Flow in a rock-fracture network: The permeability of fractured rock is largely controlled by the geometry and "connectivity" of the fractures. Describing flow within a fracture network requires applying principles of conservation of mass to each fracture to account for this connectivity — an approach that is quite different from traditional descriptions of flow in geological porous media based on Darcy’s Law.
Glacier hypsometry and response to climate change: The areal distribution of a glacier over elevation strongly influences its response — the magnitude of advance or retreat — to changes in climate. Describing this response requires considering where mass is exchanged across the glacier surface in relation to its changing hypsometry.
Bubble over-pressurization in magma chambers: It has been suggested that the growth and ascent of bubbles in a magma chamber can have the effect of pressurizing the magma, possibly leading to eruption. Describing this behavior requires taking into account bubble growth and magma chamber geometry.
Geyser/volcanic jet behavior: Considerable attention has been given to estimating flow speeds of geological "jets" — for example the Old Faithful geyser and the Mt. Saint Helens eruptions. Significant insight about these eruptions can be gained by straightforward applications of conservation of mass and energy.
Hillslope diffusion by soil creep: The long-term evolution of a hillslope whose soil is transported by "creep" can be described as a diffusion process. This opens the possibility of "dating" fault scarps or river terraces based on the amount of geomorphic degradation of these landforms.
Landslide run-out distance: Landslide-hazard mapping involves assessing the likely distances that landslides will travel downslope after failure. This distance is a function of land-surface steepness and geometry, landslide size, and detrainment of landslide material by friction during motion.
Calcite crystal growth/dissolution: Experiments suggest that calcite (CaCO3) crystals immersed in a water-CO2 solution dissolve at rates that vary with the degree of saturation with respect to Ca. Describing this dissolution process requires accounting for changing crystal size and solution chemistry, and associated changes in the rate of dissolution.
Algae-zooplankton interactions in a river/lake/estuary: Under the right conditions, algae reproduce fast. Zooplankton, which eat algae, reproduce at rates depending on algae abundance. Meanwhile, algae and zooplankton are transported by flow, and also undergo settling. Thus, the distribution of algae and zooplankton over space and time can be complex. To characterize this behavior involves applying principles of conservation to algae and zooplankton biomass, accounting for their interactions.
Flow/cooling of magma in a dike/sill: It is well known that the size of crystals in a solidified dike or sill partly depends on the rate of cooling/solidification. But how long does cooling take? A scaling analysis indicates that this depends on the magma geometry and thermal conductivity of the country rock. (Incidently, the viscosity of basaltic magma is about the same as that of ordinary hair shampoo!)
Lake hypsometry and response to weather: The water level in a lake responds to river and groundwater inflows/outflows, and to weather (precipitation and evaporation). But it also depends on the geometry of the lake basin. In turn, groundwater inflows/outflows and evaporation may depend on water level, which constitutes a system "feedback." This means that lakes with disparate geometries may respond differently to changes in weather.
Fracture enlargement by CaCO3 dissolution: It is believed that the initial growth of limestone caves starts with enlargement of fractures through dissolution by natural, weak acids such as carbonic acid (H2CO3). The source of CO2 (to produce carbonic acid) is provided by the atmosphere, and by microbial respiration in soils. A possible additional, but unexplored, source of CO2 may be provided by bacteria residing in the groundwater/fracture system. How might bacteria figure into the process of fracture enlargement by dissolution?
Temperature profiles in ice sheets: It has been suggested that vertical temperature profiles in ice sheets might provide a record of previous climate (temperature) conditions at their surfaces. Testing whether this idea is feasible involves accounting for the heat energy that is added to the surface with snow versus diffusion of heat upward and downward within the ice.
Transport of radionuclides in groundwater: Tritium ("heavy water") releases into the atmosphere from bomb testing during the 1950's and 1960's produced an important groundwater "tracer." Such radionuclide tracers open the possibility of assigning "ages" to ground water (the time at which precipitation entered a groundwater system); but doing so correctly requires accounting for transport of the radionuclide, and its radioactive decay, simultaneously.
The analogy between Ohms Law and Darcy’s Law: Groundwater flow perpendicular to sedimentary bedding obeys a rule that is remarkably similar to that governing the flow of electricity through a set of resistors in series; and water flow parallel to bedding is remarkably similar to the flow of electricity through a set of resistors in parallel. This behavior, deriving from conservation of mass, provides a clear explanation why sedimentary materials typically exhibit horizontal permeabilities that are larger than vertical permeabilities.
Other: Why do some petroleum fields become highly pressurized? How quickly do deep-sea sediments become compacted? What conditions lead to landslides? Why do Mississippi River floods that wreak havoc in the mid-west have only limited impact near New Orleans? What is the origin of submarine meanders and levees on the delta fan of the Amazon River? Why do salmon lay their eggs specifically on the downstream ends of pools in rivers? Why do liquid drops form on spider webs, beneath a slowly running faucet, and with the spewing of erupting magma?
