The Proceedings of the Eighth International Conference on Creationism (2018)

and temporal forms of artificial heat sink, in order to investigate possible ways of achieving the necessary cooling within biblical time scales. Accelerated plate motion defines the relationship between time and distance from the spreading centre in these cases; without this the predicted bathymetry would be hopelessly at odds with real ocean floor bathymetry. In this connection we note that in developing models of Catastrophic Plate Tectonics (or CPT, Austin et al. 1994), Baumgardner (2003) predicts maximum plate speeds measured in metres per second, about 9-10 orders of magnitude faster than present-day values. In this paper we ignore the possible impact of accelerated nuclear decay in order to address in isolation the problem of generating the earth’s oceanic lithosphere by cooling within the post-Flood period. The key observables from each modeling exercise are plate vertical shrinkage (manifested as bathymetry) and surface heat flow. Comparison of these with global field data then reveals whether the models we are analysing stand any chance of explaining, even at the crudest level, how ocean lithosphere could have formed in a short time. Even at the outset we make no claim to be able to solve the post-Flood ocean floor heat problem, nor to determine whether supernatural intervention is needed. Rather, we seek to define the key characteristics of cooling processes which could have produced today’s ocean floor bathymetry and heat flows within a biblically compatible time scale. In the following sections we describe the modeling procedure – model structure and parameters, and the physical processes represented in our models. We then describe the methods of solution, the issues raised by the presence of a thermal boundary layer, and the inclusion of plate motion. Our results are described in four sections – the uniformitarian case, accelerated thermal conduction, a uniform heat sink and a tailored heat sink. We then discuss specific issues arising from our results, viz. the enhanced thermal conduction hypothesis, the impact of the initial conditions, the role of the thermal boundary layer and suggestions for further work. This is followed by our conclusion. MODEL DESCRIPTION 1. Physical Parameters Our reference model, including the necessary physical parameter values, is that of Stein and Stein (1992), referred to as GDH1 (for global depth and heat flow). This is based on the earlier work of Parsons and Sclater (1977), whose main plate model is known as PSM. Stein and Stein used a much larger database than Parsons and Sclater and considered the effect of varying a number of input parameters used by Parsons and Sclater in order to optimize the fit of their model results to the available ocean floor heat flow and bathymetry data from the North Pacific and Northwest Atlantic; GDH1 is intended as a global reference model. The parameter values chosen by Stein and Stein, and also used here, are given in Table 1, which also includes their estimated margins of uncertainty. Although in reality the thermal conductivity and thermal expansion coefficient of the cooling lithosphere depend on temperature and pressure, for simplicity these are treated as constant both here and in the literature. The temperature at the surface is implicitly fixed at 0ºC. 2. Physical Processes The fundamental process modelled here is the conduction of heat through the bulk of the cooling lithosphere, into it at the base and out of it at the surface. Because of motion away from the spreading centre (mid-ocean ridge), the governing equation of energy flow includes both convective and diffusive terms. In practice temperature gradients in the spreading direction are much smaller than in the vertical direction such that horizontal heat flow, both convective and diffusive, can safely be neglected. The equation to be solved thus reduces to the one-dimensional time-dependent heat diffusion equation, viz. where T is temperature, t time, κ thermal diffusivity (≡ k / ρC p ), and z distance below the surface. The boundary conditions for plate models are fixed temperature, viz. T = T 0 at z =0 and T=T 1 at z=L , where L is the plate thickness. The initial condition is T=T 1 everywhere except at z =0; this introduces a singularity in the solution at z =0 , t =0. This does not cause any significant problems in the solution procedure for the long time scale model. For the short time scale calculations it does introduce problems related to mesh resolution and the occurrence of a near-surface thermal boundary layer; these are considered in the ‘Methods of solution’ section (part 3), the ‘Results’ section (part 4) and the ‘Discussion’ section (part 3). Because of the above decoupling of the heat diffusion process from the outward material motion, the solution to equation (1) at any Worraker and Ward ◀ Ocean floor cooling ▶ 2018 ICC 674 Parameter Symbol Value Units Notes Plate thickness L 95(±15) km PSM: 125(±10) Basal temperature T 1 1450(±250) ºC PSM: 1350(±275) Coefficient of thermal expansion α 3.1(±0.8)×10 -5 K -1 PSM: 3.2(±1.1)×10 -5 Specific heat C p 1171 J kg -1 K -1 Thermal Conductivity k 3.138 W m -1 K -1 Mantle density ρ m 3330 kg m -3 Water density ρ w 1000 kg m -3 Ridge depth d R 2.6 km PSM: 2.5 Table 1. Model parameter values used by Stein and Stein (1992) in their GDH1 model and in the baseline model employed here. PSM refers to the values used by Parsons and Sclater (1977). The figures prefixed by ± are the 1σ uncertainty margins estimated by the respective authors.