Journal ArticleDOI
Convection in multi-component rotating fluid layers via the auxiliary system method
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In this article, the onset of thermal convection in a uniformly rotating horizontal layer filled by a Navier-Stokes multi-component fluid mixture, heated from below and salted partly from above and partly from below, is investigated via the new approach named auxiliary system method Rionero.Abstract:
The onset of thermal convection in a uniformly rotating horizontal layer filled by a Navier–Stokes multi-component fluid mixture, heated from below and salted partly from above and partly from below, is investigated via the new approach named auxiliary system method Rionero (Rend Lincei Mat Appl 25:1–44, 2014). In the free–free case, via the generalization of the Rionero Linearization Principle: “Decay of linear energy for any initial data implies decay of nonlinear energy at any instant” [given in Rionero (Rend Lincei Mat Appl 25:1–44, 2014) in the absence of rotation], it is shown that conditions guaranteeing linear stability of thermal conduction solution guarantee also absence of subcritical instabilities and global exponential asymptotic nonlinear stability. The classical Benard problem is investigated via a procedure different from the celebrated one given in Chandrasekhar (Hydrodynamic and hydromagnetic stability, 1981).read more
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Journal ArticleDOI
Modelling and optimization of least-cost water distribution networks with multiple supply sources and users
TL;DR: A least-cost optimization model is proposed, able to design a water distribution network with multiple supply sources and multiple users, and an application of the model to the real case of the province of Croton, Southern Italy is presented.
Journal ArticleDOI
The non-linear energy stability of Brinkman thermosolutal convection with reaction
TL;DR: In this article, the authors used the energy method to obtain the non-linear stability threshold for thermosolutal convection porous media of Brinkman type with reaction, and the obtained nonlinear boundaries for different values of the reaction terms are compared with the relevant linear instability boundaries obtained by Wang and Tan (Phys Lett A 373:776-780, 2009).
Journal ArticleDOI
Dynamic of rotating fluid layers: $$L^2$$ L 2 -absorbing sets and onset of convection
TL;DR: In this paper, Rionero et al. investigated the lifetime behavior of Navier-Stokes fluid mixtures filling horizontal rotating layers uniformly heated from below and salted by one salt.
Journal ArticleDOI
Transitions in a stratified Kolmogorov flow
TL;DR: In this article, the Kolmogorov flow with weak stratification was studied under a stabilizing uniform temperature gradient and the transitions leading the flow to chaotic states were modeled numerically.
References
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Book
Convection in Porous Media
Donald A. Nield,Adrian Bejan +1 more
TL;DR: In this paper, an introduction to convection in porous media assumes the reader is familiar with basic fluid mechanics and heat transfer, going on to cover insulation of buildings, energy storage and recovery, geothermal reservoirs, nuclear waste disposal, chemical reactor engineering and the storage of heat-generating materials like grain and coal.
Book
The Energy Method, Stability, and Nonlinear Convection
TL;DR: In this article, the Lyapunov method was used to solve the Navier-Stokes equations and the Benard problem for convection problems in a half-space.
BookDOI
Introduction to the theory of stability
TL;DR: In this paper, Liapunov's Theorem of motion instability was applied to the analysis of linear and nonlinear control systems, and the effect of force type on stability of motion was discussed.
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