Measurement and modelling of bed shear induced by solitary waves

Abstract

Tsunamis are a geo-hazard that have a high potential to devastate majority of infrastructure in their path. Considering the threat from possible tsunami around the Australian coast, CSIRO Australia, under the Wealth from Ocean Flagship program, initiated studies on tsunami induced hazards to the submarine infrastructure along the northwest Australian coast. This thesis is part of the research work initiated by CSIRO Australia. Experimental and numerical model studies are carried out at UQ to understand the tsunami effects on the seabed especially continental slope and continental shelf. Solitary waves are considered to represent the leading waves of a tsunami. Breaking and non-breaking solitary waves over smooth and rough beds (d50=0.2mm) were generated in the laboratory and the corresponding shear stresses were measured using a Shear Plate apparatus. A physical model was set up in the laboratory that represented the deep horizontal ocean floor, inclined continental slope and the shallow horizontal continental shelf. Measurements of bed shear stress, surface elevation and flow velocities were carried out. Periodic waves were also generated and the bed shear stresses measured over a horizontal bed were found to be comparable with the earlier studies and theoretical estimates. The total force (sum of bed shear stress and pressure gradient force) measured using the shear plate is important in determining the stability of submarine sediment and in sheet flow regimes. The bed shear stresses generated by breaking and non-breaking solitary waves were in laminar and transitional flow regimes (~104<Re<~105), and showed reversal of sign during the deceleration phase of the solitary wave, although the flow did not change its direction. The non-breaking solitary wave height to still water depth ratio over the horizontal smooth bed varied between 0.12 and 0.68. The maximum near bed velocity varied between 0.16 m/s and 0.51 m/s and the peak positive total shear stress varied between 0.386 N/m2 and 2.06 N/m2. The maximum positive total shear stress magnitudes over smooth bed were observed to increase up the slope and further on the shelf for a given h/d ratio. For rough bed cases, the peak positive total shear stress was an order of magnitude larger than that of smooth bed cases, with increasing peak positive total shear stress as the wave propagated up slope. Wave friction factors are found to vary depending on the choice of normalizing velocity used in the drag law, i.e., either using the maximum velocity, as is conventional, or the instantaneous velocity corresponding to the shear stress. To understand the impact of the phase difference of the velocity and shear stress on friction factors, friction factors were estimated from bed shear stress at different instances over the wave, viz., time of maximum positive total shear stress, maximum bed shear stress and at the time of maximum velocity, using both the maximum velocity and the instantaneous velocity at that phase of the wave cycle. Friction factors are consistent with previous data for monochromatic waves, and are found to vary inversely with the square-root of the Reynolds number. The phase difference between the maximum bed shear stress and the maximum velocity was about 30° for the smooth horizontal bed and it was about 38° for the rough horizontal bed. The median phase difference for the sloping bed was between 24° to 28° and for the horizontal bed beyond the slope was about 34°. A convolution model forced with the measured free stream acceleration is used to predict total and bed shear stresses. The peak positive value of the total and bed shear stresses are considered for comparison between measurements and model results. Modelled and measured peak positive bed shear stresses correlated well with the measurements for the horizontal bed data. However, for the sloping bed region, the model generally resulted in under estimation of the bed shear stress, few reasons could be attributed to changing eddy viscosity during upslope flow propagation or could be due to excessive estimation of the pressure gradient forces. For the rough bed cases, the model behaved similarly to that over the smooth bed, with appropriate roughness incorporated in the model. However, the model did not predict well for breaking wave conditions. Due to the inherent formulation of the convolution model, it is found that the model fails for steady flow cases. Further work related to a comprehensive model including steady flow and unsteady flow would be required. The convolution model and conventional drag law model to estimate the shear stress are applied to tsunami induced flow over the slope and shelf region of the northwest Australian (NWA) coast and the south east Indian coast. MIKE3 - a 3D hydrodynamic numerical model was used to obtain the tsunami induced flow field. The results suggest that tsunami is highly likely to induce significant sediment mobility at shallower depths. However, to identify the hotspots of high sediment mobility which could trigger submarine slides, careful study is required since the tsunami induced flow field is site specific.