Numerical Investigation of Scour Beneath Pipelines Subjected to an Oscillatory Flow Condition

The present study carries out two-dimensional numerical simulations to investigate scour beneath a single pipeline and piggyback pipelines subjected to an oscillatory flow condition at a Keulegan–Carpenter (KC) number of 11 using SedFoam (an open-source, multi-dimensional Eulerian two-phase solver for sediment transport based on OpenFOAM). The turbulence flow is resolved using the two-phase modified k−ω 2006 model. The particle stresses due to the binary collisions and enduring contacts among the sediments are modeled using the rheology model of granular flow. The present numerical model is validated for the scour beneath a single pipeline, and the simulated sediment profiles are compared with published experimental data and numerical simulation results. The scour process beneath three different piggyback pipelines under the same flow condition are also considered, and the scour development and surrounding flow patterns are discussed in detail. Typical steady-streaming structures around the pipeline due to the oscillatory flow condition are captured. The scour depth during the initial development of the scour process for the piggyback pipeline with the small pipeline placed above the large one is the largest among all the investigated configurations. The phase-averaged flow fields show that the flow patterns are influenced by the additional small pipeline.

On the stability of the boundary layer at the bottom of propagating surface waves

This study contributes to an improved understanding of the stability of the boundary layer generated at the bottom of a propagating surface wave of small but finite amplitude such that both a second harmonic component and a steady streaming component, which are superimposed on the main oscillatory flow, assume significant values. A linear stability analysis of the laminar flow is made to determine the conditions leading to transition and turbulence appearance. The Reynolds number of the phenomenon is assumed to be large and a ‘momentary’ criterion of stability is used. The results show that, at a given location, the laminar regime becomes unstable when the flow close to the bottom reverses its direction from the onshore to the offshore direction and the Reynolds number exceeds a first critical value $R_{\delta ,c1}$ . However, close to the critical condition, the flow is expected to relaminarize during the other phases of the cycle. Only when the Reynolds number is increased does turbulence tend to appear also after the passage of the wave trough when the flow close to the bottom reverses from the offshore to the onshore direction. When the Reynolds number is further increased and becomes larger than a second ‘threshold’ value, the growth rate of the perturbations becomes positive over the entire wave period. The obtained results suggest the existence of four different flow regimes: the laminar regime, the disturbed laminar regime, the intermittently turbulent regime and the fully developed turbulent regime.

From steady streaming to oscillations: the role of subglacial drainage and temperate ice in ice-stream dynamics

<p>The majority of Antarctic ice is discharged through fast-flowing ice streams. Some of these ice streams exhibit variations in velocities and ice stream discharge on decadal to centennial time scales, but the factors controlling these variations are still insufficiently understood.  Using computational models of ice flow and hydrology, we predict the existence of two dynamical regimes: stable ice streaming associated with high hydraulic permeability of the bed, and ‘binge-purge’ oscillations associated with low permeability.</p><p>Observations indicate that the fast-flow of ice streams is enabled by meltwater lubricating the ice stream bed, and models suggest that this lubrication is the result of a positive feedback between fast flow, heat dissipation at the ice stream bed and meltwater production within the ice. In particular, recent studies have highlighted that heat dissipation in temperate ice stream margins, which are regions of high lateral strain, can contribute significantly to the subglacial water balance. However, the role of this meltwater flux in ice stream dynamics remains unclear. Here, we investigate the roles of subglacial drainage and feedbacks between fast flow and heat dissipation in ice-stream evolution. </p><p>The ice is modelled as a vertically uniform plug flow. Water flow at the bed is modelled as a Darcian system whose hydraulic transmissivity increases with decreasing effective pressure. Dynamical feedbacks in the energy balance include both frictional heating along the bed and lateral shear heating. Within our model, two distinct dynamic regimes can be identified: if the hydraulic permeability of the bed is sufficiently high to evacuate all meltwater produced at the ice stream bed and in its margins, a moderately-fast steady ice stream forms. Conversely,`binge-purge’ oscillations between fast and stagnant flow emerge when the hydraulic permeability of the bed is too low to evacuate the meltwater produced within the ice stream. Topographic controls can suppress this oscillatory behaviour, while the formation of temperate ice in ice stream margins amplifies it.</p>

Steady streaming as a method for drug delivery to the inner ear

The inner ear, or cochlea, is a fluid-filled organ housing the mechanosensitive hair cells. Sound stimulation is relayed to the hair cells through waves that propagate on the elastic basilar membrane. Sensorineural hearing loss occurs from damage to the hair cells and cannot currently be cured. Although drugs have been proposed to prevent damage or restore functionality to hair cells, a difficulty with such treatments is ensuring adequate drug delivery to the cells. Because the cochlea is encased in the temporal bone, it can only be accessed from its basal end. However, the hair cells that are responsible for detecting speech-frequency sounds reside at the opposite, apical end. In this paper we show that steady streaming can be used to transport drugs along the cochlea. Steady streaming is a nonlinear process that accompanies many fluctuating fluid motions, including the sound-evoked waves in the inner ear. We combine an analytical approximation for the waves in the cochlea with computational fluid dynamic simulations to demonstrate that the combined steady streaming effects of several different frequencies can transport drugs from the base of the cochlea further towards the apex. Our results therefore show that multi-frequency sound stimulation can serve as a non-invasive method to transport drugs efficiently along the cochlea.

Peristaltic flow in the glymphatic system

The flow inside the perivascular space (PVS) is modeled using a first-principles approach in order to investigate how the cerebrospinal fluid (CSF) enters the brain through a permeable layer of glial cells. Lubrication theory is employed to deal with the flow in the thin annular gap of the perivascular space between an impermeable artery and the brain tissue. The artery has an imposed peristaltic deformation and the deformable brain tissue is modeled by means of an elastic Hooke’s law. The perivascular flow model is solved numerically, discovering that the peristaltic wave induces a steady streaming to/from the brain which strongly depends on the rigidity and the permeability of the brain tissue. A detailed quantification of the through flow across the glial boundary is obtained for a large parameter space of physiologically relevant conditions. The parameters include the elasticity and permeability of the brain, the curvature of the artery, its length and the amplitude of the peristaltic wave. A steady streaming component of the through flow due to the peristaltic wave is characterized by an in-depth physical analysis and the velocity across the glial layer is found to flow from and to the PVS, depending on the elasticity and permeability of the brain. The through CSF flow velocity is quantified to be of the order of micrometers per seconds.

Direct Numerical Simulations of the Pulsating Flow over a Plane Wall

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.