Towards Turbulent Stresses Estimates by Special Geometric Adjustment of Two ADCPs

Abstract

The calculation of the turbulent stress matrix using acoustic Doppler current profiler (ADCP) data remains a challenging problem in the study of geophysical flows. One of the ways to overcome the problem is to use a system of two coupled ADCP with pairs of beams intersecting at a certain depth. When device configuration is symmetric in horizontal, this setting makes it possible to estimate the stresses only for a small range of depths, close to the depth of beam intersection point. To overcome this restriction, in this paper the modified setting is proposed, when both devices are symmetrically turned in the horizontal plane. The X axes of the devices are not collinear for such setting, and two pairs of beams intersect at two different depths, which depend on the distance between the emitters and devices’ rotation angle, and can be chosen in advance. At each of these depths, six beam velocity variances can be directly calculated, as well as the correlation of those velocity components, which correspond to the intersecting beams. As a result, an overdetermined system of equations is derived for unknown stresses, for both depths. The method was approbated during the processing of two series of field data obtained in lakes during open water and ice-covered periods. In most cases, calculations lead to physically consistent results; in particular, the stress matrix turns out to be positive definite. The method’s limitations and perspectives of its development are discussed.