scholarly journals Geostrophic and chimney regimes in rotating horizontal convection with imposed heat flux

2017 ◽  
Vol 823 ◽  
pp. 57-99 ◽  
Author(s):  
Catherine A. Vreugdenhil ◽  
Ross W. Griffiths ◽  
Bishakhdatta Gayen
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Heat Transport ◽  
Scaling Analysis ◽  
Mean Flow ◽  
Flux Boundary Condition ◽  
Horizontal Convection ◽  
Small Depth ◽  
Basin Scale ◽  
Boundary Flux

Convection in a rotating rectangular basin with differential thermal forcing at one horizontal boundary is examined using laboratory experiments. The experiments have an imposed heat flux boundary condition, are at large values of the flux Rayleigh number ($Ra_{F}\sim O(10^{13}{-}10^{14})$ based on the box length $L$), use water with Prandtl number $Pr\approx 4$ and have a small depth to length aspect ratio. The results show the conditions for transition from non-rotating horizontal convection governed by an inertial–buoyancy balance in the thermal boundary layer, to circulation governed by geostrophic flow in the boundary layer. The geostrophic balance constrains mean flow and reduces the heat transport as Nusselt number $Nu\sim (Ra_{F}Ro)^{1/6}$, where $Ro=B^{1/2}/f^{3/2}L$ is the convective Rossby number, $B$ is the imposed buoyancy flux and $f$ is the Coriolis parameter. Thus flow in the geostrophic boundary layer regime is governed by the relative roles of horizontal convective accelerations and Coriolis accelerations, or buoyancy and rotation, in the boundary layer. Experimental evidence suggests that for more rapid rotation there is another transition to a regime in which the momentum budget is dominated by fluctuating vertical accelerations in a region of vortical plumes, which we refer to as a ‘chimney’ following related discussion of regions of deep convection in the ocean. Coupling of the chimney convection in the region of destabilising boundary flux to the diffusive boundary layer of horizontal convection in the region of stabilising boundary flux gives heat transport independent of rotation in this ‘inertial chimney’ regime, and the new scaling $Nu\sim Ra_{F}^{1/4}$. Scaling analysis predicts the transition conditions observed in the experiments, as well as a further ‘geostrophic chimney’ regime in which the vertical plumes are controlled by local geostrophy. When $Ro<10^{-1}$, the convection is also observed to produce a set of large basin-scale gyres at all depths in the time-averaged flow.

North Atlantic Circulation Regimes and Heat Transport by Synoptic Eddies

2020 ◽  
Vol 33 (11) ◽  
pp. 4769-4785 ◽  
Author(s):  
Paolo Ruggieri ◽  
M. Carmen Alvarez-Castro ◽  
Panos Athanasiadis ◽  
Alessio Bellucci ◽  
Stefano Materia ◽  
...  
Keyword(s):  
Heat Flux ◽  
Heat Transport ◽  
North Atlantic ◽  
High Latitude ◽  
Polar Regions ◽  
Mean Flow ◽  
Dynamical Interaction ◽  
Weather Regimes ◽  
Eddy Heat Flux ◽  
Synoptic Eddies

AbstractMeridional transport of heat by transient atmospheric eddies is a key component of the energy budget of the middle- and high-latitude regions. The heat flux at relevant frequencies is also part of a dynamical interaction between eddies and mean flow. In this study we investigate how the poleward heat flux by high-frequency atmospheric transient eddies is modulated by North Atlantic weather regimes in reanalysis data. Circulation regimes are estimated via a clustering method, a jet-latitude index, and a blocking index. Heat transport is defined as advection of moist static energy. The focus of the analysis is on synoptic frequencies but results for slightly longer time scales are reported. Results show that the synoptic eddy heat flux is substantially modulated by midlatitude weather regimes on a regional scale in midlatitude and polar regions. In a zonal-mean sense, the phases of the North Atlantic Oscillation do not significantly change the high-latitude synoptic heat flux, whereas Scandinavian blocking and the Atlantic ridge are associated with an intensification. A close relationship between high-latitude (midlatitude) heat flux and Atlantic jet speed (latitude) is found. The relationship between extreme events of synoptic heat flux and circulation regimes is also assessed and reveals contrasting behaviors in the polar regions. The perspective that emerges complements the traditional view of the interaction between synoptic eddies and the extratropical flow and reveals relationships with the high-latitude climate.

Linear stability and energetics of rotating radial horizontal convection

2016 ◽  
Vol 795 ◽  
pp. 1-35 ◽  
Author(s):  
Gregory J. Sheard ◽  
Wisam K. Hussam ◽  
Tzekih Tsai
Keyword(s):  
Boundary Layer ◽  
Potential Energy ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Baroclinic Instability ◽  
Mean Flow ◽  
Thermal Boundary Layer Thickness ◽  
Available Potential Energy ◽  
Horizontal Convection ◽  
The Mean

The effect of rotation on horizontal convection in a cylindrical enclosure is investigated numerically. The thermal forcing is applied radially on the bottom boundary from the coincident axes of rotation and geometric symmetry of the enclosure. First, a spectral element method is used to obtain axisymmetric basic flow solutions to the time-dependent incompressible Navier–Stokes equations coupled via a Boussinesq approximation to a thermal transport equation for temperature. Solutions are obtained primarily at Rayleigh number $\mathit{Ra}=10^{9}$ and rotation parameters up to $Q=60$ (where $Q$ is a non-dimensional ratio between thermal boundary layer thickness and Ekman layer depth) at a fixed Prandtl number $\mathit{Pr}=6.14$ representative of water and enclosure height-to-radius ratio $H/R=0.4$. The axisymmetric solutions are consistently steady state at these parameters, and transition from a regime unaffected by rotation to an intermediate regime occurs at $Q\approx 1$ in which variation in thermal boundary layer thickness and Nusselt number are shown to be governed by a scaling proposed by Stern (1975, Ocean Circulation Physics. Academic). In this regime an increase in $Q$ sees the flow accumulate available potential energy and more strongly satisfy an inviscid change in potential energy criterion for baroclinic instability. At the strongest $Q$ the flow is dominated by rotation, accumulation of available potential energy ceases and horizontal convection is suppressed. A linear stability analysis reveals several instability mode branches, with dominant wavenumbers typically scaling with $Q$. Analysis of contributing terms of an azimuthally averaged perturbation kinetic energy equation applied to instability eigenmodes reveals that energy production by shear in the axisymmetric mean flow is negligible relative to that produced by conversion of available potential energy from the mean flow. An evolution equation for the quantity that facilitates this exchange, the vertical advective buoyancy flux, reveals that a baroclinic instability mechanism dominates over $5\lesssim Q\lesssim 30$, whereas stronger and weaker rotations are destabilised by vertical thermal gradients in the mean flow.

scholarly journals Convectively driven shear and decreased heat flux

2014 ◽  
Vol 759 ◽  
pp. 360-385 ◽  
Author(s):  
David Goluskin ◽  
Hans Johnston ◽  
Glenn R. Flierl ◽  
Edward A. Spiegel
Keyword(s):  
Heat Flux ◽  
Heat Transport ◽  
Large Scale ◽  
Mean Flow ◽  
Nusselt Numbers ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Scale Shear

AbstractWe report on direct numerical simulations of two-dimensional, horizontally periodic Rayleigh–Bénard convection between free-slip boundaries. We focus on the ability of the convection to drive large-scale horizontal flow that is vertically sheared. For the Prandtl numbers ($\mathit{Pr}$) between 1 and 10 simulated here, this large-scale shear can be induced by raising the Rayleigh number ($\mathit{Ra}$) sufficiently, and we explore the resulting convection for $\mathit{Ra}$ up to $10^{10}$. When present in our simulations, the sheared mean flow accounts for a large fraction of the total kinetic energy, and this fraction tends towards unity as $\mathit{Ra}\rightarrow \infty$. The shear helps disperse convective structures, and it reduces vertical heat flux; in parameter regimes where one state with large-scale shear and one without are both stable, the Nusselt number of the state with shear is smaller and grows more slowly with $\mathit{Ra}$. When the large-scale shear is present with $\mathit{Pr}\lesssim 2$, the convection undergoes strong global oscillations on long timescales, and heat transport occurs in bursts. Nusselt numbers, time-averaged over these bursts, vary non-monotonically with $\mathit{Ra}$ for $\mathit{Pr}=1$. When the shear is present with $\mathit{Pr}\gtrsim 3$, the flow does not burst, and convective heat transport is sustained at all times. Nusselt numbers then grow roughly as powers of $\mathit{Ra}$, but the growth rates are slower than any previously reported for Rayleigh–Bénard convection without large-scale shear. We find that the Nusselt numbers grow proportionally to $\mathit{Ra}^{0.077}$ when $\mathit{Pr}=3$ and to $\mathit{Ra}^{0.19}$ when $\mathit{Pr}=10$. Analogies with tokamak plasmas are described.

scholarly journals The Role of Boundary Layer Processes in Limiting PV Homogenization

2009 ◽  
Vol 66 (6) ◽  
pp. 1612-1632 ◽  
Author(s):  
Yang Zhang ◽  
Peter H. Stone ◽  
Amy Solomon
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Temperature Gradient ◽  
Surface Friction ◽  
Mean Flow ◽  
Eddy Heat Flux ◽  
Boundary Layer Processes ◽  
The Mean ◽  
Pv Gradient

Abstract A β-plane multilevel quasigeostrophic channel model with interactive static stability and a simplified parameterization of atmospheric boundary layer physics is used to study the role of different boundary layer processes in eddy equilibration and their relative effect in maintaining the strong boundary layer potential vorticity (PV) gradient. The model results show that vertical thermal diffusion, along with the surface heat exchange, is primarily responsible for limiting PV homogenization by baroclinic eddies in the boundary layer. Under fixed SST boundary conditions, these two processes act as the source of the mean flow baroclinicity in the lower levels and result in stronger eddy heat fluxes. Reducing surface friction alone does not result in efficient elimination of the boundary layer PV gradient, but the equilibrium state temperature gradient is still largely influenced by surface friction and its response to changes in surface friction is not monotonic. In the regime of strong surface friction, with reduced poleward eddy heat flux, a strong temperature gradient is still retained. When the surface friction is sufficiently weak along with the stronger zonal wind, the critical level at the center of the jet drops below the surface. As a result, in the lower levels, the eddy heat flux forcing on the mean flow moves away from the center of the jet and the equilibrium state varies only slightly with the strength of the vertical momentum diffusion in the boundary layer.

Turbulent horizontal convection under spatially periodic forcing: a regime governed by interior inertia

2017 ◽  
Vol 831 ◽  
pp. 491-523 ◽  
Author(s):  
Madelaine G. Rosevear ◽  
Bishakhdatta Gayen ◽  
Ross W. Griffiths
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Viscous Dissipation ◽  
Deep Water ◽  
Shear Instability ◽  
Horizontal Boundary ◽  
Horizontal Convection ◽  
Horizontal Length ◽  
Flow Transitions ◽  
Almost All

Differential heating applied at a single horizontal boundary forces ‘horizontal convection’, even when there is no net heat flux through the boundary. However, almost all studies of horizontal convection have been limited to a special class of problem in which temperature or heat flux differences were applied in only one direction and over the horizontal length of a box (the Rossby problem; Rossby, Deep-Sea Res., vol. 12, 1965, pp. 9–16). These conditions strongly constrain the flow. Here we report laboratory experiments and direct numerical simulations (DNS) extending the results of Griffiths & Gayen (Phys. Rev. Lett., vol. 115, 2015, 204301) for horizontal convection forced by boundary conditions imposed in a two-dimensional periodic array at a horizontal boundary. The experiments use saline and freshwater fluxes at a permeable base with the imposed boundary salinity having a horizontal length scale one quarter of the width of the box. The flow reaches a state in which the net boundary buoyancy flux vanishes and the bulk of the fluid shows an inertial range of turbulence length scales. A regime transition is seen for increasing water depth, from an array of individual coherent plumes on the forcing scale to convection dominated by emergent larger scales of overturning. The DNS explore the analogous thermally forced case with sinusoidal boundary temperature of wavenumber $n=4$, and are used to examine the Rayleigh number ($Ra$) dependence for shallow- and deep-water cases. For shallow water the flow transitions with increasing $Ra$ from laminar to turbulent boundary layer regimes that are familiar from the Rossby problem and which have normalised heat transport scaling as $Nu\sim Ra^{1/5}$ and $Nu\sim (Ra\,Pr)^{1/5}$, with $Nu$ the Nusselt number and $Pr$ the Prandtl number, in this case maintaining a stable array of coherent turbulent plumes. For deep-water and large $Ra$ the laminar scaling transitions to $Nu\sim (Ra\,Pr)^{1/4}$, with the scales of turbulence extending to the dimensions of the box. The $1/4$ power law regime is explained in terms of the momentum of symmetric, inviscid large scales of motion in the interior coupled to diffusive loss of heat through stabilised parts of the boundary layer. The turbulence production is predominantly by shear instability rather than convection, with viscous dissipation distributed throughout the bulk of the fluid. These conditions are not seen in the highly asymmetric flow in the Rossby problem even at Rayleigh numbers up to six orders of magnitude greater than the transition found here. The new inertial interior regime has the rate of supply of available potential energy, and its removal by mixing of density, increasing as $Ra^{5/4}$, which is faster than $Ra^{6/5}$ in the Rossby problem. Irreversible mixing is confined close to the forcing boundary and is very much larger than the viscous dissipation, which is proportional to $Ra$.

scholarly journals MHD Powell–Eyring dusty nanofluid flow due to stretching surface with heat flux boundary condition

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Omima A. Abo-zaid ◽  
R. A. Mohamed ◽  
F. M. Hady ◽  
A. Mahdy
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Fluid Phase ◽  
Spherical Shape ◽  
Dust Particles ◽  
Stretching Surface ◽  
Flux Boundary Condition ◽  
Fluid Phases

AbstractA steady MHD boundary layer flow of Powell–Eyring dusty nanofluid over a stretching surface with heat flux condition is studied numerically. It is assumed that the fluid is incompressible and the impacts of thermophoresis and Brownian motion are taken into regard. In addition, the Powell–Eyring terms are considered in the momentum boundary layer and thermal boundary layer. The dust particles are seen as to be having the same size and conform to the nanoparticles in a spherical shape. We obtain a system of ordinary differential equations that are suitable for analyzed numerically using the fourth-order Runge–Kutta method via software algebraic MATLAB by applying appropriate transformations to the system of the governing partial differential equations in our problem. There is perfect compatibility between the bygone and current results when comparing our numerical solutions with the available data for values of the selected parameters. This confirms the validity of the method used here and thus the validity of the results. The influence of some parameters on the boundary layer profiles (the velocity and temperature for the particle phase and fluid phase, and nanoparticle concentration) is discussed. The results of this study display that the profiles of the velocity for particle and fluid phases increase with increasing Powell–Eyring fluid parameter, but reduce with height in magnetic field values. Mass concentration of the dust particles decreases the temperature of both the particle and fluid phases. The results also indicate the concentration of nanoparticle contraction as Schmidt number increases.

Sign in / Sign up

Export Citation Format

Share Document