Homoclinic snaking of localized states in doubly diffusive convection

Numerical continuation is used to investigate stationary spatially localized states in two-dimensional thermosolutal convection in a plane horizontal layer with no-slip boundary conditions at top and bottom. Convectons in the form of 1-pulse and 2-pulse states of both odd and even parity exhibit homoclinic snaking in a common Rayleigh number regime. In contrast to similar states in binary fluid convection, odd parity convectons do not pump concentration horizontally. Stable but time-dependent localized structures are present for Rayleigh numbers below the snaking region for stationary convectons. The computations are carried out for (inverse) Lewis number \tau = 1/15 and Prandtl numbers Pr = 1 and Pr >> 1

Modulated patterns in a reduced model of a transitional shear flow

We consider a close relative of plane Couette flow called Waleffe flow in which the fluid is confined between two free-slip walls and the flow driven by a sinusoidal force. We use a reduced model of such flows constructed elsewhere to compute stationary exact coherent structures of Waleffe flow in periodic domains with a large spanwise period. The computations reveal the emergence of stationary states exhibiting strong amplitude and wavelength modulation in the spanwise direction. These modulated states lie on branches exhibiting complex dependence on the Reynolds number but no homoclinic snaking

Towards Convectons in the Supercritical Regime: Homoclinic Snaking in Natural Doubly Diffusive Convection

Fluids subject to both thermal and compositional variations can undergo doubly diffusive convection when these properties both affect the fluid density and diffuse at different rates. A variety of patterns can arise from these buoyancy-driven flows, including spatially localised states known as convectons, which consist of convective fluid motion localised within a background of quiescent fluid. We consider these states in a vertical slot with the horizontal temperature and solutal gradients providing competing effects to the fluid density while allowing the existence of a conduction state. In this configuration, convectons have been studied with specific parameter values where the onset of convection is subcritical, and the states have been found to lie on a pair of secondary branches that undergo homoclinic snaking in a parameter regime below the onset of linear instability. In this paper, we show that convectons persist into parameter regimes in which the primary bifurcation is supercritical and there is no bistability, despite coexistence between the stable conduction state and large-amplitude convection. We detail this transition by considering spatial dynamics and observe how the structure of the secondary branches becomes increasingly complex owing to the increased role of inertia at low Prandtl numbers

Near-onset dynamics in natural doubly diffusive convection

Doubly diffusive convection is considered in a vertical slot where horizontal temperature and solutal variations provide competing effects to the fluid density while allowing the existence of a conduction state. In this configuration, the linear stability of the conductive state is known, but the convection patterns arising from the primary instability have only been studied for specific parameter values. We have extended this by determining the nature of the primary bifurcation for all values of the Lewis and Prandtl numbers using a weakly nonlinear analysis. The resulting convection branches are extended using numerical continuation and we find large-amplitude steady convection states can coexist with the stable conduction state for sub- and supercritical primary bifurcations. The stability of the convection states is investigated and attracting travelling waves and periodic orbits are identified using time-stepping when these steady states are unstable

Experimental and numerical investigation of the weld repair of superplastic forming dies

Issu de : AMPT 2003 - International conference on advances in materials and processing technologies, Dublin, IRELAND, July 8-11, 2003International audienceSuperplastic forming process (SPF) is an advanced process conducted at high temperature using moderate strain rates, typically used for shaping TAW sheets for aerospace applications. Thermomechanical stresses on the forming dies due to successive forming cycles may result in the earl), degradation and even fracture of SPF tools through fatigue crack propagation. To reduce cost and extend service life. dies are generally weld-repaired and subsequently re-used in the typical severe conditions of SPF. The implementation of robust, easy processing welding techniques resulting in high quality repair able to sustain cumulative thermomechanical stresses is of utmost concern to SPF parts manufacturers. The paper focuses on the development of an automated TIG technique to weld repair high nickel, high chromium heat resistant alloys based on a complementary approach including thermal instrumentation, numerical simulation using Sysweld(TM) and metallurgical investigation: this former being performed on either as-received, repaired and repaired plus damaged materials

Spatial localization in heterogeneous systems

We study spatial localization in the generalized Swift-Hohenberg equation with either quadratic-cubic or cubic-quintic nonlinearity subject to spatially heterogeneous forcing. Different types of forcing (sinusoidal or Gaussian) with different spatial scales are considered and the corresponding localized snaking structures are computed. The results indicate that spatial heterogeneity exerts a significant influence on the location of spatially localized structures in both parameter space and physical space, and on their stability properties. The results are expected to assist in the interpretation of experiments on localized structures where departures from spatial homogeneity are generally unavoidable

Three-dimensional doubly diffusive convectons: instability and transition to complex dynamics

Three-dimensional doubly diffusive convection in a closed vertically extended container driven by competing horizontal temperature and concentration gradients is studied by a combination of direct numerical simulation and linear stability analysis. No-slip boundary conditions are imposed on all six container walls. The buoyancy number is taken to be to ensure the presence of a conduction state. The primary instability is subcritical and generates two families of spatially localized steady states known as convectons. The convectons bifurcate directly from the conduction state and are organized in a pair of primary branches that snake within a well-defined range of Rayleigh numbers as the convectons grow in length. Secondary instabilities generating twist result in secondary snaking branches of twisted convectons. These destabilize the primary convectons and are responsible for the absence of stable steady states, localized or otherwise, in the subcritical regime. Thus all initial conditions in this regime collapse to the conduction state. As a result, once the Rayleigh number for the primary instability of the conduction state is exceeded, the system exhibits an abrupt transition to large-amplitude relaxation oscillations resembling bursts with no hysteresis. These numerical results are confirmed here by determining the stability properties of both convecton types as well as the domain-filling states. The number of unstable modes of both primary and secondary convectons of different lengths follows a pattern that allows the prediction of their stability properties based on their length alone. The instability of the convectons also results in a dramatic change in the dynamics of the system outside the snaking region that arises when the twist instability operates on a time scale faster than the time scale on which new rolls are nucleated. The results obtained are expected to be applicable in various pattern-forming systems exhibiting localized structures, including convection and shear flows

Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow

Steady states and traveling waves play a fundamental role in understanding hydrodynamic problems. Even when unstable, these states provide the bifurcation-theoretic explanation for the origin of the observed states. In turbulent wall-bounded shear flows, these states have been hypothesized to be saddle points organizing the trajectories within a chaotic attractor. These states must be computed with Newton's method or one of its generalizations, since time-integration cannot converge to unstable equilibria. The bottleneck is the solution of linear systems involving the Jacobian of the Navier-Stokes or Boussinesq equations. Originally such computations were carried out by constructing and directly inverting the Jacobian, but this is unfeasible for the matrices arising from three-dimensional hydrodynamic configurations in large domains. A popular method is to seek states that are invariant under numerical time integration. Surprisingly, equilibria may also be found by seeking flows that are invariant under a single very large Backwards-Euler Forwards-Euler timestep. We show that this method, called Stokes preconditioning, is 10 to 50 times faster at computing steady states in plane Couette flow and traveling waves in pipe flow. Moreover, it can be carried out using Channelflow (by Gibson) and Openpipeflow (by Willis) without any changes to these popular spectral codes. We explain the convergence rate as a function of the integration period and Reynolds number by computing the full spectra of the operators corresponding to the Jacobians of both methods.Comment: in Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics, ed. Alexander Gelfgat (Springer, 2018

Localized rotating convection with no-slip boundary conditions

Localized patches of stationary convection embedded in a background conduction state are called convectons. Multiple states of this type have recently been found in two-dimensional Boussinesq convection in a horizontal fluid layer with stress-free boundary conditions at top and bottom, and rotating about the vertical. The convectons differ in their lengths and in the strength of the self-generated shear within which they are embedded, and exhibit slanted snaking. We use homotopic continuation of the boundary conditions to show that similar structures exist in the presence of no-slip boundary conditions at the top and bottom of the layer and show that such structures exhibit standard snaking. The homotopic continuation allows us to study the transformation from slanted snaking characteristic of systems with a conserved quantity, here the zonal momentum, to standard snaking characteristic of systems with no conserved quantity

Rapid adaptation drives invasion of airway donor microbiota by Pseudomonas after lung transplantation.

In cystic fibrosis (CF) patients, chronic airway infection by Pseudomonas leads to progressive lung destruction ultimately requiring lung transplantation (LT). Following LT, CF-adapted Pseudomonas strains, potentially originating from the sinuses, may seed the allograft leading to infections and reduced allograft survival. We investigated whether CF-adapted Pseudomonas populations invade the donor microbiota and adapt to the non-CF allograft. We collected sequential Pseudomonas isolates and airway samples from a CF-lung transplant recipient during two years, and followed the dynamics of the microbiota and Pseudomonas populations. We show that Pseudomonas invaded the host microbiota within three days post-LT, in association with a reduction in richness and diversity. A dominant mucoid and hypermutator mutL lineage was replaced after 11 days by non-mucoid strains. Despite antibiotic therapy, Pseudomonas dominated the allograft microbiota until day 95. We observed positive selection of pre-LT variants and the appearance of novel mutations. Phenotypic adaptation resulted in increased biofilm formation and swimming motility capacities. Pseudomonas was replaced after 95 days by a microbiota dominated by Actinobacillus. In conclusion, mucoid Pseudomonas adapted to the CF-lung remained able to invade the allograft. Selection of both pre-existing non-mucoid subpopulations and of novel phenotypic traits suggests rapid adaptation of Pseudomonas to the non-CF allograft