Effect of the water depth on oscillatory flows over a flat plate: from the intermittent towards the fully turbulent regime

Steven J Kaptein,Vincenzo Armenio,Federico Roman,Matias Duran-Matute,Herman J H Clercx

doi:10.1007/s10652-019-09671-3

Steven J Kaptein, Vincenzo Armenio + Show 3 more

Open Access

https://doi.org/10.1007/s10652-019-09671-3

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Abstract

We performed high-resolution numerical simulations of a turbulent flow driven by an oscillating uniform pressure gradient. The purpose was to investigate the influence of a reduced water depth h on the structure and dynamics of the turbulent boundary layer and the transition towards a fully turbulent flow. The study is motivated by applications of oscillatory flows, such as tides, in which h is of the same order of magnitude as the thickness of the turbulent boundary layer delta. It was found that, if hsim delta, the turbulent flow is characterized by (1) an increase of the magnitude of the surface velocity, (2) an increase in the magnitude of the wall shear stress and (3) a phase lead of the velocity profiles, all with respect to the reference case for which hgg delta. These results are in agreement with analytical solutions for a laminar oscillatory flow. Nevertheless, if the value of the Reynolds number is too small and hsim delta, the flow relaminarizes.

Highlights

Oscillatory flows are of interest in the offshore industry and in coastal engineering as approximations of some of the typical flows occurring in seas, such as the currents generated by waves or by tides
In order to investigate the turbulent oscillatory flow accurately, we performed numerical simulations which we describe
Since our simulations at Re = 3460 are the first simulations at this high Reynolds number value for which the wall layer is resolved, we display the wall shear stress and four velocity profiles in Fig. 3 together with the available data of Jensen et al [1]

Summary

Introduction

Oscillatory flows are of interest in the offshore industry and in coastal engineering as approximations of some of the typical flows occurring in seas, such as the currents generated by waves or by tides. Oscillatory flows have been investigated intensively in the past both experimentally [1,2,3] and numerically [4,5,6,7,8] The majority of these studies have been performed in experimental set-ups or computational domains where the water depth h was much larger than the thickness of the turbulent boundary layer. This is a good approximation for wave boundary layers, it is, questionable for tides in several regions.

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