The influence of topography on sonic boom propagation is investigated. The full two-dimensional Euler equations in curvilinear coordinates are solved using high-order finite-difference time-domain techniques. Simple ground profiles, corresponding to a terrain depression, a hill, and a sinusoidal terrain, are examined for two sonic boom waves: a classical N-wave and a low-boom. Ground reflection of the sonic boom is affected by elevation variations: a concave ground profile induces compression, which tends to increase the peak pressure in particular, while the opposite is true for convex elevation variations, which lead to expansion and a reduction in peak pressure. The reflected boom is then strongly altered. Furthermore, a sufficiently concave topography can cause focal zones, which generate extra contributions at ground level in the form of U-waves in addition to the reflected wave. This mechanism has the largest effect on waveforms at ground level. The variations of standard metrics are of a few dBs compared to a flat ground for both sonic boom waves, and they are notably greater for the terrain depression than for the hill. Finally, in the case of a sinusoidal terrain, the pressure waveforms are composed of multiple arrivals due to successive focal zones.

中文翻译：

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通过欧拉方程的解析来表征地形对声波反射的影响

研究了地形对声波传播的影响。使用高阶有限差分时域技术求解曲线坐标中的完整二维Euler方程。针对两个声波波动波检查了与地形凹陷，丘陵和正弦波地形相对应的简单地面剖面：经典N波和低声波。声波喷杆的地面反射会受到高度变化的影响：凹形的地面轮廓会引起压缩，这尤其会增加峰值压力，而凸形的高度变化则相反，这会导致膨胀并降低峰值压力。然后，反射的吊杆将发生强烈变化。此外，足够凹的地形可能会导致焦点区域，除了反射波之外，还以U波的形式在地面产生了额外的贡献。该机制对地电平的波形影响最大。与平坦的地面相比，两种声波波动的标准度量标准差异都只有几dB，并且地形低洼处的变化明显大于丘陵处的变化。最后，在正弦地形的情况下，由于连续的聚焦带，压力波形由多次到达组成。