## Publications

63 results found

Zhang Z, Wu X, 2020, Nonlinear evolution and acoustic radiation of coherent structures in subsonic turbulent free shear layers, *Journal of Fluid Mechanics*, Vol: 884, Pages: A10-1-A10-68, ISSN: 0022-1120

Large-scale coherent structures are present in compressible free shear flows, where they are known to be a main source of aerodynamic noise. Previous studies showed that these structures may be treated as instability waves or wavepackets supported by the underlying turbulent mean flow. By adopting this viewpoint in the framework of triple decomposition of the instantaneous flow into the mean field, coherent motion and small-scale turbulence, a strongly nonlinear dynamical model was constructed to describe the formation and development of coherent structures in incompressible turbulent free shear layers (Wu & Zhuang, J. Fluid Mech., vol. 787, 2016, pp. 396–439). That model is now extended to compressible flows, for which the coherent structures are extracted through a density-weighted (Favre) phase average. The nonlinear non-equilibrium critical-layer theory for instability waves in a laminar compressible mixing layer is adapted to analyse coherent structures in its turbulent counterpart. The strong non-parallelism associated with the fast spreading of the turbulent mean flow is taken into account and found to be significant. The model also accounts for the effect of fine-scale turbulence on coherent structures via a gradient type of closure model which now allows for a phase lag between the phase-averaged small-scale Reynolds stresses and the strain rates of coherent structures. The analysis results in an evolution system comprising of an amplitude equation, the critical-layer temperature and vorticity equations along with the appropriate initial and boundary conditions. The physical processes of acoustic radiation from the coherent structures are described by examining the far-field asymptote of the hydrodynamic fluctuations. We demonstrate that the nonlinearly generated slowly breathing mean-flow distortion radiates low-frequency sound waves. The true physical sources are identified. Equivalent sources in a Lighthill type of acoustic analogy context also

Wu X, Zhang Z, 2019, First-principle description of acoustic radiation of shear flows, *Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences*, Vol: 377, Pages: 1-18, ISSN: 1364-503X

As a methodology complementary to acoustic analogy, the asymptotic approach to aeroacoustics seeks to predict aerodynamical noise on the basis of first principles by probing into the physical processes of acoustic radiation. The present paper highlights the principal ideas and recent developments of this approach, which have shed light on some of the fundamental issues in sound generation in shear flows. The theoretical work on sound wave emission by nonlinearly modulated wavepackets of supersonic and subsonic instability modes in free shear flows identifies the respective physical sources or emitters. A wavepacket of supersonic modes is itself an efficient emitter, radiating directly intensive sound in the form of a Mach wave beam, the frequencies of which are in the same band as those of the modes in the packet. By contrast, a wavepacket of subsonic modes radiates very weak sound directly. However, the nonlinear self-interaction of such a wavepacket generates a slowly modulated mean-flow distortion, which then emits sound waves with low frequencies and long wavelengths on the scale of the wavepacket envelope. In both cases, the acoustic waves emitted to the far field are explicitly expressed in terms of the amplitude function of the wavepacket. The asymptotic approach has also been applied to analyse generation of sound waves in wall-bounded shear flows on the triple-deck scale. Several subtleties have been found. The near-field approximation has to be worked out to a sufficiently higher order in order just to calculate the far-field sound at leading order. The back action of the radiated sound on the flow in the viscous sublayer and the main shear layer is accounted for by an impedance coefficient. This effect is of higher order in the subsonic regime, but becomes a leading order in the transonic and supersonic regimes.

Gonzalez Hernandez C, Wu X, 2019, Receptivity of supersonic boundary layers over smooth and wavy surfaces to impinging slow acoustic waves, *Journal of Fluid Mechanics*, Vol: 872, Pages: 849-888, ISSN: 0022-1120

In this paper, we investigate the receptivity of a supersonic boundary layer toimpinging acoustic waves. Unlike previous studies of acoustic receptivity, wherethe sound waves have phase speeds comparable with or larger than the free-streamvelocity U∞, the acoustic waves here have much slower (O(R−1/8U∞)) phase velocity,and their characteristic wavelength and frequency are of O(R−3/8L) and O(R1/4U∞/L)respectively, compatible with the triple-deck structure, where L is the distance to theleading edge and R the Reynolds number based on L and U∞. A significant feature ofa sound wave on the triple-deck scale is that an O(εs) perturbation in the free streamgenerates much stronger (O(εsR1/8)) velocity fluctuations in the boundary layer. Tworeceptivity mechanisms are considered. The first is new, involving the interaction oftwo such acoustic waves and operating in a boundary layer over a smooth wall. Thesecond involves the interaction between an acoustic wave and the steady perturbationinduced by a wavy wall. The sound–sound, or sound–roughness, interactions generatea forcing in resonance with a neutral Tollmien–Schlichting (T–S) wave. The latter isthus excited near the lower branch of the neutral curve, and subsequently undergoesexponential amplification. The excitation through sound–sound interaction may offera possible explanation for the appearance of instability modes downstream of theirneutral locations as was observed in a supersonic boundary layer over a smoothwall. The triple-deck formalism is adopted to describe impingement and reflection ofthe acoustic waves, and ensuing receptivity, allowing the coupling coefficient to becalculated. The two receptivity processes with the acoustic waves on the triple-deckscale are much more effective compared with those involving usual sound waves,with the coupling coefficient being greater by a factor of O(R1/4) and O(R1/8) inthe sound–sound a

He J, Butler A, Wu X, 2019, Effects of distributed roughness on crossflow instability through generalized resonance mechanisms, *Journal of Fluid Mechanics*, Vol: 858, Pages: 787-831, ISSN: 0022-1120

Experiments have shown that micron-sized distributed surface roughness can significantly promote transition in a three-dimensional boundary layer dominated by crossflow instability. This sensitive effect has not yet been fully explained physically and mathematically. Past studies focused on surface roughness exciting crossflow vortices and/or changing the local stability characteristics. The present paper seeks possible additional mechanisms by investigating the effects of distributed surface roughness on crossflow instability through resonant interactions with eigenmodes. A key observation is that the perturbation induced by roughness with specific wavenumbers can interact with two eigenmodes (travelling and stationary vortices) through triadic resonance, or interact with one eigenmode (stationary vortices) through Bragg scattering. Unlike the usual triadic resonance of neutral, or nearly neutral, eigenmodes, the present triadic resonance can take place among modes with growth rates, provided that these are equal; unlike the usual Bragg scattering involving neutral waves, crossflow stationary vortices can also be unstable. For these amplifying waves, the generalized triadic resonance and Bragg scattering are put forward, and the resulting corrections to the growth rates are derived by a multiple-scale method. The analysis is extended to the case where up to four crossflow vortices interact with each other in the presence of suitable roughness components. The numerical results for Falkner–Skan–Cooke boundary layers show that roughness with a small height (a few percent of the local boundary-layer thickness) can change growth rates substantially (by a more-or-less amount). This sensitive effect is attributed to two facts: (i) the resonant nature of the triadic interaction and Bragg scattering, which makes the correction to the growth rate proportional to the roughness height, and (ii) the wavenumbers of the roughness component required for the resonance

Butler A, Wu X, 2018, Stationary crossflow vortices near the leading edge of three-dimensional boundary layers: the role of non-parallelism and excitation by surface roughness, *Journal of Fluid Mechanics*, Vol: 845, Pages: 93-140, ISSN: 0022-1120

Non-parallelism, i.e. the effect of the slow variation of the boundary-layer flow in the chordwise and spanwise directions, in general produces a higher-order correction to the growth rate of instability modes. Here we investigate stationary crossflow vortices, which arise due to the instability of the three-dimensional boundary layer over a swept wing, focusing on a region near the leading edge where non-parallelism plays a leading-order role in their development. In this regime, the vortices align themselves with the local wall shear at leading order, and so have a marginally separated triple-deck structure, consisting of the inviscid main boundary layer, an upper deck and a viscous sublayer. We find that the streamwise (and spanwise) variations of both the base flow and the modal shape must be accounted for. An explicit expression for the growth rate is derived that shows a neutral point occurs in this regime, downstream of which non-parallelism has a stabilising effect. Stationary crossflow vortices thus have a viscous and non-parallel genesis near the leading edge. If an ‘effective pressure minimum’ occurs within this region then the growth rate becomes unbounded, and so the previous analysis is regularised within a localised region around it. A new instability is identified. The mode maintains its three-tiered structure, but the pressure perturbation now plays a passive role. Downstream, the instability evolves into a Cowley, Hocking & Tutty (Phys. Fluids, vol. 28, 1985, pp. 441–443) instability associated with a critical layer located in the lower deck. Finally, we consider the receptivity of the flow in the non-parallel regime: generation of stationary crossflow modes by arrays of chordwise-localised, spanwise-periodic surface roughness elements. The flow responds differently to different Fourier spectral content of the roughness, giving the lower deck a two-part structure. We find that roughness elements with sharper edges generate str

Wu X, Xu D, Zhang Y, 2017, Nonlinear evolution and secondary instability of steady and unsteady vortices induced by free-stream vortical disturbances, *Journal of Fluid Mechanics*, Vol: 829, Pages: 681-730, ISSN: 0022-1120

We study the nonlinear development and secondary instability of steady and unsteady Görtler vortices which are excited by free-stream vortical disturbances (FSVD) in a boundary layer over a concave wall. The focus is on low-frequency (long-wavelength) components of FSVD, to which the boundary layer is most receptive. For simplification, FSVD are modelled by a pair of oblique modes with opposite spanwise wavenumbers , and their intensity is strong enough (but still of low level) that the excitation and evolution of Görtler vortices are nonlinear. For the general case that the Görtler number (based on the spanwise wavelength of the disturbances) is , the formation and evolution of Görtler vortices are governed by the nonlinear unsteady boundary-region equations, supplemented by appropriate upstream and far-field boundary conditions, which characterize the impact of FSVD on the boundary layer. This initial-boundary-value problem is solved numerically. FSVD excite steady and unsteady Görtler vortices, which undergo non-modal growth, modal growth and nonlinear saturation for FSVD of moderate intensity. However, for sufficiently strong FSVD the modal stage is bypassed. Nonlinear interactions cause Görtler vortices to saturate, with the saturated amplitude being independent of FSVD intensity when . The predicted modified mean-flow profiles and structure of Görtler vortices are in excellent agreement with several steady experimental measurements. As the frequency increases, the nonlinearly generated harmonic component (which has zero frequency and wavenumber ) becomes larger, and as a result the Görtler vortices appear almost steady. The secondary instability analysis indicates that Görtler vortices become inviscidly unstable in the presence of FSVD with a high enough intensity. Three types of inviscid unstable modes, referred to as sinuous (odd) modes I, II and varicose (even) modes I, are identified, and their rel

Huang Z, Wu X, 2017, A local scattering approach for the effects of abrupt changes on boundary-layer instability and transition: a finite-Reynolds-number formulation for isolated distortions, *Journal of Fluid Mechanics*, Vol: 822, Pages: 444-483, ISSN: 0022-1120

We investigate the influence of abrupt changes on boundary-layer instability and transition. Such changes can take different forms including a local porous wall, suction/injection and surface roughness as well as junctions between rigid and porous walls. They may modify the boundary conditions and/or the mean flow, and their effects on transition have usually been assessed by performing stability analysis for the modified base flow and/or boundary conditions. However, such a conventional local linear stability theory (LST) becomes invalid if the change occurs over a relatively short scale comparable with, or even shorter than, the characteristic wavelength of the instability. In this case, the influence on transition is through scattering with the abrupt change acting as a local scatter, that is, an instability mode propagating through the region of abrupt change is scattered by the strong streamwise inhomogeneity to acquire a different amplitude. A local scattering approach (LSA) should be formulated instead, in which a transmission coefficient, defined as the ratio of the amplitude of the instability wave after the scatter to that before, is introduced to characterize the effect on instability and transition. In the present study, we present a finite-Reynolds-number formulation of LSA for isolated changes including a rigid plate interspersed by a local porous panel and a wall suction through a narrow slot. When the weak non-parallelism of the unperturbed base flow is ignored, the local scattering problem can be cast as an eigenvalue problem, in which the transmission coefficient appears as the eigenvalue. We also improved the method to take into account the non-parallelism of the unperturbed base flow, where it is found that the weak non-parallelism has a rather minor effect. The general formulation is specialized to two-dimensional Tollmien–Schlichting (T–S) waves. The resulting eigenvalue problem is solved, and full direct numerical simulations (DNS)

Marensi E, Ricco P, Wu X, 2017, Nonlinear unsteady streaks engendered by the interaction of free-stream vorticity with a compressible boundary layer, *JOURNAL OF FLUID MECHANICS*, Vol: 817, Pages: 80-121, ISSN: 0022-1120

Qin F, Wu X, 2016, Response and receptivity of the hypersonic boundary layer past awedge to free-stream acoustic, vortical and entropy disturbances, *Journal of Fluid Mechanics*, Vol: 797, Pages: 874-915, ISSN: 0022-1120

This paper analyses the response and receptivity of the hypersonic boundary layerover a wedge to free-stream disturbances including acoustic, vortical and entropyfluctuations. Due to the presence of an attached oblique shock, the boundary layer isknown to support viscous instability modes whose eigenfunctions are oscillatory in thefar field. These modes acquire a triple-deck structure. Any of three elementary typesof disturbances with frequency and wavelength on the triple-deck scales interacts withthe shock to generate a slow acoustic perturbation, which is reflected between theshock and the wall. Through this induced acoustic perturbation, vortical and entropyfree-stream disturbances drive significant velocity and temperature fluctuations withinthe boundary layer, which is impossible when the shock is absent. A quasi-resonancewas identified, due to which the boundary layer exhibits a strong response to a continuumof high-frequency disturbances within a narrow band of streamwise wavenumbers.Most importantly, in the vicinity of the lower-branch neutral curve the slow acousticperturbation induced by a disturbance of suitable frequency and wavenumbers is inexact resonance with a neutral eigen mode. As a result, the latter can be generated directlyby each of three types of free-stream disturbances without involving any surfaceroughness element. The amplitude of the instability mode is determined by analysingthe disturbance evolution through the resonant region. The fluctuation associatedwith the eigen mode turns out to be much stronger than free-stream disturbances dueto the resonant nature of excitation and in the case of acoustic disturbances, to thewell-known amplification effect of a strong shock. Moreover, excitation at the neutralposition means that the instability mode grows immediately without undergoingany decay, or missing any portion of the unstable region. All these indicate that thisnew mechanism is particularly efficient. The boundary-layer response and c

Wu X, Dong M, 2016, Entrainment of short-wavelength free-stream vortical disturbances in compressible and incompressible boundary layers, *Journal of Fluid Mechanics*, Vol: 797, Pages: 683-728, ISSN: 0022-1120

The fundamental difference between continuous modes of the Orr-Sommerfeld/Squireequations and the entrainment of free-stream vortical disturbances (FSVD) into theboundary layer has been investigated in a recent paper (Dong & Wu 2013, J. FluidMech.). It was shown there that the non-parallel-flow effect plays a leading-order role inthe entrainment, and neglecting it at outset, as is done in the continuous-mode formulation,leads to non-physical features of ‘Fourier entanglement’ and abnormal anisotropy.The analysis, which was for incompressible boundary layers and for FSVD with a characteristicwavelength of the order of the local boundary-layer thickness, is extended inthis paper to compressible boundary layers and FSVD with even shorter wavelengths,which are comparable with the width of the so-called edge layer. Non-parallelism remainsa leading-order effect in the present scaling, which turns out to be more general in thatthe equations and solutions in the previous paper are recovered in the appropriate limit.Appropriate asymptotic solutions in the main and edge layers are obtained to characterizethe entrainment. It is found that when the Prandtl number Pr < 1, free-streamvortical disturbances of relatively low frequency generate very strong temperature fluctuationswithin the edge layer, leading to formation of thermal streaks. A compositesolution, uniformly valid across the entire boundary layer, is constructed, and it can beused in receptivity studies and as inlet conditions for direct numerical simulations of bypasstransition. For compressible boundary layers, continuous spectra of the disturbanceequations linearised about a parallel base flow exhibit entanglement between vortical andentropy modes, namely, a vortical mode necessarily induces an entropy disturbance inthe free stream and vice versa, and this amounts to a further nonphysical behaviour.High-Reynolds-number asymptotic analysis yields the relations between the amplitudesof entangled mo

Wu X, Dong M, 2016, A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition: transmission coefficient as an eigenvalue, *Journal of Fluid Mechanics*, Vol: 794, Pages: 68-108, ISSN: 0022-1120

This paper is concerned with the rather broad issue of the impact of abrupt changes (such as isolated roughness, gaps and local suctions) on boundary-layer transition. To fix the idea, we consider the influence of a two-dimensional localized hump (or indentation) on an oncoming Tollmien-Schlichting (T-S) wave. We show that when the length scale of the former is comparable with the characteristic wavelength of the latter, the key physical mechanism to affect transition is through scattering of T-S waves by the roughness-induced mean-flow distortion. An appropriate mathematical theory, consisting of the boundary-value problem governing the local scattering,is formulated based on triple deck formalism. The transmission co efficient, defined as the ratio of the amplitude of the T-S wave downstream the roughnessto that upstream, serves to characterize the impact on transition. The transmission coefficient appears as the eigenvalue of the discretized boundary-value problem. The latter is solved numerically, and the dependenceof the eigenvalue on the height and width of the roughness and the frequencyof the T-S wave is investigated. For a roughness element without causing separation, the transmission coefficient is found to be about 1:5 for typical frequencies, indicating a moderate but appreciable destabilizing effect. For a roughness causing incipient separation, the transmission coefficient can be as large as O(10), suggesting that immediate transition may take place at the roughness site. A roughness element with a fixed height produces the strongest impact when its width is comparable with the T-S wavelength, in which case the traditional linear stability theory is in valid. The latter how ever holds approximately when the roughness width is sufficiently large. By studying the two-hump case, a criterion when two roughness elements can be regarded as being isolated is suggested. The transmission coefficient can be converted to an equivalent N-factor increment, by makin

Xu H, Sherwin S, Hall P,
et al., 2016, The behaviour of Tollmien-Schlichting waves undergoing small-scale localised distortions, *Journal of Fluid Mechanics*, Vol: 792, Pages: 499-525, ISSN: 1469-7645

This paper is concerned with the behaviour of Tollmien-Schlichting (T-S) waves experiencingsmall localised distortions within an incompressible boundary layer developingover a flat-plate. In particular, the distortion is produced by an isolated roughness elementlocated at Rexc = 440 000. We considered the amplification of an incoming T-S wavegoverned by the two-dimensional linearised Navier-Stokes equations, where the base flowis obtained from the two-dimensional non-linear Navier-Stokes equations. We comparethese solutions with asymptotic analyses which assume a linearised triple-deck theory forthe base flow and determine the validity of this theory in terms of the height of the smallscalehumps/indentations taken into account. The height of the humps/indentations isdenoted by h which is considered to be less than or equal to xcRe−5/8xc(correspondingto h/δ99 < 6% for our choice of Rexc). The rescaled width ˆd(≡ d/(xcRe−3/8xc)) ofthe distortion is of the order O(1) and the width d is shorter than the T-S wavelength(λT S = 11.3 δ99).We observe that for distortions which are smaller than 0.1 of the inner deck height(h/δ99 < 0.4%) the numerical simulations confirm the asymptotic theory in the vicinityof the distortion. For larger distortions which are still within the inner deck (0.4% <h/δ99 < 5.5%) and where the flow is still attached the numerical solutions show thatboth humps and indentations are destabilising and deviate from the linear theory evenin the vicinity of the distortion.We numerically determine the transmission coefficient which provides the relative amplificationof the T-S wave over the distortion as compared to the flat-plate. We observethat for small distortions, h/δ99 < 5.5%, where the width of the distortion is of orderof the boundary layer a maximum amplification of only 2% is achieved. This amplificationcan however be increased as the width of the distortion is increased or

Wu X, Zhuang X, 2016, Nonlinear dynamics of large-scale coherent structures in turbulent free shear layers, *Journal of Fluid Mechanics*, Vol: 787, Pages: 396-439, ISSN: 1469-7645

Fully developed turbulent free shear layers exhibit a high degree of order, characterized by large-scale coherent structures in the form of spanwise vortex rollers. Extensive experimental investigations show that such organized motions bear remarkable resemblance to instability waves, and their main characteristics, including the length scales, propagation speeds and transverse structures, are reasonably well predicted by linear stability analysis of the mean flow. In this paper, we present a mathematical theory to describe the nonlinear dynamics of coherent structures. The formulation is based on the triple decomposition of the instantaneous flow into a mean field, coherent fluctuations and small-scale turbulence but with the mean-flow distortion induced by nonlinear interactions of coherent fluctuations being treated as part of the organized motion. The system is closed by employing a gradient type of model for the time- and phase-averaged Reynolds stresses of fine-scale turbulence. In the high-Reynolds-number limit, the nonlinear non-equilibrium critical-layer theory for laminar-flow instabilities is adapted to turbulent shear layers by accounting for (1) the enhanced non-parallelism associated with fast spreading of the mean flow, and (2) the influence of small-scale turbulence on coherent structures. The combination of these factors with nonlinearity leads to an interesting evolution system, consisting of coupled amplitude and vorticity equations, in which non-parallelism contributes the so-called translating critical-layer effect. Numerical solutions of the evolution system capture vortex roll-up, which is the hallmark of a turbulent mixing layer, and the predicted amplitude development mimics the qualitative feature of oscillatory saturation that has been observed in a number of experiments. A fair degree of quantitative agreement is obtained with one set of experimental data.

Huang Z, Wu X, 2015, A non-perturbative approach to spatial instability of weakly non-parallel shear flows, *PHYSICS OF FLUIDS*, Vol: 27, ISSN: 1070-6631

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Butler A, Wu X, 2015, Non-Parallel-Flow Effects on Stationary Crossflow Vortices at Their Genesis, IUTAM/ABCM Symposium on Laminar Turbulent Transition, Publisher: ELSEVIER SCIENCE BV, Pages: 311-320, ISSN: 2210-9838

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Marensi E, Ricco P, Wu X, 2015, Nonlinear response of a compressible boundary layer to free-stream vortical disturbances, IUTAM/ABCM Symposium on Laminar Turbulent Transition, Publisher: ELSEVIER SCIENCE BV, Pages: 105-114, ISSN: 2210-9838

Huang Z, Wu X, 2015, Non-parallel-flow effect on compressible boundary layer on a flat plate, 7th International Conference on Fluid Mechanics, Publisher: ELSEVIER SCIENCE BV, Pages: 78-82, ISSN: 1877-7058

Dong M, Wu X, 2015, Entrainment of Short-wavelength Free-stream Vortical Disturbances into Boundary Layers, IUTAM/ABCM Symposium on Laminar Turbulent Transition, Publisher: ELSEVIER SCIENCE BV, Pages: 96-104, ISSN: 2210-9838

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Wu X, Assier RC, 2014, Linear and weakly nonlinear instability of a premixed curved flame under the influence of its spontaneous acoustic field, *Journal of Fluid Mechanics*, Vol: 758, Pages: 180-220, ISSN: 1469-7645

The stability of premixed flames in a duct is investigated using an asymptotic formulation, which is derived from first principles and based on high-activation-energy and low-Mach-number assumptions (Wu et al., J. Fluid Mech., vol. 497, 2003, pp. 23–53). The present approach takes into account the dynamic coupling between the flame and its spontaneous acoustic field, as well as the interactions between the hydrodynamic field and the flame. The focus is on the fundamental mechanisms of combustion instability. To this end, a linear stability analysis of some steady curved flames is undertaken. These steady flames are known to be stable when the spontaneous acoustic perturbations are ignored. However, we demonstrate that they are actually unstable when the latter effect is included. In order to corroborate this result, and also to provide a relatively simple model guiding active control, we derived an extended Michelson–Sivashinsky equation, which governs the linear and weakly nonlinear evolution of a perturbed flame under the influence of its spontaneous sound. Numerical solutions to the initial-value problem confirm the linear instability result, and show how the flame evolves nonlinearly with time. They also indicate that in certain parameter regimes the spontaneous sound can induce a strong secondary subharmonic parametric instability. This behaviour is explained and justified mathematically by resorting to Floquet theory. Finally we compare our theoretical results with experimental observations, showing that our model captures some of the observed behaviour of propagating flames.

Wu X, 2014, On the role of acoustic feedback in boundary-layer instability, *PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES*, Vol: 372, ISSN: 1364-503X

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Dong M, Wu X, 2013, On continuous spectra of the Orr-Sommerfeld/Squire equations and entrainment of free-stream vortical disturbances, *JOURNAL OF FLUID MECHANICS*, Vol: 732, Pages: 616-659, ISSN: 0022-1120

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Wu X, 2013, The Role of Acoustic Feedback in Boundary-layer Instability, 11th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM), Publisher: AMER INST PHYSICS, Pages: 300-303, ISSN: 0094-243X

Luzzato CM, Assier RC, Morgans AS, et al., 2013, Modelling thermo-acoustic instabilities of an anchored laminar flame in a simple lean premixed combustor: Including hydrodynamic effects

Lean premixed combustors reduce oxide of nitrogen (NOx) emissions but are also prone to self sustained thermo-acoustic instabilities. Attempting to model these instabilities has become a popular research topic, and asymptotic based flame modelling allows us to capture all of the length scales involved in the instability. This paper presents a method for solving the full acoustic, hydrodynamic and flame coupling of an anchored laminar V-flame within a simple combustor. This allows us to model the Darrieus-Landau instability effects, and show how they influence the general behaviour and stability of the combustor when compared to G-Equation numerical results.

Wu X, Tian F, 2012, Spectral broadening and flow randomization in free shear layers, *JOURNAL OF FLUID MECHANICS*, Vol: 706, Pages: 431-469, ISSN: 0022-1120

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, 2011, Nonlinear response of a laminar boundary layer to isotropic and spanwise localized free-stream turbulence, *6th AIAA Theoretical Fluid Mechanics Conference*

This paper is concerned with the nonlinear response of a pre-transitional flat-plate boundary layer to isotropic and spanwise localized free-stream turbulence (FST). The turbulence is represented as a superposition of Fourier modes and the displacement effect of the boundary layer on FST is taken into consideration. The responses of the boundary layer to FST are low-frequency streamwise streaks, and their development is obtained by numerically solving the nonlinear unsteady boundary-region (NUBR) equations. Direct numerical simulations (DNS) are carried out to validate the results. Nonlinearity is stabilizing in that it reduces the root mean square (rms) of the perturbation velocity in the boundary layer for small FST Reynolds number RL11, while it is destabilizing for large RL11. The issue of upstream-downstream versus top-down mechanisms is investigated. Streaks primarily develop from the upstream forcing; the top-down forcing plays a minor role. The numerical calculations for isotropic FST are compared with DNS results of Ovchinnikov et al. and experimental data of Roach & Brierley. The computed disturbances do not reach the levels in the DNS and experiment. However, good quantitative agreement is obtained when the anisotropy of FST induced by the blunt leading edge is accounted for. The results suggest that the blunt leading edge can play a key role in explaining the large amplitudes of streaks in that it leads to the deviation from pure isotropy of the FST. The numerical calculation for spanwise localized FST is compared with experimental data of Westin et al. Agreement is obtained except for the amplitude of the disturbances, which is due to the lack of the velocity spectral information of FST in experiment. The viscous secondary instability analysis indicates that there is strong instability in the streaky boundary layer before bypass transition. The maximum growth rate of the unstable modes is larger than that of Tollmien-Schlichting (T-S) waves in the B

Wu X, 2011, On generation of sound in wall-bounded shear flows: back action of sound and global acoustic coupling, *JOURNAL OF FLUID MECHANICS*, Vol: 689, Pages: 279-316, ISSN: 0022-1120

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Wu X, Zhao D, Luo J, 2011, Excitation of steady and unsteady Gortler vortices by free-stream vortical disturbances, *JOURNAL OF FLUID MECHANICS*, Vol: 682, Pages: 66-100, ISSN: 0022-1120

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Ricco P, Luo J, Wu X, 2011, Evolution and instability of unsteady nonlinear streaks generated by free-stream vortical disturbances, *JOURNAL OF FLUID MECHANICS*, Vol: 677, Pages: 1-38, ISSN: 0022-1120

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Wu X, Moin P, 2010, Large-activation-energy theory for premixed combustion under the influence of enthalpy fluctuations, *JOURNAL OF FLUID MECHANICS*, Vol: 655, Pages: 3-37, ISSN: 0022-1120

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Luo J, Wu X, 2010, On the linear instability of a finite Stokes layer: Instantaneous versus Floquet modes, *PHYSICS OF FLUIDS*, Vol: 22, ISSN: 1070-6631

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