Steady Streaming Induced by Asymmetric Oscillatory Flows over a Rippled Bed

Pietro Scandura,Paolo Blondeaux,Carla Faraci

doi:10.3390/jmse8020142

Pietro Scandura, Paolo Blondeaux + Show 1 more

Open Access

https://doi.org/10.3390/jmse8020142

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Abstract

The flow induced by progressive water waves propagating over a rippled bed is reproduced by means of the numerical solution of momentum and continuity equations to gain insights on the steady streaming induced in the bottom boundary layer. When the pressure gradient that drives the flow is given by the sum of two harmonic components an offshore steady streaming is generated within the boundary layer which persists in the irrotational region. This steady streaming depends on the Reynolds number and on the geometrical characteristics of the ripples. Nothwithstanding the presence of a steady velocity component, the time-average of the force on the ripples vanishes.

Highlights

The knowledge of the flow induced by surface waves close the bottom of the sea is important to predict the vertical distribution of the wave induced velocity and to formulate reliable models of sediment transport
The steady streaming generated over a rippled bed by a purely oscillating pressure gradient is investigated
When the driving pressure gradient is made up of a single harmonic component of angular frequency σ∗, the time-averaged velocity field consists of recirculating cells confined near the bed and the time average of both the mean velocity away from the bed and the mean flow rate in the boundary layer vanish

Summary

Introduction

The knowledge of the flow induced by surface waves close the bottom of the sea is important to predict the vertical distribution of the wave induced velocity and to formulate reliable models of sediment transport. When the ripples are asymmetric and/or the pressure gradient driving the flow is the sum of two or more harmonic components, as it occurs under asymmetric or skewed waves [13], the steady velocity component persists at the outer edge of the bottom boundary layer, even at low Reynolds numbers, and affects the flow in the entire water column [14,15] This is due to the turbulence associated with flow separation at the ripple crests, which, in the cases mentioned above, causes a non-vanishing mean value of the Reynolds stress. Attention is focused on the velocity field averaged over the period of the imposed oscillations and on the force exerted by the fluid on the rippled bed

Formulation of the Problem

Analysis of the Mechanisms Inducing the Steady Streaming

Numerical Results

Conclusions