ross griffiths

Transport by deep convection in basin-scale geostrophic circulation: turbulence-resolving simulations

Publisher: Cambridge University Press (CUP)

Date: 26-02-2019

DOI: 10.1017/JFM.2019.64

Abstract: Direct numerical simulations are used to investigate the nature of fully resolved small-scale convection and its role in large-scale circulation in a rotating $f$ -plane rectangular basin with imposed surface temperature difference. The large-scale circulation has a horizontal geostrophic component and a deep vertical overturning. This paper focuses on convective circulation with no wind stress, and buoyancy forcing sufficiently strong to ensure turbulent convection within the thermal boundary layer (horizontal Rayleigh numbers $Ra\\approx 10^{12}{-}10^{13}$ ). The dynamics are found to depend on the value of a convective Rossby number, $Ro_{\\unicode[STIX]{x0394}T}$ , which represents the strength of buoyancy forcing relative to Coriolis forces. Vertical convection shifts from a mean endwall plume under weak rotation ( $Ro_{\\unicode[STIX]{x0394}T} ^{-1}$ ) to ‘open ocean’ chimney convection plus mean vertical plumes at the side boundaries under strong rotation ( $Ro_{\\unicode[STIX]{x0394}T} ^{-1}$ ). The overall heat throughput, horizontal gyre transport and zonally integrated overturning transport are then consistent with scaling predictions for flow constrained by thermal wind balance in the thermal boundary layer coupled to vertical advection–diffusion balance in the boundary layer. For small Rossby numbers relevant to circulation in an ocean basin, vertical heat transport from the surface layer into the deep interior occurs mostly in ‘open ocean’ chimney convection while most vertical mass transport is against the side boundaries. Both heat throughput and the mean circulation (in geostrophic gyres, boundary currents and overturning) are reduced by geostrophic constraints.

Ablation of sloping ice faces into polar seawater

Publisher: Cambridge University Press (CUP)

Date: 28-01-2019

DOI: 10.1017/JFM.2018.970

Abstract: The effects of the slope of an ice–seawater interface on the mechanisms and rate of ablation of the ice by natural convection are examined using turbulence-resolving simulations. Solutions are obtained for ice slopes $\\unicode[STIX]{x1D703}=2^{\\circ }{-}90^{\\circ }$ , at a fixed ambient salinity and temperature, chosen to represent common Antarctic ocean conditions. For laminar boundary layers the ablation rate decreases with height, whereas in the turbulent regime the ablation rate is found to be height independent. The simulated laminar ablation rates scale with $(\\sin \\unicode[STIX]{x1D703})^{1/4}$ , whereas in the turbulent regime it follows a $(\\sin \\unicode[STIX]{x1D703})^{2/3}$ scaling, both consistent with the theoretical predictions developed here. The reduction in the ablation rate with shallower slopes arises as a result of the development of stable density stratification beneath the ice face, which reduces turbulent buoyancy fluxes to the ice. The turbulent kinetic energy budget of the flow shows that, for very steep slopes, both buoyancy and shear production are drivers of turbulence, whereas for shallower slopes shear production becomes the dominant mechanism for sustaining turbulence in the convective boundary layer.

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

Publisher: Cambridge University Press (CUP)

Date: 13-10-2017

DOI: 10.1017/JFM.2017.640

Abstract: 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 in idual 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 $Ra$ .

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

Publisher: Cambridge University Press (CUP)

Date: 15-06-2017

DOI: 10.1017/JFM.2017.249

Abstract: 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 $Ro ^{-1}$ , the convection is also observed to produce a set of large basin-scale gyres at all depths in the time-averaged flow.

Australian National University

Location: Australia

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