The growth of point source plumes at Rayleigh numbers up to 108 and Prandtl numbers up to 1000

Two-dimensional numerical simulations were conducted of the growth of thermal plumes from a point heat source at Rayleigh numbers up to 108 and Prandtl numbers up to 1000. Scaling the convection equations by the free fall velocity rather than the thermal diffusivity, increased the Prandtl number range available to numerical simulation by one order of magnitude from Prandtl number 100 to 1000. We present animations showing how the plumes grow with time for different Prandtl numbers. Plumes with Prandtl numbers around 7 (water) were found to be unstable to sinuous instabilities; whereas those at Prandtl numbers of 1000 had straight stems and fewer sinuous instabilities. Wavelet analysis was used to analyze the scales at which plumes initiated, and the scales at which sinuous instabilities occurred. The scale of both the plume structures and instabilities was found to decrease with Prandtl number.     

How flat is the lower-mantle temperature gradient?

The temperature gradient in the lower mantle is fundamental in prescribing many transport properties, such as the viscosity, thermal conductivity and electrical conductivity. The adiabatic temperature gradient is commonly employed for estimating these transport properties in the lower mantle. We have carried out a series of high-resolution 3-D anelastic compressible convections in a spherical shell with the PREM seismic model as the background density and bulk modulus and the thermal expansivity decreasing with depth. Our purpose was to assess how close under realistic conditions the horizontally averaged thermal gradient would lie to the adiabatic gradient derived from the convection model. These models all have an endothermic phase change at 660 km depth with a Clapeyron slope of around −3 MPa K⁻¹, uniform internal heating and a viscosity increase of 30 across the phase transition. The global Rayleigh number for basal heating is around 2×10⁶, while an internal heating Rayleigh number as high as 10⁸ has been employed. The pattern of convection is generally partially layered with a jump of the geotherm across the phase change of at most 300 K. In all thermally equilibrated situations the geothermal gradients in the lower mantle are small, around 0.1 K km⁻¹, and are subadiabatic. Such a low gradient would produce a high peak in the lower-mantle viscosity, if the temperature is substituted into a recently proposed rheological law in the lower mantle. Although the endothermic phase transition may only cause partial layering in the present-day mantle, its presence can exert a profound influence on the state of adiabaticity over the entire mantle.     

Modeling and Visualization of Tsunamis

Modeling tsunami wave propagation is a very challenging numerical task, because it involves many facets: Such as the formation of various types of waves and the impingement of these waves on the coast. We will discuss the different levels of approximations made in numerical modeling of 2-D and 3-D tsunami waves and their relative difficulties. In this paper new attempts are proposed to evaluate the hazards of tsunami’s and visualization of large-scale numerical results generated from tsunami simulations. Specialized low-level computer language, based on a parallel computing environment, is also employed here for generating FORTRAN source code for finite elements. This code can then be run very efficiently in parallel on distributed computing systems. We will also discuss the need to study tsunami waves with modern software and visualization hardware.     

Landslides, Ice Quakes, Earthquakes: A Thermodynamic Approach to Surface Instabilities

The total rate of rock deformation results from competing deformation processes, including ductile and brittle mechanisms. Particular deformation styles arise from the dominance of certain mechanisms over others at different ambient conditions. Surprisingly, rates of deformation in naturally deformed rocks are found to cluster around two extremes, representing coseismic slip rates or viscous creep rates. Classical rock mechanics is traditionally used to interpret these instabilities. These approaches consider the principle of conservation of energy. We propose to go one step further and introduce a nonlinear far-from-equilibrium thermodynamic approach in which the central and explicit role of entropy controls instabilities. We also show how this quantity might be calculated for complex crustal systems. This approach provides strain-rate partitioning for natural deformation processes occurring at rates in the order of 10^-3 to 10^-9 s^-1. We discuss these processes using examples of landslides and ice quakes or glacial surges. We will then illustrate how the mechanical mechanisms derived from these near-surface processes can be applied to deformation near the base of the seismogenic crust, especially to the phenomenon of slow earthquakes.     

Ice Storm ’98 in Southcentral Canada and Northeastern United States: A Climatological Perspective

Summary Dubbed Ice Storm ’98, an extreme weather event characterized by two synoptic systems in succession dropped about 70–100 mm (in terms of water equivalent) of freezing precipitation over southeastern Ontario, southwestern Quebec and northeastern New York during a 6-day period from January 5 to 10 in 1998. Individually, the two synoptic systems were not dramatically more extreme in freezing precipitation than other major freezing rain events (4 since 1961) which occurred in the past over the affected area. Some regions in the target area, however, were impacted more by the second system. Based on an analysis of the 500 hPa vorticity field during the ’98 event, we suggest that the 1997/98 El Ni?o had a role in creating a flow environment conducive to the rapid formation of the second synoptic system. In contrast, other major freezing rain events in the last 30 years involved only one synoptic system per event lasting no more than 3 days, and producing 20–50 mm of precipitation. We have also found that, 3 out of 4 past major freezing rain events since 1958 were associated with the positive phase of the North Atlantic Oscillation (NAO). Consistent with this usual past association between the NAO and a major freezing rain event, Ice Storm ’98 also occurred when the phase of the NAO was positive. Analysis of these 3 past and the ’98 events also indicates an apparent connection between the positive phase of the NAO and the northern Quebec high pressure system, which is an essential synoptic feature of a major freezing rain occurrence over the southcentral region of Canada. As measured by their respective indices, the maximum positive NAO state leads the maximum northern Quebec high by about 2 days (5 days in the ’98 event). There is some suggestive evidence to indicate that the persistence of the northern Quebec high pressure system is connected to the persistence of the positive phase of the NAO. Received January 17, 2000     

Modeling of Rapidly Rotating Thermal Convection Using Vorticity and Vector Potential

We have used a numerical scheme based on higher-order finite differences to investigate effects of adiabatic heating and viscous dissipation on 3-D rapidly rotating thermal convection in a Cartesian box with an aspect-ratio of 221. Although we omitted coupling with the magnetic field, which can play a key role in the dynamics of the Earth's core, the understanding of non-linear rotating convection including realistic thermodynamic effects is a necessary prerequisite for understanding the full complexity of the Earth's core dynamics. The system of coupled partial differential equations has been solved in terms of the principal variables vorticity , vector potential A and temperature T. The use of the vector potential A allows the velocity field to be calculated with one spatial differentiation in contrast to the spheroidal and toroidal function approach. The temporal evolution is governed by a coupled time-dependent system consisting of and T. The equations are discretized in all directions by using an eighth-order, variable spaced scheme. Rayleigh number Ra of 10⁶, Taylor number Ta of 10⁸ and a Prandtl number Pr of 1 have been employed. The dissipation number of the outer core was taken to be 0.2. A stretched grid has been employed in the vertical direction for resolving the thin shear boundary layers at the top and bottom. This vertical resolution corresponds to around 240 regularly spaced points with an eighth-order accuracy. For the regime appropriate to the Earth's outer core, the dimensionless surface temperature T ₀ takes a large value, around 4. This large value in the adiabatic heating/cooling term is found to cause stabilization of both the temperature and velocity fields.