关键词: XBT探头, 非线性水动力, 微分解析解

Abstract: The expendable bathythermograph (XBT) is capable of measuring hydrological data across ocean depth profiles， so the precision of the XBT probe's operational depth is crucial to the system's accuracy. Based on nonlinear hydrodynamic theory and integrated with large-eddy simulation methods， this paper establishes a scaled three-dimensional computational fluid dynamics (CFD) numerical model and nonlinear hydrodynamic motion equations. Through numerical analysis of the probe's external flow field characteristics， the drag coefficient is extracted and utilized as a boundary condition to solve for the solution which can estimate the motion depth. Experiments conducted to verify the accuracy of the motion depth estimated. The results reveal that the error in the drag coefficient calculated by the numerical model is less than 4.39%. The drag on the XBT probe originates from the stagnation zone at the head and the adverse pressure gradient flow in the middle section. Using the drag coefficient as a boundary condition， the second-order differential motion equation， known as the nonlinear falling equation (FRE)， can be derived. The hyperbolic arctangent analytical solution of the FRE exhibits a maximum velocity deviation of 6.2% and a distance deviation of 3.2% compared to experimentally measured values. This methodology provides accurate speed and depth references for the design and engineering application of XBT probes， laying a foundation for the digital integration of this type of product and enhancing the accuracy of depth calibration.

Key words: XBT probe, nonlinear hydrodynamics, differential analytical solution