CHARACTERIZATION OF MANTLE CONVECTION EXPERIMENTS USING 2-POINT CORRELATION-FUNCTIONS

Snapshots of the temperature T(r,phi,t), horizontal flow velocity u(r, phi,t), and radial flow velocity w(r,phi,r) obtained from numerical co nvection experiments of time-dependent flows in annular cylindrical ge ometry are taken to be samples of stationary, rotationally invariant r andom fields. For such a field f(r,phi,t), the spatio-temporal two-poi nt correlation function, C-ff(r,r',Delta,t), is constructed by averag ing over rotational transformations of this ensemble, To assess the st ructural differences among mantle convection experiments we construct three spatial subfunctions of C-ff(r,r',Delta,t): the rms variation, phi(f)(r) correlaton function R(f)(r,r'), and the angular correlation function, A(f)(r,Delta). R(f)(r,r') and A(f)(r,Delta) are symmetric ab out the loci r = r' and Delta = 0, respectively where they achieve the ir maximum value of unity. The falloff of R(f) and A(f) away from thei r symmetry axes can be quantified by a correlation length rho(f)(r) an d a correlation angle alpha(f)(r),which we define to be the half width s of the central peaks at the correlation level 0.75. The behavior of rho(f) is a diagnostic of radial structure, while alpha(f) measures av erage plume width. We have used two-point correlation functions of the temperature field (T-diagnostics) and flow velocity fields (V-diagnos tics) to quantify some important aspects of mantle convection experime nts. We explore the dependence of different correlation diagnostics on Rayleigh number, internal heating rate, and depth- and temperature-de pendent viscosity. For isoviscous flows in an annulus, we show how rad ial averages of sigma(T), rho T,and alpha(T) scale with Rayleigh numbe r for various internal heating rates, A break in the power-law relatio nship at the transition from steady to lime dependent regimes is evide nt for rho(T) and alpha(T) but not for sigma(T) or the Nusselt number. A rapid tenfold to thirtyfold viscosity increase with depth yields we akly stratified flows, quantified by sigma(w), which is a measure of r adial flux. The horizontal flux diagnostic, sigma(u), reveals that the flow organization is sensitive to the depth of the viscosity increase . A jump at middepth induces a significant horizontal return flow at t he base of the upper layer, absent in models with a jump at quarter-de pth. We illustrate that T-diagnostics, which are more easily relatable to geophysical observables, can serve as proxies for the V-diagnostic s. A viscosity increase with depth is evident as an increase in the T- diagnostics in the high-viscosity region. For numerical experiments wi th a temperature-dependent rheology we employ a mobilization scheme fo r the upper boundary layer. Temperature dependence does not appreciabl y perturb the sigma-diagnostics or alpha(T) in the convecting interior . Changes in the radial correlation length are twofold. First, the gre ater viscosity of cold downwellings leads to an increase in height and width of the radial correlation maximum near the top. Second, the inc rease in rho(T) associated with a viscosity jump is markedly reduced. The latter effect can be explained by weaker, less stationary hot upwe llings, mobilized by the temperature-dependent theology and disrupted by the cold, high-viscosity downwellings.