Theoretical models and experiments for the time-space characteristics of internal waves generated by towed bodies

Abstract

In this paper, we perform experiments on the time-space characteristics of internal waves generated by horizontally towed bodies with three aspect ratios in a stratified fluid with a halocline. By the real-time measurements of conductivity probe arrays which are arranged symmetrically in the transverse section of the stratified fluid tank, it is shown that the transition between the body-generated internal wave and the wake-generated internal wave is related to a critical Froude number Frc, which is linearly dependent on the aspect ratio. For FrFrc, the correlation velocities of internal waves are consistent with the towing speeds of the towed bodies, indicating that such internal waves in this range are dominated by the body-forced effect. The heights of such body-generated internal waves first increase with the increase of Fr until Fr reaches a certain value of Frp, which is also linearly dependent on the aspect ratio, and then decrease. For FrFrc, the correlation velocities of internal waves are noticeably lower than the towing speeds, indicating that such internal waves in this range are dominated by the wake-forced effect, and that the Froude numbers with respect to the correlation velocities of such internal waves vary in a range from 0.43 to 1.18. The heights of such wake-generated internal waves nearly linearly increase with Fr increasing regardless of the aspect ratio. Moreover, the patterns of body-generated waves are symmetric, while the patterns of wake-generated waves are not symmetric. Based on the experimental results and the equivalent source method which has been proposed to simulate the internal waves generated by a towed sphere, a new equivalent source method is developed to calculate the internal waves generated by towed slender bodies. For the body-generated waves, the method of designing the speed, length and diameter of the equivalent source is proposed. The symmetrical and anti-symmetrical equivalent source and their speed and size are also proposed for the wake-generated waves. The numerical results are in good accordance with the experimental results in the heights and patterns of waves, indicating that such a theoretical method and its parameter settings are reasonable and effective.