Direct Numerical Simulations of the Pulsating Flow over a Plane Wall

Giovanna Vittori,Marco Mazzuoli,Paolo Blondeaux

doi:10.3390/jmse8110893

Giovanna Vittori, Marco Mazzuoli + Show 1 more

Open Access

https://doi.org/10.3390/jmse8110893

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Abstract

The results of direct numerical simulations of the flow generated in a plane duct by a pressure gradient which is the sum of two terms are described. The first term of the pressure gradient is constant in space but it oscillates in time whereas the second term is constant both in space and in time. Therefore, a pulsating flow is generated, similar to that generated at the bottom of a monochromatic propagating surface wave when nonlinear effects are taken into account. The simulations are carried out for values of the parameters similar to those considered in previous investigations. It is shown that even a small constant pressure gradient influences the flow regime in the bottom boundary layer. In particular, turbulence strength is damped when the steady velocity component has the direction opposite to the oscillating velocity component whereas turbulence strength increases when the steady and oscillating components point in the same direction. Even though the flow is not exactly equal to that generated at the bottom of sea waves, where second order effects in the wave steepness induce a steady streaming in the direction of wave propagation, our results provide information on the interaction of the steady streaming with the oscillatory flow and are also relevant for investigating the dynamics of sediment close to the sea bottom. Indeed, since the turbulent eddies tend to pick-up the sediment from the bottom, it can be inferred that the triggering of turbulence enhances sediment transport towards the shore.

Highlights

A fair approximation of the flow field generated by a propagating surface wave is obtained by assuming the flow to be irrotational and the fluid to be inviscid
In a purely oscillatory boundary layer, for values of the Reynolds number larger than a first critical value ranging between 500 and 600, the transition to turbulence takes place every half cycle and it is followed by a phase during which turbulence decays and the flow recovers a laminar-like behaviour [19]
The time development of the turbulent kinetic energy (K∗), averaged over horizontal planes and integrated into the vertical direction, shows that the pressure gradient has different effects on the flow, depending on the direction of the oscillatory velocity component with respect to the direction of the current induced by the steady pressure gradient

Summary

Introduction

A fair approximation of the flow field generated by a propagating surface wave is obtained by assuming the flow to be irrotational and the fluid to be inviscid. The measurements of Hino et al [2] show that the velocity field is characterized by the appearance of turbulent oscillations towards the end of the accelerating phases of the cycle when the Reynolds number is larger than a value approximately equal to 500. The numerical simulations are carried out for values of the parameters similar to those considered by [18,19] Since both theoretical analyses and previous numerical simulations show that wall imperfections play a key role in triggering turbulence appearance, in the present numerical simulations the wall is not perfectly plane but characterized by the presence of a small waviness, the amplitude of which is so small that the wall is flat from a macroscopic point of view.

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