Abstract
A theoretical and numerical study is carried out to investigate the transformation of the wave boundary layer from non-depth-limited (wave-like boundary layer) to depth-limited one (current-like boundary layer) over a smooth bottom. A long period of wave motion is not sufficient to induce depth-limited properties, although it has simply been assumed in various situations under long waves, such as tsunami and tidal currents. Four criteria are obtained theoretically for recognizing the inception of the depth-limited condition under waves. To validate the theoretical criteria, numerical simulation results using a turbulence model as well as laboratory experiment data are employed. In addition, typical field situations induced by tidal motion and tsunami are discussed to show the usefulness of the proposed criteria.
Highlights
Unlike steady flow in an open channel, the wave boundary layer is generally confined in the immediate vicinity of the bottom, resulting in large bottom shear stress due to its steep velocity gradient near the bed
In order to make a closer inspection of the transitional behavior in the shear stress in Figure 4, Figure 5 is plotted as a relationship between τ*m, t*m, and R
Theoretical results based on the wave boundary layer thickness and the friction factor yields similar demarcations
Summary
Unlike steady flow in an open channel, the wave boundary layer is generally confined in the immediate vicinity of the bottom, resulting in large bottom shear stress due to its steep velocity gradient near the bed. T = 1–2 s, boundary layer thickness becomes thinner in the order of O(0.1 cm) For this reason, a detailed measurement of flow velocity distribution in a wave boundary layer is extremely difficult in a laboratory scale wave flume. Placement of large roughness elements on the bottom in an oscillatory tunnel facilitates precise measurement of fluid motion in a wave boundary layer by increasing the boundary layer thickness. Using these types of the flow generation system, study on wave boundary has been made by various researchers [13,14,15,16,17]. The demarcation between non-depth-limited and depth-limited boundary layers over a smooth bottom is theoretically derived and validated using various data sources including the recent numerical computation results of Kaptein et al [32]
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