Numerical simulation of oscillatory flows over a rippled bed by immersed boundary method

Shen, Linwei; Chan, Eng Soon

doi:10.1016/j.apor.2013.07.005

Cited by 3 publications

(2 citation statements)

References 21 publications

(31 reference statements)

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“…The oscillating flow over a wavy bottom problem has been approached by many authors due to its implication in sediment transport and ripple formation at the bottom of sea waves. In addition to the analytical approaches developed by Lyne [10], Kaneko and Honji [11], and Vittori [12], the works by Hara and Mei [21], Nishimura et al [22], and Shen and Chan [23] can be mentioned. In all the above studies, the generatrix of the bed undulations is transverse to the direction of the main flow, as sketched in Figure 1.…”

Section: Introduction and Objectivementioning

confidence: 99%

“…The original problem is highly complex due to the interaction between the flow and the soil. As the soil erodes, it alters the geometry, subsequently changing the flow characteristics, and so on, until eventually reaching a final equilibrium [4,5,9,[13][14][15][16][17][18][19][20]; (e) flow resulting from the motion of a wavy bottom [9,34]; and (f) oscillatory flow over a wavy bottom [10][11][12][21][22][23].…”

Section: Introduction and Objectivementioning

confidence: 99%

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Velocity Field due to a Vertical Deformation of the Bottom of a Laminar Free-Surface Fluid Flow

González,

Tamburrino

2024

Mathematics

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This article investigates the velocity field of a free-surface flow subjected to harmonic deformation of the channel bottom, progressing asymptotically from a flat initial state to a maximum amplitude. Assuming a uniform main flow with the primary velocity component transverse to the bed undulation, analytical solutions are obtained for the three velocity components and free surface distortion using the method of perturbations. The perturbation components of the velocity field, streamlines, and surface deformation depend on a dimensionless parameter that reflects the fluid inertia induced by bed deformation relative to viscous resistance. When viscous effects dominate, a monotonic decay of the perturbations from the bed to the free surface is observed. In contrast, when inertia dominates, the perturbations can exhibit an oscillatory behavior and introduce circulation cells in the plane normal to the main flow. The interplay between inertia and viscosity reveals scenarios where surface and bed deformations are either in or out of phase, influencing vertical velocity components. Figures illustrate these phenomena, providing insights into the complex dynamics of free-surface flows with harmonic bed deformation in the direction normal to the main flow, and amplitude growing with time. The results are limited to small deformations of the channel bottom, as imposed by the linearization of the momentum equations. Even so, to the best of the authors’ knowledge, this problem has not been addressed before.

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Section: Introduction and Objectivementioning

confidence: 99%

Section: Introduction and Objectivementioning

confidence: 99%

Velocity Field due to a Vertical Deformation of the Bottom of a Laminar Free-Surface Fluid Flow

González,

Tamburrino

2024

Mathematics

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Oscillatory flow regimes for a circular cylinder near a plane boundary

et al. 2018

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Oscillatory flow around a circular cylinder close to a plane boundary is numerically investigated at low-to-intermediate Keulegan–Carpenter ($KC$) and Stokes numbers ($\unicode[STIX]{x1D6FD}$) for different gap-to-diameter ratios ($e/D$). A set of unique flow regimes is observed and classified based on the established nomenclature in the ($KC,\unicode[STIX]{x1D6FD}$)-space. It is found that the flow is not only influenced by $e/D$ but also by the ratio of the thickness of the Stokes boundary layer ($\unicode[STIX]{x1D6FF}$) to the gap size (e). At relatively large $\unicode[STIX]{x1D6FF}/e$ values, vortex shedding through the gap is suppressed and vortices are only shed from the top of the cylinder. At intermediate values of $\unicode[STIX]{x1D6FF}/e$, flow through the gap is enhanced, resulting in horizontal gap vortex shedding. As $\unicode[STIX]{x1D6FF}/e$ is further reduced below a critical value, the influence of $\unicode[STIX]{x1D6FF}/e$ becomes negligible and the flow is largely dependent on $e/D$. A hysteresis phenomenon is observed for the transitions in the flow regime. The physical mechanisms responsible for the hysteresis and the variation of marginal stability curves with $e/D$ are explored at $KC=6$ through specifically designed numerical simulations. The Stokes boundary layer over the plane boundary is found to be responsible for the relatively large hysteresis range over $0.25<e/D<1.0$. Three mechanisms have been identified to the change of the marginal stability curve over $e/D$, which are the blockage effect due to the geometry setting, the favourable pressure gradient over the gap and the location of the leading eigenmode relative to the cylinder.

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Influence of plane boundary proximity on the Honji instability

et al. 2018

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This paper presents a numerical investigation of oscillatory flow around a circular cylinder that is placed in proximity to a plane boundary that is parallel to the cylinder axis. The onset and development of the Honji instability are studied over a range of Stokes numbers ($\unicode[STIX]{x1D6FD}$) and gap-to-diameter ratios ($e/D$) at a fixed Keulegan–Carpenter number ($KC=2$). Four flow regimes are identified in the ($e/D,\unicode[STIX]{x1D6FD}$)-plane: (I) featureless two-dimensional flow, (II) stable Honji vortex, (III) unstable Honji vortex and (IV) chaotic flow. As $e/D$ increases from $-0.5$ (embedment) to $1$, the critical Stokes number $\unicode[STIX]{x1D6FD}_{cr}$ for the onset of the Honji instability follows two side-by-side convex functions, peaking at the connection point of $e/D=0.125$ and reaching troughs at $e/D=0$ and 0.375. The Honji instability is always initiated on the gap side of the cylinder surface for $0.375\leqslant e/D\leqslant 2$ and occurs only on the top side for $-0.5\leqslant e/D<0.125$. The location for the initiation of the Honji instability switches from the gap side to the top side of the cylinder surface for $0.125<e/D<0.375$. No Honji instability is observed at $e/D=0.125$, where the flow three-dimensionality is developed through a different flow mechanism. Consistently, the three-dimensional kinetic energy of the flow, which represents a measure of the strength of flow three-dimensionality, varies with $e/D$ in a trend opposite to that of $\unicode[STIX]{x1D6FD}_{cr}$. Three physical mechanisms are identified as being responsible for the observed variation trend of $\unicode[STIX]{x1D6FD}_{cr}$ with $e/D$ and for various flow phenomena, which are the blockage effect induced by the geometry setting, the existence of the Stokes layer on the plane boundary and the favourable pressure gradient in the flow direction over the gap between the cylinder and the plane surface.

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Numerical simulation of oscillatory flows over a rippled bed by immersed boundary method

Cited by 3 publications

References 21 publications

Velocity Field due to a Vertical Deformation of the Bottom of a Laminar Free-Surface Fluid Flow

Velocity Field due to a Vertical Deformation of the Bottom of a Laminar Free-Surface Fluid Flow

Oscillatory flow regimes for a circular cylinder near a plane boundary

Influence of plane boundary proximity on the Honji instability

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