance profile, which is introduced to characterize the strength of the jet fluctuation and named the ’fluctuation strength’, is proportional to the third power of the jet velocity. Some properties of the fluctuation strength correspond to properties of the sound intensity, including the first mode having larger amplitude than the second mode, and the way of deviating from the power law at smaller values of jet velocity and in the mode transition region. It is proposed that the third-power law exhibited by behavior of the fluctuation strength could be related to the increase of the skewness observed in the velocity profile with increase of jet velocity, and a model calculation is used to support this proposal.

通过高精度和可靠的可压缩Navier-Stokes方程直接数值模拟方法研究了边缘色调的二维模型，并将其用于验证先前实验和数值研究中观察到的关键特征，并发现与之相关的新特征。喷射运动和边缘色调生成机制。数值再现的边缘色调的第一和第二模式与布朗方程式非常吻合。在模式转变区域中，以固定的射流速度观察到动态模式转变。对于第一和第二模式，压力分布相对于边缘板是不对称的，并且声音强度与射流速度的五次方成正比。这些结果与从偶极子源辐射出的边缘色调一致。还研究了在包括模式过渡机制在内的射流速度范围内，每种模式的速度和振荡射流速度变化的空间分布。速度振荡的幅度随射流速度的增加而变得恒定，而速度变化曲线的幅度的量度（用来表征射流起伏的强度并称为“波动强度”）与三次方成正比。射流速度 波动强度的一些属性对应于声音强度的属性，包括具有比第二模式大的振幅的第一模式，以及在较小的射流速度值和模式过渡区域中偏离幂律的方式。