Etude de la convection mixte entre deux plans horizontaux à températures différentes—III

Linear stability of Rayleigh–Benard–Poiseuille convection for electrochemical system

“…Here, (1) is the Navier-Stokes equation that accounts for the buoyancy forces, (2) is the condition of incompressibility, (3) is the equation of electroactive ion transfer (Cu 2+ in the above examples), (4) is the transfer equation of fictitious electrolyte, which is introduced in order to eliminate the migration current [9,10], (5) is the condition of liquid adhesion to the cell walls, boundary conditions (6) show that the electrochemical reaction on the lower Nomenclature c m concentration of ions of mth type C 1 dimensionless concentration of electroactive ion,…”

“…This means that, in the case of plane liquid layer, to the linear approximation, forced convection only directs convective rolls and does not change the convective stability of system as a whole. However, in more complex geometric conditions, when transversal and longitudinal perturbations are not equally favored by influence of the sidewalls, shear flow can has a determining effect on the system stability [6].…”

Augmented Lagrangian Method and Open Boundary Conditions in 2d Simulation of Poiseuille–bénard Channel Flow

“…The subscript P refers to the central control volume point (i, k) and subscripts E, N, W and S refer to its neighbouring points to the east, north, west and south respectively (see Figure 2). To be able to compute the linear system corresponding to (9) for all the control volumes, equation (9) must be veri®ed everywhere, even at the outlet boundary. However, this is not always possible when, for example, f E is unknown on this boundary.…”

Noise sustained pattern growth: Bulk versus boundary effects

“…The final nonlinear stucture [4,5,9,10,[13][14][15]36] resulting in such a situation is self sustained and stable. For sufficiently large amplitudes this structure is dominated by the deterministic contributions in the relevant balance equations and thus it is insensitive to, say, thermal noise.…”

“…Nonequilibrium extended systems that undergo a pattern forming instability with nonzero group velocity [1] -whether the latter arises in open-flow configurations [2,3] via an imposed through-flow [4][5][6][7][8][9][10][11][12][13][14][15] or internally from a bifurcation to travelling waves [16][17][18] show a peculiar sensitivity to perturbations in the so called convectively unstable parameter regime [19,20]. Therein initially spatially localized perturbations superimposed on some basic unstable, macroscopically unstructured nonequilibrium state of the system are advected downstream by the group velocity.…”