Improvement of the Full-Range Equation for Wave Boundary Layer Thickness

Abstract

In order to improve the accuracy of the original full-range equation for wave boundary layer thickness, with special reference to increasing its applicability to tsunami-scale waves, a theoretical investigation is carried out to derive a dimensionless expression which is valid under both smooth and rough turbulent regimes. A coefficient in the equation is determined through a comparison with k-ω model computation results for tsunami-waves along with laboratory scale oscillatory flow experiments. Thus, the improved full-range equation for wave boundary layer thickness enables us to cover a wide range of wave periods from wind-wave to tsunami.

Development of Depth-Limited Wave Boundary Layers over a Smooth Bottom

“…As a result, it was shown that even at the water depth of 10 m, the depth-limited condition was not satisfied. Recently, Tanaka et al [22] used a newly proposed full-range equation for wave boundary layer thickness by Tanaka et al [23], and obtained a result similar to Tinh and Tanaka [18].…”

“…Kaptein et al [32] reported Van der Giessen et al's [58] field observation results of tide-induced boundary layer development in the Rhine River Estuary, the Netherlands. The measurement results are summarized in Table 3, in which the boundary layer thickness δ is calculated using Equation ( 14) for smooth bottom proposed by Tanaka et al [23]. Judging from /ℎ ratio in Table 3, it is clear that the tide-induced boundary layer in the Rhine Estuary is under depth-limited condition.…”

“…By equating wave-induced boundary layer thickness δ and water depth h, Tinh and Tanaka [18] proposed an equation and a diagram for demarcating wave friction zone and steady friction zone under a rough turbulent regime. Similarly, under smooth turbulent condition, the following equation recently proposed by Tanaka et al [23] can be applied to obtain a criterion in terms of wave boundary layer thickness:…”

Transitional Behavior of a Flow Regime in Shoaling Tsunami Boundary Layers

“…For computing wave boundary layer thickness under a shoaling tsunami, the full-range equation originally proposed by Sana and Tanaka [20,21] and recently modified by the authors [22] will be applied. The definition of wave boundary thickness proposed by Jensen et al [23] is used in this study, which is the height of overshooting at σt = 0 under the wave crest as defined in Figure 1b.…”

“…There are alternative definitions for wave boundary layer thickness, such as Jonsson [10] based on the minimum distance from the bottom to an elevation where the velocity equals the amplitude of the free-stream velocity, U m , and Sleath [24] and Yuan and Madsen [25] in terms of the distance where the defect velocity amplitude is 1% or 5% of the free-stream amplitude. Among these definitions, that of Jensen et al [23] has successfully been applied for demarcating the friction factor under the tsunami [22].…”