Transitional Behavior of a Flow Regime in Shoaling Tsunami Boundary Layers

Abstract

The transitional flow regime of the bottom boundary layer under hypothetical shoaling tsunamis is investigated in the entire region from the tsunami source to the shallow sea area. In order to calculate the shoaling process of a tsunami, an analytical method based on Green’s law and the linear long wave theory are employed, and flow regime criteria for the wave boundary layer proposed by one of the authors are applied. It is found that the bottom boundary layer in a tsunami source area is located in the laminar regime. Subsequently, transition occurs to the smooth turbulence during the shoaling process, with a transition from the smooth to the rough turbulent region in the shallow area. For precise evaluation of bottom friction acting on the sea bed and the resulting energy dissipation beneath the tsunami, it is highly necessary to include such transitional behavior in sea bottom boundary layers.

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].…”

“…However, investigations on depth-limited boundary layers for a smooth bottom have never been made in the past. It should be noted that, according to a recent investigation by Tanaka et al [22] on flow regime under the tsunami, laminar regime, and smooth turbulent regime are commonly observed during the tsunami shoaling process from the tsunami source area to the shallow region. In the present investigation, therefore, 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].…”

Numerical Simulation of the Boundary Layer Flow Generated in Monterey Bay, California, by the 2010 Chilean Tsunami: Case Study

“…While many studies of tsunamis emphasize their run-up and inundation, the nature of their-induced boundary layer flows (essential e.g. for understanding their induced sediment transport and scour around coastal structures) has also been studied realistically in controlled experimental (Larsen et al 2018;Tanaka et al 1999) or numerical (Williams and Fuhrman 2016;Larsen et al 2017;Larsen and Fuhrman 2019a;Larsen and Fuhrman 2019b;Tinh and Tanaka 2019;Tanaka et al 2020) environments. Due to their infrequent and unpredictable occurrence, actual field data involving the detailed boundary layer flow structure induced by tsunamis is elusive, seemingly being limited to the measurements of Lacy et al (2012), who were the first to measure detailed velocities within the boundary layer of a tsunami-induced flow.…”