Heat Flux Partitioning in Open-Ocean Convection

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  • 1 Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada
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Abstract

Cold air blowing out over a warm ocean leads to convection over an isolated region of the ocean basin. This phenomenon, known as open-ocean convection, is often simulated by convective forcing from a circular disk much smaller than the dimension of the domain. An important feature of these simulations is the development of eddies at the edge of the disk that serve to transport heat horizontally. This has sparked interest in the heat-flux characteristics of such a system.

This paper deals with the thermodynamic properties of this type of convective flow, using a rotating tank with bottom-mounted hotplate as the experimental apparatus. Experiments are performed, in an initially unstratified fluid, for a set of values of the nondimensional forcing parameter Rc = B1/2/(Hf3/2), where B is the buoyancy flux, H is the fluid depth, and f is the Coriolis parameter. The ratio of the frontal eddy size to the hotplate radius, ε, is shown to be an important parameter. The experiments reported are for the regime ε ∼ O(1), consistent with those of other researchers. The author shows that ε ≪ 1 is the more relevant case oceanographically, a fact that is likely more important thermodynamically than dynamically. The evolution of the mean temperature (difference) above the heating region is determined, from which can he deduced the vertical/horizontal heat flux partitioning as a function of time and Rc.

The average behavior of the mean temperature field () above the plate follows a relation: (t) = Te tanh(t/τ), where t is time and Te and τ are functions of Rc. The nondimensional adjustment timescale is found to be τf = 4.27 Rc−2/3, which implies that the dimensional timescale τ is, remarkably, independent of the rotation rate. The equilibrium temperature scale Te, expressed as a buoyancy deficit and nondimensionalized, is well described by gαTe/H1/3 = (4.67) Rc−0.075 and is thus also effectively independent of f.

A heton-type model for the mean temperature field is developed with (t) as solution to its associated differential equation. The physical model, the differential equation, plus the (determined) properties of its solution constitute a parameterized thermodynamic model of this form of convection with potential use in meso-scale ocean climate models. Ideas are presented on how this could be done.

Abstract

Cold air blowing out over a warm ocean leads to convection over an isolated region of the ocean basin. This phenomenon, known as open-ocean convection, is often simulated by convective forcing from a circular disk much smaller than the dimension of the domain. An important feature of these simulations is the development of eddies at the edge of the disk that serve to transport heat horizontally. This has sparked interest in the heat-flux characteristics of such a system.

This paper deals with the thermodynamic properties of this type of convective flow, using a rotating tank with bottom-mounted hotplate as the experimental apparatus. Experiments are performed, in an initially unstratified fluid, for a set of values of the nondimensional forcing parameter Rc = B1/2/(Hf3/2), where B is the buoyancy flux, H is the fluid depth, and f is the Coriolis parameter. The ratio of the frontal eddy size to the hotplate radius, ε, is shown to be an important parameter. The experiments reported are for the regime ε ∼ O(1), consistent with those of other researchers. The author shows that ε ≪ 1 is the more relevant case oceanographically, a fact that is likely more important thermodynamically than dynamically. The evolution of the mean temperature (difference) above the heating region is determined, from which can he deduced the vertical/horizontal heat flux partitioning as a function of time and Rc.

The average behavior of the mean temperature field () above the plate follows a relation: (t) = Te tanh(t/τ), where t is time and Te and τ are functions of Rc. The nondimensional adjustment timescale is found to be τf = 4.27 Rc−2/3, which implies that the dimensional timescale τ is, remarkably, independent of the rotation rate. The equilibrium temperature scale Te, expressed as a buoyancy deficit and nondimensionalized, is well described by gαTe/H1/3 = (4.67) Rc−0.075 and is thus also effectively independent of f.

A heton-type model for the mean temperature field is developed with (t) as solution to its associated differential equation. The physical model, the differential equation, plus the (determined) properties of its solution constitute a parameterized thermodynamic model of this form of convection with potential use in meso-scale ocean climate models. Ideas are presented on how this could be done.

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