Effect of horizontal pressure gradient on Rayleigh–Bénard convection of a Newtonian nanoliquid in a high porosity medium using a local thermal non‐equilibrium model

Heat Transfer ◽  
2020 ◽  
Author(s):  
T. N. Sakshath ◽  
Arundhathi Joshi
Keyword(s):  
Pressure Gradient ◽  
Equilibrium Model ◽  
High Porosity ◽  
Horizontal Pressure Gradient ◽  
Bénard Convection ◽  
Benard Convection ◽  
Horizontal Pressure ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Non Equilibrium

Force balance in rapidly rotating Rayleigh–Bénard convection

2021 ◽  
Vol 928 ◽  
Author(s):  
Andrés J. Aguirre Guzmán ◽  
Matteo Madonia ◽  
Jonathan S. Cheng ◽  
Rodolfo Ostilla-Mónico ◽  
Herman J.H. Clercx ◽  
...  
Keyword(s):  
Pressure Gradient ◽  
Large Scale ◽  
Force Balance ◽  
Bénard Convection ◽  
Benard Convection ◽  
Buoyancy Forces ◽  
Kinetic Boundary Layers ◽  
Gradient Forces ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The force balance of rotating Rayleigh–Bénard convection regimes is investigated using direct numerical simulation on a laterally periodic domain, vertically bounded by no-slip walls. We provide a comprehensive view of the interplay between governing forces both in the bulk and near the walls. We observe, as in other prior studies, regimes of cells, convective Taylor columns, plumes, large-scale vortices (LSVs) and rotation-affected convection. Regimes of rapidly rotating convection are dominated by geostrophy, the balance between Coriolis and pressure-gradient forces. The higher-order interplay between inertial, viscous and buoyancy forces defines a subdominant balance that distinguishes the geostrophic states. It consists of viscous and buoyancy forces for cells and columns, inertial, viscous and buoyancy forces for plumes, and inertial forces for LSVs. In rotation-affected convection, inertial and pressure-gradient forces constitute the dominant balance; Coriolis, viscous and buoyancy forces form the subdominant balance. Near the walls, in geostrophic regimes, force magnitudes are larger than in the bulk; buoyancy contributes little to the subdominant balance of cells, columns and plumes. Increased force magnitudes denote increased ageostrophy near the walls. Nonetheless, the flow is geostrophic as the bulk. Inertia becomes increasingly more important compared with the bulk, and enters the subdominant balance of columns. As the bulk, the near-wall flow loses rotational constraint in rotation-affected convection. Consequently, kinetic boundary layers deviate from the expected behaviour from linear Ekman boundary layer theory. Our findings elucidate the dynamical balances of rotating thermal convection under realistic top/bottom boundary conditions, relevant to laboratory settings and large-scale natural flows.

scholarly journals Rayleigh-Benard convection in a viscoelastic fluid-filled high-porosity medium with nonuniform basic temperature gradient

2001 ◽  
Vol 25 (9) ◽  
pp. 609-619 ◽  
Author(s):  
Pradeep G. Siddheshwar ◽  
C. V. Sri Krishna
Keyword(s):  
Stability Analysis ◽  
Temperature Gradient ◽  
Viscoelastic Fluid ◽  
High Porosity ◽  
Rigid Boundary ◽  
Viscoelastic Problem ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The qualitative effect of nonuniform temperature gradient on the linear stability analysis of the Rayleigh-Benard convection problem in a Boussinesquian, viscoelastic fluid-filled, high-porosity medium is studied numerically using the single-term Galerkin technique. The eigenvalue is obtained for free-free, free-rigid, and rigid-rigid boundary combinations with isothermal temperature conditions. Thermodynamics and also the present stability analysis dictates the strain retardation time to be less than the stress relaxation time for convection to set in as oscillatory motions in a high-porosity medium. Furthermore, the analysis predicts the critical eigenvalue for the viscoelastic problem to be less than that of the corresponding Newtonian fluid problem.

Plumes in rotating convection. Part 1. Ensemble statistics and dynamical balances

1999 ◽  
Vol 391 ◽  
pp. 151-187 ◽  
Author(s):  
KEITH JULIEN ◽  
SONYA LEGG ◽  
JAMES McWILLIAMS ◽  
JOSEPH WERNE
Keyword(s):  
Kinetic Energy ◽  
Pressure Gradient ◽  
Conditional Sampling ◽  
Typical Structure ◽  
Bénard Convection ◽  
Benard Convection ◽  
Turbulent Plume ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Oceanic Convection

Atmospheric and oceanic convection often occurs over areas occupied by many localized circulation elements known as plumes. The convective transports therefore may depend not only on the individual elements, but also on the interactions between plumes and the turbulent environment created by other plumes. However, many attempts to understand these plumes focus on individual isolated elements, and the behaviour of an ensemble is not understood. Geophysical convection may be influenced by rotation when the transit time of a convecting element is long compared to an inertial period (for example in deep oceanic convection). Much recent attention has been given to the effect of rotation on individual plumes, but the role of rotation in modifying the behaviour of an ensemble is not fully understood. Here we examine the behaviour of plumes within an ensemble, both with and without rotation, to identify the influence of rotation on ensemble plume dynamics.We identify the coherent structures (plumes) present in numerical solutions of turbulent Rayleigh–Bénard convection, a canonical example of a turbulent plume ensemble. We use a conditional sampling compositing technique to extract the typical structure in both non-rotating and rotating solutions. The dynamical balances of these composite plumes are evaluated and compared with entraining plume models. We find many differences between non-rotating and rotating plumes in their transports of mass, buoyancy and momentum. As shown in previous studies, the expansion of the turbulent plume by entrainment of exterior fluid is suppressed by strong rotation. Our most significant new result is quantification of the continuous mixing between the plume and ambient fluid which occurs at high rotation without any net changes in plume volume. This mixing is generated by the plume–plume interactions and acts to reduce the buoyancy anomaly of the plume. By contrast, in the non-rotating case, no such loss of buoyancy by mixing occurs. As a result, the total buoyancy transport by upwardly moving plumes diminishes across the layer in the rotating case, while remaining approximately constant in the non-rotating case. At high values of rotation, the net vertical acceleration is considerably reduced compared to the non-rotating case due to loss of momentum through entrainment and mixing and a decelerating pressure gradient which partially balances the buoyancy-driven acceleration of plumes. As a result of the dilution of buoyancy, the pressure-gradient deceleration and the loss of momentum due to mixing with the environment in the rotating solutions, the conversion of potential energy to kinetic energy is significantly less than that of non-rotating plumes.The combination of efficient lateral mixing and slow vertical movement by the plumes accounts for the unstable mean temperature gradient that occurs in rotating Rayleigh–Bénard convection, while the less penetrative convection found at low Rossby number is a consequence of the reduced kinetic energy transport. Within the ensemble of plumes identified by the conditional sampling algorithm, distributions of vertical velocity, buoyancy and vorticity mimic those of the volume as a whole. Plumes cover a small fraction of the total area, yet account for most of the vertical heat flux.

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