ORCID Profile
0000-0002-5428-2387
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Publisher: Springer-Verlag
Date: 2005
Publisher: The Royal Society
Date: 08-11-2004
Publisher: AIP Publishing
Date: 07-2022
DOI: 10.1063/5.0098609
Abstract: A linear stability investigation is undertaken on the two-dimensional flow that develops in a channel whose walls are coated with a superhydrophobic material. The surfaces are modeled as classical slip surfaces, exploiting a linear Navier slip condition imposed on the channel walls. Both symmetric and asymmetric slip walls are considered, whereby the linearized stability of the flow is determined via an Orr–Sommerfeld normal-mode approach. In both instances, the application of slip establishes a significant stabilizing effect and increases the critical Reynolds number associated with the onset of linearly unstable behavior. Indeed, for sufficiently large slip lengths, the upper and lower branches of the neutral stability curve coalesce. Consequently, the flow becomes linearly stable to all disturbances for all wavelengths and Reynolds numbers.
Publisher: AIP Publishing
Date: 07-2020
DOI: 10.1063/5.0012795
Publisher: Springer Science and Business Media LLC
Date: 10-01-2008
Publisher: The Royal Society
Date: 09-2015
Abstract: We consider the flow induced by a sphere, contained in an otherwise quiescent body of fluid, that is suddenly imparted with angular momentum. This classical problem is known to exhibit a finite-time singularity in the boundary-layer equations, due to the viscous boundary layer, induced by the sudden rotation, colliding at the sphere's equator. We consider this flow from the perspective of the post-collision dynamics, showing that the collision gives rises to a radial jet headed by a swirling toroidal starting vortex pair. The starting vortex propagates away from the sphere and, in doing so, loses angular momentum. The jet, in turn, develops an absolute instability which propagates back towards the sphere's equator. The starting vortex pair detaches from the jet and expands as a coherent (non-swirling) toroidal vortex pair. We also present results of some new experiments which show good qualitative agreement with our computational results.
Publisher: IOP Publishing
Date: 02-2001
Publisher: Cambridge University Press (CUP)
Date: 25-05-1996
DOI: 10.1017/S0022112096002431
Abstract: We consider weakly nonlinear wave motions in a thermally stratified boundary layer. Attention is focused on the upper branch of the neutral stability curve, corresponding to small wavelengths and large Reynolds number. In this limit the motion is governed by a first harmonic/mean flow interaction theory in which the wave-induced mean flow is of the same order of magnitude as the wave component of the flow. We show that the flow is governed by a system of three coupled partial differential equations which admit finite- litude periodic solutions bifurcating from the linear, neutral points.
Publisher: Oxford University Press (OUP)
Date: 20-10-2006
DOI: 10.1093/QJMAM/HBL021
Publisher: AIP Publishing
Date: 06-2017
DOI: 10.1063/1.4986262
Abstract: In this work, we compute steep forced solitary wave solutions for the problem of free-surface flow over a localised topographic disturbance in an otherwise flat horizontal channel bottom. A single forced solitary wave and a double-crested forced solitary wave solution are shown to exist, both of which approach the Stokes limiting configuration of an included angle of 120° and a stagnation point at the wave crests. The solution space for the topographically forced problem is compared to that found in Wade et al. [“On the free-surface flow of very steep forced solitary waves,” J. Fluid Mech. 739, 1–21 (2014)], who considered forcing due to a localised distribution of pressure applied to the free surface. The main feature that differentiates the two types of forcing is an additional solution that exists in the pressure-forced problem, a steep wave with a cusp at a single wave crest. Our numerical results suggest that this cusped-wave solution does not exist in the topographically forced problem.
Publisher: Wiley
Date: 02-1999
Publisher: The Royal Society
Date: 15-04-1991
Abstract: The receptivity problem for Görtler vortices induced by wall roughness is investigated. The roughness is modelled by small litude perturbations to the curved wall over which the flow takes place. The litude of these perturbations is taken to be sufficiently small for the induced Görtler vortices to be described by linear theory. The roughness is assumed to vary in the spanwise direction on the boundary-layer lengthscale, whilst in the flow direction the corresponding variation is on the lengthscale over which the wall curvature varies. In fact the latter condition can be relaxed to allow for a faster streamwise roughness variation so long as the variation does not become as fast as that in the spanwise direction. The function that describes the roughness is assumed to be such that its spanwise and streamwise dependences can be separated this enables us to make progress by taking Fourier or Laplace transforms where appropriate. The cases of isolated and distributed roughness elements are investigated and the coupling coefficient which relates the litude of the forcing and the induced vortex litude is found asymptotically in the small wavelength limit. It is shown that this coefficient is exponentially small in the latter limit so that it is unlikely that this mode can be stimulated directly by wall roughness. The situation at O (1) wavelengths is quite different and this is investigated numerically for different forcing functions. It is found that an isolated roughness element induces a vortex field which grows within a wedge at a finite distance downstream of the element. However, immediately downstream of the obstacle the disturbed flow produced by the element decays in litude. The receptivity problem at larger Görtler numbers appropriate to relatively large wall curvature is discussed in detail. It is found that the fastest growing linear mode of the Görtler instability equations has wavenumber proportional to the one-fifth power of the Gortler number. The mode can be related to both inviscid disturbances and the disturbances appropriate to the right-hand branch of the neutral curve for Görtler vortices. The coupling coefficient between this, the fastest growing vortex, and the forcing function is found in closed form.
Publisher: Cambridge University Press (CUP)
Date: 13-12-2013
DOI: 10.1017/JFM.2013.590
Abstract: The free-surface flow of very steep forced and unforced solitary waves is considered. The forcing is due to a distribution of pressure on the free surface. Four types of forced solution are identified which all approach the Stokes-limiting configuration of an included angle of $12{0}^{\\circ } $ and a stagnation point at the wave crests. For each type of forced solution the almost-highest wave does not contain the most energy, nor is it the fastest, similar to what has been observed previously in the unforced case. Nonlinear solutions are obtained by deriving and solving numerically a boundary integral equation. A weakly nonlinear approximation to the flow problem helps with the identification and classification of the forced types of solution, and their stability.
Publisher: Cambridge University Press (CUP)
Date: 25-10-2019
DOI: 10.1017/JFM.2019.783
Abstract: The unsteady flow due to a sphere, immersed in a quiescent fluid, and suddenly rotated, is a paradigm for the development of unsteady boundary layers and their collision. Such a collision arises when the boundary layers on the surface of the sphere are advected towards the equator, where they collide, serving to generate a radial jet. We present the first particle image velocimetry measurements of this collision process, the resulting starting vortex and development of the radial jet. Coupled with new computations, we demonstrate that the post-collision steady flow detaches smoothly from the sphere’s surface, in qualitative agreement with the analysis of Stewartson ( Grenzschichtforschung/Boundary Layer Research (ed. H. Görtler), Springer, 1958, pp. 60–70), with no evidence of a recirculation zone, contrary to the conjectured structure of Smith & Duck ( Q. J. Mech. Appl. Maths , vol. 20, 1977, pp. 143–156).
Publisher: AIP Publishing
Date: 08-1991
DOI: 10.1063/1.857932
Abstract: The stability of the flow of a viscous incompressible fluid over a curved compliant wall to longitudinal Goertler vortices is investigated. The compliant wall is modeled by a particularly simple equation relating the induced wall displacement to the pressure in the overlying fluid. Attention is restricted to the large Goertler number regime this regime being appropriate to the most unstable Goertler mode. The effect of wall compliance on this most unstable mode is investigated.
Publisher: Cambridge University Press (CUP)
Date: 23-11-2015
DOI: 10.1017/JFM.2015.627
Abstract: The stability of an almost inviscid compressible fluid flowing over a rigid heated surface is considered. We focus on the boundary layer that arises. The effect of surface heating is known to induce a streamwise acceleration in the boundary layer near the surface. This manifests in a streamwise velocity which exhibits a maximum larger than the free-stream velocity (i.e. the streamwise velocity exhibits an ‘overshoot’ region). We explore the impact of this overshoot on the stability of the boundary layer, demonstrating that the compressible form of the classical Rayleigh equation (which governs the development of short wavelength instabilities) possesses a new unstable mode that is a direct consequence of this overshoot. The structure of this new class of modes in the small wavenumber limit is detailed, providing a valuable confirmation of our numerical results obtained from the full inviscid eigenvalue problem.
Publisher: AIP Publishing
Date: 12-2008
DOI: 10.1063/1.3054146
Abstract: We report the results of an experimental investigation into fluid motion induced by the deceleration to rest of a rigidly rotating fluid-filled torus. Transition to a transient turbulent state is found where the onset of the complicated motion is triggered by a small-scale wavelike instability. The wave forms on a front that propagates from the inner wall of the toroidal container after it is stopped. We reveal the origins of the front through a combination of careful experimental measurements, boundary-layer analysis, and computation of the axisymmetric Navier–Stokes equations.
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 25-09-2017
Publisher: American Physical Society (APS)
Date: 16-07-2019
Publisher: Elsevier BV
Date: 08-2013
Publisher: Cambridge University Press (CUP)
Date: 20-10-2011
DOI: 10.1017/JFM.2011.366
Abstract: We consider the temporal evolution of a viscous incompressible fluid in a torus of finite curvature a problem first investigated by Madden & Mullin ( J. Fluid Mech. , vol. 265, 1994, pp. 265–217). The system is initially in a state of rigid-body rotation (about the axis of rotational symmetry) and the container’s rotation rate is then changed impulsively. We describe the transient flow that is induced at small values of the Ekman number, over a time scale that is comparable to one complete rotation of the container. We show that (rotationally symmetric) eruptive singularities (of the boundary layer) occur at the inner or outer bend of the pipe for a decrease or an increase in rotation rate respectively. Moreover, on allowing for a change in direction of rotation, there is a (negative) ratio of initial-to-final rotation frequencies for which eruptive singularities can occur at both the inner and outer bend simultaneously. We also demonstrate that the flow is susceptible to a combination of axisymmetric centrifugal and non-axisymmetric inflectional instabilities. The inflectional instability arises as a consequence of the developing eruption and is shown to be in qualitative agreement with the experimental observations of Madden & Mullin (1994). Throughout our work, detailed quantitative comparisons are made between asymptotic predictions and finite- (but small-) Ekman-number Navier–Stokes computations using a finite-element method. We find that the boundary-layer results correctly capture the (finite-Ekman-number) rotationally symmetric flow and its global stability to linearised perturbations.
Publisher: The Royal Society
Date: 08-10-1998
Publisher: AIP Publishing
Date: 06-1999
DOI: 10.1063/1.870012
Abstract: It is well known that buoyancy forces and centrifugal effects can render a flow unstable to longitudinal vortex structures. Such competing instability mechanisms can be found in flows such as the curved mixing layer formed by the passage of two streams of fluid at different temperatures in the wake of a curved body. Via an asymptotic consideration of the problem we are able to characterize the interplay between these mechanisms. We are also able to determine the level of convex curvature required to stabilize unstably stratified mixing layers and the level of concave curvature required to destabilize stably stratified mixing layers.
Publisher: Springer Science and Business Media LLC
Date: 10-2014
Publisher: Oxford University Press (OUP)
Date: 1992
Publisher: Elsevier BV
Date: 09-2003
Publisher: AIP Publishing
Date: 23-11-2004
DOI: 10.1063/1.1814583
Abstract: We identify the dominant, or most unstable, wave mode for the flow in a trailing line vortex. This dominant mode is found to reside in a wavenumber regime between that of inviscid wave modes and the viscous upper branch neutral wave modes. A reevaluation of the growth rate in the vicinity of the upper branch of the curve of neutral stability allows us to predict the neutral value of the azimuthal and axial wavenumber as a function of the imposed swirl within the trailing line vortex.
Publisher: Cambridge University Press (CUP)
Date: 31-01-2013
DOI: 10.1017/JFM.2012.578
Abstract: We consider the development of Dean vortices in a curved channel of finite aspect ratio. Solutions to the axisymmetric Navier–Stokes equations are obtained through a finite-element analysis, allowing us to explore the complex and rich bifurcation pattern of the flow as the aspect ratio and Dean number vary. We demonstrate a new class of finite- litude vortices and discuss their relationship to similar structures seen in finite-length Taylor–Couette flow.
Publisher: Wiley
Date: 04-1996
Publisher: Elsevier BV
Date: 12-1999
Publisher: Cambridge University Press (CUP)
Date: 10-11-2004
Publisher: Elsevier BV
Date: 10-2018
DOI: 10.1016/J.JBIOMECH.2018.07.044
Abstract: A fluid dynamic study of blood flow within the umbilical vessels of the human maternal-fetal circulatory system is considered. It is found that the umbilical coiling index (UCI) is unable to distinguish between cords of significantly varying pressure and flow characteristics, which are typically determined by the vessel curvature, torsion and length. Larger scale geometric non-uniformities superposed over the inherent coiling, including cords exhibiting width and/or local UCI variations as well as loose true knots, typically produce a small effect on the total pressure drop. Crucially, this implies that a helical geometry of mean coiling may be used to determine the steady vessel pressure drop through a more complex cord. The presence of vessel constriction, however, drastically increases the steady pressure drop and alters the flow profile. For pulsatile-flow within the arteries, the steady pressure approximates the time-averaged value with high accuracy over a wide range of cords. Furthermore, the relative peak systolic pressure measured over the period is virtually constant and approximately 25% below the equivalent straight-pipe value for a large range of non-straight vessels. Interestingly, this suggests that the presence of vessel helicity d ens extreme pressures within the arterial cycle and may provide another possible evolutionary benefit to the coiled structure of the cord.
Publisher: Cambridge University Press (CUP)
Date: 08-11-2022
DOI: 10.1017/JFM.2022.863
Abstract: A numerical study on the effect of surface slip on the flow in a constricted channel is presented, with the aim of exploring the use of surface slip to control flow separation. Our focus is on two-dimensional flow in a channel over a bump, with a fixed aspect ratio, upon which a Robin-type slip boundary condition is imposed. When the channel walls are fully no-slip, such a flow is known to develop a region of separation behind the bump, at sufficiently large Reynolds numbers. The effect of slip on the separation bubble dynamics occurring behind the bump is investigated, for Reynolds numbers $2000$ and $4000$ . It is shown that surface slip (i) attenuates the intensity of separation as it diminishes the minimum of the streamwise velocity within the recirculation region (ii) delays the onset of flow separation, shifting it downstream, along the bump, and (iii) reduces the dimensions of the separation bubble behind the bump, allowing the flow to reattach sooner. Ultimately, slip inhibits separation, with both the points of separation and reattachment coalescing, for a slip length $\\lambda$ of approximately $0.2$ .
Publisher: Cambridge University Press (CUP)
Date: 07-08-2013
DOI: 10.1017/JFM.2013.360
Abstract: We consider the decay to rest of initially laminar flow within the end region of a suddenly blocked pipe. Here the flow is dominated by two temporally developing boundary layers, one on the pipe wall and one located at the blockage. The evolution and interaction of these boundary layers contributes to the creation and annihilation of toroidal vortices in the end-region flow, the number and extent growing with increasing Reynolds numbers. For larger Reynolds numbers, these nonlinear vortices delay the decay process within the end region, decaying at a slower rate than flow far downstream of the blockage. Our numerical simulations for pre-blockage Reynolds numbers up to 3000 indicate that the flow in this end region is stable to axisymmetric disturbances.
Publisher: Springer Science and Business Media LLC
Date: 30-10-2018
Publisher: Cambridge University Press (CUP)
Date: 10-03-2005
Publisher: Cambridge University Press (CUP)
Date: 12-02-2015
DOI: 10.1017/JFM.2015.46
Abstract: We consider the behaviour of the flow within a fluid-filled torus when there is a sudden change in the rotation rate of the torus. Experimental work on this problem by Madden & Mullin ( J. Fluid Mech. , vol. 265, 1994, p. 217) demonstrated a flow with a rich and complex dynamics. In particular, planar (top-down) flow visualisation images show a well-defined laminar band at both the inner and outer bend of the toroidal pipe. Hewitt et al. ( J. Fluid Mech. , vol. 688, 2011, pp. 88–119) demonstrated the existence of finite-time singularities in the resulting viscous boundary layers, and linked the post-singularity structure to one of the laminar bands identified in experiments (Madden & Mullin J. Fluid Mech. , vol. 265, 1994, p. 217 del Pino et al. Phys. Fluids , vol. 20 (12), 2008, 124104). The second band (or laminar front) identified by Madden & Mullin was conjectured by Hewitt et al. to be the result of a centrifugal instability, perhaps generated by small imperfections in the experimental apparatus. Here we explore this conjecture further, demonstrating that a small seam imperfection can generate substantial secondary motion but with considerably different dynamics than the centrifugally driven instability of Hewitt et al.
Publisher: Cambridge University Press (CUP)
Date: 02-1993
DOI: 10.1017/S0022112093000357
Abstract: The nonlinear development of the most unstable Görtler vortex mode in boundary-layer flows over curved walls is investigated. The most unstable Görtler mode is confined to a viscous wall layer of thickness O ( G −1/5 ) and has spanwise wavelength O ( G −1/5 ) it is, of course, most relevant to flow situations where the Görtler number G [Gt ] 1. The nonlinear equations governing the evolution of this mode over an O ( G −3/5 ) streamwise lengthscale are derived and are found to be of a fully non-parallel nature. The solution of these equations is achieved by making use of the numerical scheme used by Hall (1988) for the numerical solution of the nonlinear Görtler equations valid for O (1) Görtler numbers. Thus, the spanwise dependence of the flow is described by a Fourier expansion whereas the streamwise and normal variations of the flow are dealt with by employing a suitable finite-difference discretization of the governing equations. Our calculations demonstrate that, given a suitable initial disturbance, after a brief interval of decay, the energy in all the higher harmonics grows until a singularity is encountered at some downstream position. The structure of the flow field as this singularity is approached suggests that the singularity is responsible for the vortices, which are initially confined to the thin viscous wall layer, moving away from the wall and into the core of the boundary layer.
Publisher: Springer Science and Business Media LLC
Date: 22-12-2015
No related grants have been discovered for Jim Denier.