0000000000013951

AUTHOR

G. Ponetti

showing 4 related works from this author

Complex singularities in KdV solutions

2016

In the small dispersion regime, the KdV solution exhibits rapid oscillations in its spatio-temporal dependence. We show that these oscillations are caused by the presence of complex singularities that approach the real axis. We give a numerical estimate of the asymptotic dynamics of the poles.

Complex singularities Padé approximation Borel and power series methods Dispersive shocksApplied MathematicsGeneral MathematicsNumerical analysis010102 general mathematicsMathematical analysis01 natural sciences010305 fluids & plasmasAsymptotic dynamics0103 physical sciencesPadé approximantGravitational singularity0101 mathematicsAlgebra over a fieldKorteweg–de Vries equationDispersion (water waves)Complex planeMathematics
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Route to chaos in the weakly stratified Kolmogorov flow

2019

We consider a two-dimensional fluid exposed to Kolmogorov’s forcing cos(ny) and heated from above. The stabilizing effects of temperature are taken into account using the Boussinesq approximation. The fluid with no temperature stratification has been widely studied and, although relying on strong simplifications, it is considered an important tool for the theoretical and experimental study of transition to turbulence. In this paper, we are interested in the set of transitions leading the temperature stratified fluid from the laminar solution [U∝cos(ny),0, T ∝ y] to more complex states until the onset of chaotic states. We will consider Reynolds numbers 0 < Re ≤ 30, while the Richardson numb…

Fluid Flow and Transfer ProcessesPhysicsRichardson numberTurbulenceMechanical EngineeringMathematical analysisComputational MechanicsReynolds numberLaminar flowCondensed Matter Physics01 natural sciences010305 fluids & plasmasPhysics::Fluid Dynamicssymbols.namesakeTemperature gradientMechanics of Materials0103 physical sciencessymbolsBifurcation Computational complexity Reynolds number Boussinesq approximations Chaotic solutions Richardson number Stabilizing effects Stratified fluid Temperature stratification Transition to turbulence Weak stratificationStratified flowBoussinesq approximation (water waves)010306 general physicsSettore MAT/07 - Fisica MatematicaBifurcation
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Transitions in a stratified Kolmogorov flow

2016

We study the Kolmogorov flow with weak stratification. We consider a stabilizing uniform temperature gradient and examine the transitions leading the flow to chaotic states. By solving the equations numerically we construct the bifurcation diagram describing how the Kolmogorov flow, through a sequence of transitions, passes from its laminar solution toward weakly chaotic states. We consider the case when the Richardson number (measure of the intensity of the temperature gradient) is $$Ri=10^{-5}$$ , and restrict our analysis to the range $$0<Re<30$$ . The effect of the stabilizing temperature is to shift bifurcation points and to reduce the region of existence of stable drifting states. The…

Period-doubling bifurcationRichardson numberApplied MathematicsGeneral Mathematics010102 general mathematicsMathematical analysisChaoticThermodynamicsLaminar flowSaddle-node bifurcationBifurcation diagram01 natural sciences010305 fluids & plasmasNonlinear Sciences::Chaotic DynamicsTranscritical bifurcation0103 physical sciences0101 mathematicsStabilizing temperature gradient Equilibria Bifurcation analysisBifurcationMathematicsRicerche di Matematica
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Formation of Coherent Structures in Kolmogorov Flow with Stratification and Drag

2014

We study a weakly stratified Kolmogorov flow under the effect of a small linear drag. We perform a linear stability analysis of the basic state. We construct the finite dimensional dynamical system deriving from the truncated Fourier mode approximation. Using the Reynolds number as bifurcation parameter we build the corresponding diagram up to Re=100. We observe the coexistence of three coherent structures.

Partial differential equationApplied MathematicsDiagramMathematical analysisReynolds numberDynamical systemPhysics::Fluid DynamicsLinear stability analysisymbols.namesakeFourier transformBifurcation theoryDragsymbolsBifurcation theoryEquilibriaTruncated Navier-Stokes equationsSettore MAT/07 - Fisica MatematicaBifurcationMathematics
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