Transport and fluxes of atmospheric models deduced from laboratory data

Isaac M. Held writes in his introduction of the book by Schneider and Sobel (2007) "A theory for the general circulation of the atmosphere has at its core a theory for the quasi-horizontal eddy fluxes of energy, angular momentum, and water vapor by the macro-turbulence of the troposphere." An analog of this atmospheric macro-turbulence can be studied by using data from the differentially heated rotating annulus laboratory experiment (e.g. Fowlis and Hide, 1965). From simultaneous measurements of surface temperature and horizontal flow it is possible to study elementary structures of Lagrangian tracer fluxes (Agaoglou, 2024) as well as eddy fluxes of heat and momentum. In a fluid layer, the three fluxes for PV, momentum M, and heat  T are connected via the Margules equation PV=∂M/∂y + f/H T. Here y is the north-south direction, f is the Coriolis parameter and H the layer depth. From our data we are able to compute all three fluxes and it is instructive to compare the results with fluxes from simplified models. E.g., in the Eady model T does not depend on z and we can thus obtain the total heat flux from this model using the surface data. Moreover, since M is zero for the Eady model, the PV flux is proportional to the heat flux. Using an even simpler model, the surface geostrophic approximation, we can deduce the flow from the temperature field alone. However, this model does not have the correct phase difference between the velocity and the temperature field and gives a wrong mean heat flux. Applying a phase difference such that the heat flux becomes comparable to the one from the Eady model allows to estimate the vertical flow structure from the temperature field alone. The result might be helpful for the construction of flow fields from satellite sea surface temperature data (LaCasce and Mahadevan, 2006).  

M. Agaoglou and V. J. García-Garrido and U. Harlander and A. M. Mancho (2024) Building transport models from baroclinic wave experimental data, Physics of Fluids, in press.

W. W. Fowlis and R. Hide (1965) Thermal convection in a rotating annulus of liquid: effect of viscosity on the transition between axisymmetric and non-axisymmetric flow regimes, J. Atmos. Sci., 22, 541-558.
 
J. H. LaCasce and A. Mahadevan (2006) Estimating subsurface horizontal and vertical velocities from sea-surface temperature, Journal of Marine Research 64, 695–721.
    
T. Schneider and A. H. Sobel (Eds.) (2007) The Global Circulation of the Atmosphere, Princeton University Press.