• Previous Article
    q-Gaussian integrable Hamiltonian reductions in anisentropic gasdynamics
  • DCDS-B Home
  • This Issue
  • Next Article
    On some properties of the Mittag-Leffler function $\mathbf{E_\alpha(-t^\alpha)}$, completely monotone for $\mathbf{t> 0}$ with $\mathbf{0<\alpha<1}$
September  2014, 19(7): 2279-2296. doi: 10.3934/dcdsb.2014.19.2279

Onset of convection in rotating porous layers via a new approach

1. 

University of Naples Federico II, Department of Mathematics and Applications, "Renato Caccioppoli", Via Cinzia 80126. Naples, Italy

Received  April 2013 Revised  September 2013 Published  August 2014

Via a new approach, ternary fluid mixtures saturating rotating horizontal porous layers, heated from below and salted from above and below, are investigated. With or without the presence of Brinkman viscosity, the absence of subcritical instabilities is shown together with the coincidence of linear and non-linear global stability of the thermal conduction solution. The stability-instability conditions are found to be given by simple algebraic conditions in closed forms.
Citation: Salvatore Rionero. Onset of convection in rotating porous layers via a new approach. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 2279-2296. doi: 10.3934/dcdsb.2014.19.2279
References:
[1]

F. Capone and R. De Luca, Onset of convection for ternary fluid mixtures saturating horizontal porous layers with large pores,, Rend. Lincei Mat. Appl., 23 (2012), 405.  doi: 10.4171/RLM/636.  Google Scholar

[2]

F. Capone and R. De Luca, Ultimately boundedness and stability of triply diffusive mixtures in rotating porous layers under the action of Brinkman law,, Int. J. Nonlinear Mech., 47 (2012), 799.   Google Scholar

[3]

S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability,, Dover, (1981).   Google Scholar

[4]

J. Flavin and S. Rionero, Qualitative Estimates for Partial Differential Equations,, An Introduction. CRC Press, (1996).   Google Scholar

[5]

F. R. Gantmaker, The Theory Of Matrices,, Vol 1-2 AMS (Chelsea Publishing), (2000), 1.   Google Scholar

[6]

M. Lappa, Rotating Thermal Flows in Natural and Industrial Processes,, Wiley, (2012).  doi: 10.1002/9781118342411.  Google Scholar

[7]

A. Lopez, L. Romero and A. Pearlstein, Effect of rigid boundaries on the onset of convection in a triply diffusive fluid layer,, Phys. Fluids A, 2 (1990), 897.   Google Scholar

[8]

D. R. Merkin, Introduction to the Theory of Stability,, Texts in Applied Mathematics, 24 (1997).   Google Scholar

[9]

D. A. Nield and A. Bejan, Conduction in Porous Media,, 2nd edition, (1999).  doi: 10.1007/978-1-4757-3033-3.  Google Scholar

[10]

R. A. Noutly and D. G. Leaist, Quaternary diffusion in acqueous $KCl-KH_2PO_4-H_3PO_4$ mixtures,, J. Phys. Chem., 91 (1987), 1655.   Google Scholar

[11]

A. J. Pearlstein, R. M. Harris and G. Terrones, The onset of convective instability in a triply diffusive fluid layer,, J.Fluid Mech., 202 (1989), 443.  doi: 10.1017/S0022112089001242.  Google Scholar

[12]

S. Rionero, Absence of subcritical instabilities and global nonlinear stability for porous ternary diffusive-convective fluid mixtures,, Phys. Fluids, 24 (2012).  doi: 10.1063/1.4757858.  Google Scholar

[13]

S. Rionero, Long time behaviour of multicomponent fluid mixture in porous media,, Int. J. of Eng. Sci., 48 (2010), 1519.  doi: 10.1016/j.ijengsci.2010.07.007.  Google Scholar

[14]

S. Rionero, Global nonlinear stability for a triply diffusive-convection in a porous layer,, Contin. Mech. Thermodyn., 24 (2012), 629.  doi: 10.1007/s00161-011-0219-4.  Google Scholar

[15]

S. Rionero, On the nonlinear stability of ternary porous media via only one necessary and sufficient algebraic condition,, (submitted to EECT, ().   Google Scholar

[16]

S. Rionero, Symmetries and skew-symmetries against onset of convection in porous layers salted from above and below,, Int. J. Non-linear Mech., 47 (2012), 61.   Google Scholar

[17]

S. Rionero, Multicomponent diffusive-convective fluid motions in porous layers: ultimately boundedness, absence of subcritical instabilities and global nonlinear stability for any number of salts,, Phys. Fluids, 25 (2013).  doi: 10.1063/1.4802629.  Google Scholar

[18]

B. Straughan, The Energy Method, Stability and Nonlinear Convection,, Second edition. Applied Mathematical Sciences, (2004).  doi: 10.1007/978-0-387-21740-6.  Google Scholar

[19]

B. Straughan, Stability and Wave Motion in Porous Media,, Applied Mathematical Sciences, (2008).   Google Scholar

[20]

B. Straughan and J. Tracey, Multi-component convection-diffusion with internal heating or cooling,, Acta Mechanica, 133 (1999), 219.   Google Scholar

[21]

J. Tracey, Multi-component convection-diffusion in a porous medium,, Continuum Mech. Thermodyn., 8 (1996), 361.   Google Scholar

show all references

References:
[1]

F. Capone and R. De Luca, Onset of convection for ternary fluid mixtures saturating horizontal porous layers with large pores,, Rend. Lincei Mat. Appl., 23 (2012), 405.  doi: 10.4171/RLM/636.  Google Scholar

[2]

F. Capone and R. De Luca, Ultimately boundedness and stability of triply diffusive mixtures in rotating porous layers under the action of Brinkman law,, Int. J. Nonlinear Mech., 47 (2012), 799.   Google Scholar

[3]

S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability,, Dover, (1981).   Google Scholar

[4]

J. Flavin and S. Rionero, Qualitative Estimates for Partial Differential Equations,, An Introduction. CRC Press, (1996).   Google Scholar

[5]

F. R. Gantmaker, The Theory Of Matrices,, Vol 1-2 AMS (Chelsea Publishing), (2000), 1.   Google Scholar

[6]

M. Lappa, Rotating Thermal Flows in Natural and Industrial Processes,, Wiley, (2012).  doi: 10.1002/9781118342411.  Google Scholar

[7]

A. Lopez, L. Romero and A. Pearlstein, Effect of rigid boundaries on the onset of convection in a triply diffusive fluid layer,, Phys. Fluids A, 2 (1990), 897.   Google Scholar

[8]

D. R. Merkin, Introduction to the Theory of Stability,, Texts in Applied Mathematics, 24 (1997).   Google Scholar

[9]

D. A. Nield and A. Bejan, Conduction in Porous Media,, 2nd edition, (1999).  doi: 10.1007/978-1-4757-3033-3.  Google Scholar

[10]

R. A. Noutly and D. G. Leaist, Quaternary diffusion in acqueous $KCl-KH_2PO_4-H_3PO_4$ mixtures,, J. Phys. Chem., 91 (1987), 1655.   Google Scholar

[11]

A. J. Pearlstein, R. M. Harris and G. Terrones, The onset of convective instability in a triply diffusive fluid layer,, J.Fluid Mech., 202 (1989), 443.  doi: 10.1017/S0022112089001242.  Google Scholar

[12]

S. Rionero, Absence of subcritical instabilities and global nonlinear stability for porous ternary diffusive-convective fluid mixtures,, Phys. Fluids, 24 (2012).  doi: 10.1063/1.4757858.  Google Scholar

[13]

S. Rionero, Long time behaviour of multicomponent fluid mixture in porous media,, Int. J. of Eng. Sci., 48 (2010), 1519.  doi: 10.1016/j.ijengsci.2010.07.007.  Google Scholar

[14]

S. Rionero, Global nonlinear stability for a triply diffusive-convection in a porous layer,, Contin. Mech. Thermodyn., 24 (2012), 629.  doi: 10.1007/s00161-011-0219-4.  Google Scholar

[15]

S. Rionero, On the nonlinear stability of ternary porous media via only one necessary and sufficient algebraic condition,, (submitted to EECT, ().   Google Scholar

[16]

S. Rionero, Symmetries and skew-symmetries against onset of convection in porous layers salted from above and below,, Int. J. Non-linear Mech., 47 (2012), 61.   Google Scholar

[17]

S. Rionero, Multicomponent diffusive-convective fluid motions in porous layers: ultimately boundedness, absence of subcritical instabilities and global nonlinear stability for any number of salts,, Phys. Fluids, 25 (2013).  doi: 10.1063/1.4802629.  Google Scholar

[18]

B. Straughan, The Energy Method, Stability and Nonlinear Convection,, Second edition. Applied Mathematical Sciences, (2004).  doi: 10.1007/978-0-387-21740-6.  Google Scholar

[19]

B. Straughan, Stability and Wave Motion in Porous Media,, Applied Mathematical Sciences, (2008).   Google Scholar

[20]

B. Straughan and J. Tracey, Multi-component convection-diffusion with internal heating or cooling,, Acta Mechanica, 133 (1999), 219.   Google Scholar

[21]

J. Tracey, Multi-component convection-diffusion in a porous medium,, Continuum Mech. Thermodyn., 8 (1996), 361.   Google Scholar

[1]

Noufel Frikha, Valentin Konakov, Stéphane Menozzi. Well-posedness of some non-linear stable driven SDEs. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 849-898. doi: 10.3934/dcds.2020302

[2]

Touria Karite, Ali Boutoulout. Global and regional constrained controllability for distributed parabolic linear systems: RHUM approach. Numerical Algebra, Control & Optimization, 2020  doi: 10.3934/naco.2020055

[3]

Adrian Constantin, Darren G. Crowdy, Vikas S. Krishnamurthy, Miles H. Wheeler. Stuart-type polar vortices on a rotating sphere. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 201-215. doi: 10.3934/dcds.2020263

[4]

Antoine Benoit. Weak well-posedness of hyperbolic boundary value problems in a strip: when instabilities do not reflect the geometry. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5475-5486. doi: 10.3934/cpaa.2020248

[5]

Leanne Dong. Random attractors for stochastic Navier-Stokes equation on a 2D rotating sphere with stable Lévy noise. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020352

[6]

Awais Younus, Zoubia Dastgeer, Nudrat Ishaq, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Devendra Kumar. On the observability of conformable linear time-invariant control systems. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020444

[7]

Haiyu Liu, Rongmin Zhu, Yuxian Geng. Gorenstein global dimensions relative to balanced pairs. Electronic Research Archive, 2020, 28 (4) : 1563-1571. doi: 10.3934/era.2020082

[8]

Jianhua Huang, Yanbin Tang, Ming Wang. Singular support of the global attractor for a damped BBM equation. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020345

[9]

Eduard Feireisl, Elisabetta Rocca, Giulio Schimperna, Arghir Zarnescu. Weak sequential stability for a nonlinear model of nematic electrolytes. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 219-241. doi: 10.3934/dcdss.2020366

[10]

Bernold Fiedler. Global Hopf bifurcation in networks with fast feedback cycles. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 177-203. doi: 10.3934/dcdss.2020344

[11]

Yongge Tian, Pengyang Xie. Simultaneous optimal predictions under two seemingly unrelated linear random-effects models. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020168

[12]

Chao Wang, Qihuai Liu, Zhiguo Wang. Periodic bouncing solutions for Hill's type sub-linear oscillators with obstacles. Communications on Pure & Applied Analysis, 2021, 20 (1) : 281-300. doi: 10.3934/cpaa.2020266

[13]

Cheng He, Changzheng Qu. Global weak solutions for the two-component Novikov equation. Electronic Research Archive, 2020, 28 (4) : 1545-1562. doi: 10.3934/era.2020081

[14]

Reza Chaharpashlou, Abdon Atangana, Reza Saadati. On the fuzzy stability results for fractional stochastic Volterra integral equation. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020432

[15]

Scipio Cuccagna, Masaya Maeda. A survey on asymptotic stability of ground states of nonlinear Schrödinger equations II. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020450

[16]

Gloria Paoli, Gianpaolo Piscitelli, Rossanno Sannipoli. A stability result for the Steklov Laplacian Eigenvalue Problem with a spherical obstacle. Communications on Pure & Applied Analysis, 2021, 20 (1) : 145-158. doi: 10.3934/cpaa.2020261

[17]

Hao Wang. Uniform stability estimate for the Vlasov-Poisson-Boltzmann system. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 657-680. doi: 10.3934/dcds.2020292

[18]

Vieri Benci, Marco Cococcioni. The algorithmic numbers in non-archimedean numerical computing environments. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020449

[19]

Héctor Barge. Čech cohomology, homoclinic trajectories and robustness of non-saddle sets. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020381

[20]

Ying Lin, Qi Ye. Support vector machine classifiers by non-Euclidean margins. Mathematical Foundations of Computing, 2020, 3 (4) : 279-300. doi: 10.3934/mfc.2020018

2019 Impact Factor: 1.27

Metrics

  • PDF downloads (30)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]