During motion from deep to shallow water, multiple equilibria may emerge, each with identical drag—a phenomenon that can be explained by a localized amplification of the wave drag near the shallow wave speed. The implication of this is the emergence of several previously unstudied bifurcation patterns and hysteresis routes. Here, we address these nonlinear dynamics by considering the quasisteady motion of a body between deep and shallow water, where the depth is slowly varying. We survey several theoretical models for the drag, compare these against our tow-tank experimental measurements, and then use the validated theory to explore the bifurcation patterns using two parameters: the depth of motion and the forcing. In particular, using a case study of a lake with a sinusoidal depth profile, we illustrate that hysteresis effects can play a significant role on the speed of motion and journey time, presenting interesting implications for naval and racing applications.

中文翻译：

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滞波在浅水中拖曳

在从深水运动到浅水的过程中，可能会出现多个平衡点，每个平衡点具有相同的阻力-这种现象可以通过在浅波速度附近局部放大波浪阻力来解释。这就意味着出现了一些以前未被研究的分叉模式和滞后路径。在这里，我们通过考虑深度在缓慢变化的深水和浅水之间的物体的准稳态运动来解决这些非线性动力学问题。我们调查了阻力的几种理论模型，并将其与我们的拖船实验测量结果进行比较，然后使用经过验证的理论通过两个参数（运动深度和受力）探索分叉模式。特别是，以一个具有正弦深度剖面的湖泊为例，