Microwave Doppler radar has been used to make noncontact river flow measurements and offers a high resolution and a wide range. However, discharge estimation with microwave Doppler radar is challenging due to the inability to measure flow velocity below the river surface based on the Doppler shift. To address this problem, a velocity distribution inversion method based on the Reynolds-Averaged Navier-Stokes (RANS) equations is proposed. A classical two-region model which divides the flow into the inner region and the outer region is applied. Velocity at the inner-outer boundary is estimated using surface velocity and the log law is used to estimate velocity distribution of the inner region. Taking velocities at the surface and the inner-outer boundary as boundary conditions, the velocity distribution in the outer region is derived by solving the RANS equations. Discharge is calculated by combining the proposed method with the velocity-area method. The results illustrated that the velocity distribution obtained by the proposed method and measured by an acoustic instrument are in reasonable agreement. Discharge estimated using the obtained velocity distribution has an error less than 10%. The work indicates the potential of microwave Doppler radar to retrieve the river cross section velocity distribution and estimate discharge.

中文翻译：

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基于RANS方程的微波多普勒雷达速度分布反演方法


微波多普勒雷达已用于进行非接触式河流流量测量，并提供高分辨率和宽范围。然而，由于无法根据多普勒频移测量河面以下的流速，因此利用微波多普勒雷达进行流量估算具有挑战性。针对这一问题，提出了一种基于雷诺平均纳维-斯托克斯（RANS）方程的速度分布反演方法。应用经典的两区域模型，将流分为内部区域和外部区域。使用表面速度估计内外边界处的速度，并使用对数定律估计内部区域的速度分布。以地表和内外边界速度为边界条件，通过求解RANS方程得到外部区域的速度分布。通过将所提出的方法与速度面积法相结合来计算流量。结果表明，该方法获得的速度分布与声学仪器测量的速度分布具有合理的一致性。使用获得的速度分布估计流量的误差小于10%。这项工作表明了微波多普勒雷达在检索河流断面速度分布和估算流量方面的潜力。