Publications
55 results found
Deguchi K, Hall P, 2014, Free-stream coherent structures in parallel boundary-layer flows, Journal of Fluid Mechanics, Vol: 752, Pages: 602-625, ISSN: 0022-1120
Our concern in this paper is with high-Reynolds-number nonlinear equilibrium solutions of the Navier–Stokes equations for boundary-layer flows. Here we consider the asymptotic suction boundary layer (ASBL) which we take as a prototype parallel boundary layer. Solutions of the equations of motion are obtained using a homotopy continuation from two known types of solutions for plane Couette flow. At high Reynolds numbers, it is shown that the first type of solution takes the form of a vortex–wave interaction (VWI) state, see Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666), and is located in the main part of the boundary layer. On the other hand, here the second type is found to support an equilibrium solution of the unit-Reynolds-number Navier–Stokes equations in a layer located a distance of O(lnRe) from the wall. Here Re is the Reynolds number based on the free-stream speed and the unperturbed boundary-layer thickness. The streaky field produced by the interaction grows exponentially below the layer and takes its maximum size within the unperturbed boundary layer. The results suggest the possibility of two distinct types of streaky coherent structures existing, possibly simultaneously, in disturbed boundary layers.
Deguchi K, Hall P, 2014, Canonical exact coherent structures embedded in high Reynolds number flows, PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 372, ISSN: 1364-503X
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- Citations: 18
Hall P, 2013, On the breakdown of Rayleigh’s criterion for curved shear flows: a destabilization mechanism for a class of inviscidly stable flows, Journal of Fluid Mechanics, Vol: 734, Pages: 36-82, ISSN: 0022-1120
Deguchi K, Hall P, Walton AG, 2013, The emergence of localized vortex-wave interaction states in plane Couette flow, Journal of Fluid Mechanics, Vol: 721, Pages: 58-85
The recently understood relationship between high Reynolds number vortex-wave interactiontheory and computationally-generated self-sustaining processes provides a possibleroute to an understanding of some of the underlying structures of fully turbulent flows.Here vortex-wave interaction theory, which we now refer to as VWI, is used in the longstreamwise wavelength limit to continue the development found at order one wavelengthsby Hall and Sherwin (2010). The asymptotic description given reduces the Navier-Stokesequations to the so-called boundary-region equations for which we find equilibrium statesdescribing the change in the VWI as the wavelength of the wave increases from O(h) toO(Rh) where R is the Reynolds number and 2h is the depth of the channel. The reducedequations do not include the streamwise pressure gradient of the perturbation or theeffect of streamwise diffusion of the wave-vortex states. The solutions we calculate havean asymptotic error proportional to R−2 when compared to the full Navier-Stokes equations.The results found correspond to the minimum drag configuration for VWI statesand might therefore be of relevance to the control of turbulent flows. The key feature ofthe new states discussed here is the thickening of the critical layer structure associatedwith the wave part of the flow to completely fill the channel so that the roll part ofthe flow is driven throughout the flow rather than as in Hall and Sherwin (2010) as astress discontinuity across the critical layer. We identify a critical streamwise wavenumberscaling which when approached causes the flow to localise and take on similaritieswith computationally-generated or experimentally-observed turbulent spots. In effect theidentification of this critical wavenumber for a given value of the assumed high Reynoldsnumber fixes a minimum box length necessary for the emergence of localized structures.Whereas nonlinear equilibrium states of the Navier-Stokes equations are thought to forma bac
Hall P, 2012, Vortex-wave interactions: long-wavelength streaks and spatial localization in natural convection, JOURNAL OF FLUID MECHANICS, Vol: 703, Pages: 99-110, ISSN: 0022-1120
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- Citations: 5
Hall P, 2012, Vortex-Wave Interactions/Self-Sustained Processes in High Prandtl Number Natural Convection in A Vertical Channel with Moving Sidewalls, STUDIES IN APPLIED MATHEMATICS, Vol: 129, Pages: 1-25, ISSN: 0022-2526
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- Citations: 2
Hall P, Sherwin S, 2010, Streamwise vortices in shear flows: harbingers of transition and the skeleton of coherent structures, J. Fluid Mechanics, Vol: 661, Pages: 178-205, ISSN: 0022-1120
The relationship between asymptotic descriptions of vortex-wave interactions and more recent work on ’exact coherent structures’ is investigated. In recent years immense in- terest has been focused on so-called self-sustained processes in turbulent shear flows where the importance of waves interacting with streamwise vortex flows has been eluci- dated in a number of papers. In this paper it is shown that the so-called ’lower branch’ state which has been shown to play a crucial role in these self-sustained processes is a finite Reynolds number analogue of a Rayleigh vortex-wave interaction with scales ap- propriately modified from those for external flows to Couette flow the flow of interest here. Remarkable agreement between the asymptotic theory and numerical simulations is found even down to relatively small Reynolds numbers thereby suggesting the possible importance of vortex-wave interaction theory in turbulent shear flows. The relevance of the work to more general shear flows is also discussed.
Hall P, 2006, Nonlinear evolution equations and the braiding of weakly transporting flows over gravel beds, STUDIES IN APPLIED MATHEMATICS, Vol: 117, Pages: 27-69, ISSN: 0022-2526
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- Citations: 4
Galionis I, Hall P, 2006, Stability of the flow in a slowly diverging rectangular duct, JOURNAL OF FLUID MECHANICS, Vol: 555, Pages: 43-58, ISSN: 0022-1120
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- Citations: 3
Galionis I, Hall P, 2005, Spatial stability of the incompressible corner flow, THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS, Vol: 19, Pages: 77-113, ISSN: 0935-4964
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- Citations: 18
Hall P, 2005, On the non-parallel instability of sediment-carrying channels of slowly varying width, JOURNAL OF FLUID MECHANICS, Vol: 529, Pages: 1-32, ISSN: 0022-1120
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- Citations: 5
Galionis I, Hall P, 2005, On the stabilization of the most amplified Gortler vortex on a concave surface by spanwise oscillations, JOURNAL OF FLUID MECHANICS, Vol: 527, Pages: 265-283, ISSN: 0022-1120
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- Citations: 7
Hall P, 2004, Alternating bar instabilities in unsteady channel flows over erodible beds, JOURNAL OF FLUID MECHANICS, Vol: 499, Pages: 49-73, ISSN: 0022-1120
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- Citations: 27
Hall P, 2003, On the instability of Stokes layers at high Reynolds numbers, JOURNAL OF FLUID MECHANICS, Vol: 482, Pages: 1-15, ISSN: 0022-1120
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- Citations: 20
Blyth MG, Hall P, Papageorgiou DT, 2003, Chaotic flows in pulsating cylindrical tubes: a class of exact Navier-Stokes solutions, JOURNAL OF FLUID MECHANICS, Vol: 481, Pages: 187-213, ISSN: 0022-1120
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- Citations: 8
Blyth MG, Hall P, 2003, Oscillatory flow near a stagnation point, SIAM J APPL MATH
Brown BM, Hall P, Young GA, 2001, The smoothed median and the bootstrap, BIOMETRIKA, Vol: 88, Pages: 519-534, ISSN: 0006-3444
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- Citations: 7
Hall P, 2001, On the nonlinear initial value problem for vortex-wave interactions in shear flows, STUDIES IN APPLIED MATHEMATICS, Vol: 106, Pages: 69-83, ISSN: 0022-2526
Dando AH, Hall P, Papageorgiou DT, 2000, The modulational stability of Taylor vortices in a curved channel, SIAM Journal on Applied Mathematics, Vol: 60, Pages: 1543-1564, ISSN: 0036-1399
Balakumar P, Hall P, 1999, On the control of the fastest growing Gortler vortex, THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS, Vol: 13, Pages: 21-31, ISSN: 0935-4964
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- Citations: 3
Balakumar P, Hall P, 1999, Optimum suction distribution for transition control, THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS, Vol: 13, Pages: 1-19, ISSN: 0935-4964
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- Citations: 21
Shortis TA, Hall P, 1999, On the nonlinear stability of the oscillatory viscous flow of an incompressible fluid in a curved pipe, Journal of Fluid Mechanics, Vol: 379, Pages: 145-163, ISSN: 0022-1120
Hall P, Papageorgiou DT, 1999, The onset of chaos in a class of Navier-Stokes solutions, Journal of Fluid Mechanics, Vol: 393, Pages: 59-87, ISSN: 0022-1120
Hewitt RE, Hall P, 1998, The evolution of finite-amplitude wavetrains in plane channel flow, Philosophical Transactions of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, Vol: 356, Pages: 2413-2446, ISSN: 1364-503X
Hall P, Papageorgiou D, 1997, On the modulational instability of O(1) amplitude waves in supersonic boundary layers, SIAM JOURNAL ON APPLIED MATHEMATICS, Vol: 57, Pages: 929-958, ISSN: 0036-1399
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- Citations: 1
Blackaby N, Dando A, Hall P, 1997, The nonlinear evolution of inviscid Gortler vortices in three-dimensional boundary layers, Philosophical Transactions of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, Vol: 355, Pages: 975-1016, ISSN: 0962-8428
COWLEY S, HALL P, 1990, ON THE INSTABILITY OF HYPERSONIC FLOW PAST A WEDGE, JOURNAL OF FLUID MECHANICS, Vol: 214, Pages: 17-42, ISSN: 0022-1120
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- Citations: 47
HALL P, 1985, THE GORTLER VORTEX INSTABILITY MECHANISM IN 3-DIMENSIONAL BOUNDARY-LAYERS, PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 399, Pages: 135-152, ISSN: 1364-5021
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- Citations: 36
DIPRIMA RC, HALL P, 1984, COMPLEX EIGENVALUES FOR THE STABILITY OF COUETTE-FLOW, PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 396, Pages: 75-94, ISSN: 1364-5021
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- Citations: 11
HALL P, 1984, EVOLUTION-EQUATIONS FOR TAYLOR VORTICES IN THE SMALL-GAP LIMIT, PHYSICAL REVIEW A, Vol: 29, Pages: 2921-2923, ISSN: 1050-2947
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- Citations: 28
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