6533b82afe1ef96bd128b790
RESEARCH PRODUCT
Route to chaos in the weakly stratified Kolmogorov flow
Marco SammartinoFrancesco GarganoG. PonettiVincenzo Sciaccasubject
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 MatematicaBifurcationdescription
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 numbers shall be kept in the regime of weak stratifications (Ri ≤ 5 × 10−3). We shall first review the non-stratified Kolmogorov flow and find a new period-tripling bifurcation as the precursor of chaotic states. Introducing the stabilizing temperature gradient, we shall observe that higher Re are required to trigger instabilities. More importantly, we shall see new states and phenomena: the newly discovered period-tripling bifurcation is supercritical or subcritical according to Ri; more period-tripling and doubling bifurcations may depart from this new state; strong enough stratifications trigger new regions of chaotic solutions and, on the drifting solution branch, non-chaotic bursting solutions.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 numbers shall be kept in the regime of weak stratifications (Ri ≤ 5 × 10−3). We shall first review the non-stratified Kolmogorov flow and find a new period-tripling bifurcation as the precursor of chaotic states. Introducing the stabilizing temperature gradient, we shall observe that higher Re are required to trigger instab...
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-02-01 |