Disturbances due to the motion of a cylinder in a two-layer liquid system

Abstract

Thc di s tur?ance .created at the inte~'face o~ a two-lay~r liquid system by the horizontal motIOn of a cy l~nd~r In th~ upper lay~r IS studIed for vanous sizes a nd shapes of cylinders, depths of the hqlllds, cyllllder velO CItIes, and d ensity ratios. The disturbances fall into thrce categori es. First, when the layers are of equal thickness in most cases a train of progressi ve o.scillatory waves is produced at the interface. Seco;ld, when the d epth of the d e nscr layer IS much less than the d epth of the fres h-water layer, the profile of th e interface us ua lly resembles that corresponding to positive internal solitary waves. Third, when the d e pt h of the denser layer IS much greater than the d epth of the fr esh-water layer in most cases an internal hydra ulic jump is produced. The characteristics of the di sturbances in ea~h category a!'e related to t he size of the cylinder, the d epths of the liquids, the cylinder velOCIty, the denSIty ratIO, a nd the total distance of travel of the cylinder. A t heoretical a nalysis is gi ven for disturbances of the first category.

Experimental and numerical study of the hydrodynamic forces acting on a surface-piercing hydrofoil in muddy environments

“…(𝐹 𝑟 < 0.2). Moreover, depending on the properties and thickness of the fluid layers, the 𝐹 𝑟 𝑑 typically remains in the subcritical regime (𝐹 𝑟 𝑑 < 1) and is under these conditions when the largest amplitude of the internal wave occurs in two-layer flow systems (Carpenter and Keulegan (1960); Arntsen (1996); Sotelo et al (2023)), affecting drastically the hydrodynamic forces acting on the body. In the case of the towing tests presented in this work, the majority of the towing velocity range is supercritical (𝐹 𝑟 𝑑 > 1), which means that the influence of the internal wave is small.…”

The dual nature of the dead-water phenomenology: Nansen versus Ekman wave-making drags

“…We choose to name the first "Nansen wave-making drag", and the second, the "Ekman wave-making drag" which is more extensively probed in this paper. Some studies [8,10,11,12,13] make the choice to pull at constant speed, to probe the stationary Nansen wave-making drag, without the dynamic Ekman wave-making drag which is explored by towing at constant force. [14] (multiplied by a corrective factor 0.8 in the Ekman-like experiment).…”

Theoretical and Experimental Study of Internal Waves Generated by a Density Current Down a Sloping Bottom

“…5. Carpenter and Keulegan [5] generated internal waves by moving a cylinder in a two-layer liquid system. They found that if the two layers were approximately the same thickness, then the waves generated at the interface were of the progressive oscillatory type.…”

“…Lofquist [32] made observations of a density current system in a salt water turbulent flow under a layer of fresh water. The effects of moving objects in a two-layer system were studied by Carpenter and Keulegan [5] .…”