Influences of fluid accelerations on the threshold of motion

The hydraulic stability of rocks and other non-cohesive sediments is often described by so-called threshold conditions. These conditions describe the stability of the stones in terms of critical values of the velocity, wave height, or shear stress. The influence of fluid accelerations in most of these conventional design methods has been neglected or has been processed empirically. For various purposes however (as bottom protection in constrictions, wave attack on a mild slope, or the behavior of sediments in the surf zone) the stability of stones does not only depend on the flow velocity (or shear stress) but also on the influence that fluid particle accelerations have on these sediments. As only little is known on the background of these processes a pilot experiment in a wave flume has been carried out to help identify key processes and to find out whether these fluid accelerations, do influence the threshold of motion. During the experiment 78 test series have been performed with changing wave steepnesses in order to create scenarios of similar horizontal near-bed velocities, but with different accelerations. Another 22 of such tests series have been carried out with stones that have a smaller diameter. It has been assumed that if there is a relation between the threshold of motion and accelerations then for some combinations of a velocity and acceleration there are stones that move while in other cases with the same near-bed velocities, but a lower acceleration, there will be no movement of the same stones. After analysis of the experimental data it appears that both the fluid accelerations and the fluid velocities influence the threshold of motion. This can be shown with the help of two different approaches Usage of an instantaneous approach requires some skills and is very time-consuming, but leads to very satisfying results. With use of video monitoring it appears that the initial motion of stones starts somewhere between 0.15s and 0.05s before passage of the wave top. This interval also happens to be the interval at which the velocities and accelerations have large values in the direction of the wave propagation. Using these velocities and accelerations in a Morison-like equation proofs that the threshold of motion is dependent on both the horizontal near-bed velocities and the accelerations. The second used approach was by means of a waveform approach. Such an approach is easier to use and has no problems of finding the exact momentary forces. Also with use of this approach it is possible to show that the threshold of motion depends in some measure on fluid accelerations in addition to fluid velocities. A dimensional form of acceleration skewness as introduced by Drake and Calantoni (2001) is very use to show this. Furthermore it is shown that the acceleration term becomes increasingly significant as the wave becomes more peaked. Finally during the analysis an attempt has been made to find a stability relation, in which both accelerations and velocities are present. A dimensionless entrainment parameter and force parameter have been designed, in order to use this relation for various stone sizes. The relation does show an increase of entrainment when the wave forces are enlarged, but there is still a lot of scatter in the diagram. M.Sc Thesis Maarten Tromp ii Delft University of Technology Table of contents Table of contents PREFACE ...................................................................................................................................... 1 ABSTRACT ................................................................................................................................... 2 TABLE OF CONTENTS.............................................................................................................. 3 LIST OF FIGURES....................................................................................................................... 5 1 PROBLEM DESCRIPTION ................................................................................................ 7 1.1 GENERAL INTRODUCTION.............................................................................................................. 7 1.2 PROBLEM ANALYSIS ...................................................................................................................... 7 1.3 PROJECT DEFINITION...................................................................................................................... 8 1.4 OBJECTIVE..................................................................................................................................... 8 2 THEORY................................................................................................................................ 9 2.