Abstract. The concept of topographic steady state has substantially informed our understanding of the relationships between landscapes, tectonics, climate, and lithology. In topographic steady state, erosion rates are equal everywhere, and steepness adjusts to enable equal erosion rates in rocks of different strengths. This conceptual model makes an implicit assumption of vertical contacts between different rock types. Here we hypothesize that landscapes in layered rocks will be driven toward a state of erosional continuity, where retreat rates on either side of a contact are equal in a direction parallel to the contact rather than in the vertical direction. For vertical contacts, erosional continuity is the same as topographic steady state, whereas for horizontal contacts it is equivalent to equal rates of horizontal retreat on either side of a rock contact. Using analytical solutions and numerical simulations, we show that erosional continuity predicts the form of flux steady-state landscapes that develop in simulations with horizontally layered rocks. For stream power erosion, the nature of continuity steady state depends on the exponent, n, in the erosion model. For n = 1, the landscape cannot maintain continuity. For cases where n ≠ 1, continuity is maintained, and steepness is a function of erodibility that is predicted by the theory. The landscape in continuity steady state can be quite different from that predicted by topographic steady state. For n < 1 continuity predicts that channels incising subhorizontal layers will be steeper in the weaker rock layers. For subhorizontal layered rocks with different erodibilities, continuity also predicts larger slope contrasts than in topographic steady state. Therefore, the relationship between steepness and erodibility within a sequence of layered rocks is a function of contact dip. For the subhorizontal limit, the history of layers exposed at base level also influences the steepness–erodibility relationship. If uplift rate is constant, continuity steady state is perturbed near base level, but these perturbations decay rapidly if there is a substantial contrast in erodibility. Though examples explored here utilize the stream power erosion model, continuity steady state provides a general mathematical tool that may also be useful to understand landscapes that develop by other erosion processes.
IzvlečekUDK 551.44:53 Matthew D. Covington & Matija Perne: Vzemimo valjasto jamo: pogled fizika na znanost o jamah in krasu V članku pregledava trenutno poznavanje fizike jam in krasa. Pri tem se osredotočava na raziskave, ki so razumevanje kraških procesov poglobile z uporabo preprostih modelov na osnovi fizike. Obravnavava vedenje jamskega ozračja, transport v kraških kanalih in modele nastanka jam ter povezanih procesov. Izpostavljava sodobna dognanja na teh področjih in iščeva obetavne teme za nadaljnje raziskave. Po najinem mnenju so mnoga med bolj privlačnimi odprtimi vprašanji povezana z medsebojnim vplivom med obravnavanimi tremi skupinami procesov. AbstractUDC 551.44:53 Matthew D. Covington & Matija Perne: Consider a cylindrical cave: A physicist's view of cave and karst scienceWe review the current understanding of the physics of caves and karst. Our review focuses on research that has used simple physically based models to improve understanding of processes that occur in karst. The topics we cover include cave atmosphere dynamics, transport within karst conduits, and models of speleogenesis and related processes. We highlight recent advances in these subjects and attempt to identify promising areas for future work. In our judgment, many of the most intriguing open questions relate to the interactions between these three groups of processes.
Abstract. Water temperature is a non-conservative tracer in the environment. Variations in recharge temperature are damped and retarded as water moves through an aquifer due to heat exchange between water and rock. However, within karst aquifers, seasonal and short-term fluctuations in recharge temperature are often transmitted over long distances before they are fully damped. Using analytical solutions and numerical simulations, we develop relationships that describe the effect of flow path properties, flow-through time, recharge characteristics, and water and rock physical properties on the damping and retardation of thermal peaks/troughs in karst conduits. Using these relationships, one can estimate the thermal retardation and damping that would occur under given conditions with a given conduit geometry. Ultimately, these relationships can be used with thermal damping and retardation field data to estimate parameters such as conduit diameter. We also examine sets of numerical simulations where we relax some of the assumptions used to develop these relationships, testing the effects of variable diameter, variable velocity, open channels, and recharge shape on thermal damping and retardation to provide some constraints on uncertainty. Finally, we discuss a multitracer experiment that provides some field confirmation of our relationships. High temporal resolution water temperature data are required to obtain sufficient constraints on the magnitude and timing of thermal peaks and troughs in order to take full advantage of water temperature as a tracer.
Condensation of water from warm, humid air to cold rock walls in caves is regarded to play a significant role in speleogenesis. The water condensing to the cave walls quickly attains equilibrium with the carbon dioxide in the surrounding air, and consequently dissolves limestone or gypsum forming various types of macro-,meso-, and micromorphologies. In this paper we present the basic physical principles of condensation and give equations, which allow a satisfactory estimation of condensation rates. Water condensing to a cooler wall releases heat of condensation, which raises the temperature of the wall thus reducing the temperature difference ΔT between the warm air and the cave wall. Furthermore one has to take into account the heat flux from the air to the cave wall. This defines the boundary conditions for the equation of heat conduction. For a constant temperature of the air initial condensation rates are high but then drop down rapidly by orders of magnitude during the first few days. Finally constant condensation rates are attained, when the heat flux into the rock is fully transmitted to the surface of the karst plateau. For spherical and cylindrical conduits these can be obtained as a function of the depth Z below the surface. When diurnal or seasonal variations of the air temperature are active as is the case close to cave entrances, condensation rates can become quite significant, up to about 10 -6 m/year. The theoretical results are applied also to corrosion of speleothems and the formation of »röhrenkarren« as described by Simms (2003). To convert condensation rates into retreat of bedrock the saturation state of the solution must be known. In the appendix we present experiments, which prove that in any case the solution flowing off the rock is saturated with respect to limestone or gypsum, respectively.. O speleogenetskem pomenu vode, ki iz toplega vlažnega zraka kondenzira na hladne jamske stene je napisanega veliko. Kondenzirana voda se hitro uravnoteži z ogljikovem dioksidom v jamski atmosferi, zato raztaplja apnenec in pri tem tvori različne skalne oblike. V članku predstavimo fizikalne osnove in podamo enačbe, ki omogočajo približno oceno hitrosti kondenzacije v različnih pogojih. Zaradi kondenzacijske toplote in prenosa toplote iz zraka na steno, se temperatura stene viša, pri čemer se zmanjšuje razlika temperature med zrakom in steno. To predstavlja robni pogoj za prevajanje toplote iz jame. Pri konstantni temperaturi zraka, hitrost kondenzacije v nekaj dneh pade za več velikostnih redov, dokler ne doseže končne vrednosti, pri kateri se ves toplotni tok prenese na površje. Slednjo za primer krogelnih in valjastih prostorov opišemo kot funkcijo globine rova Z. Pri dnevnih in sezonskih spemembah temperature, značilnih v bližini jamskih vhodov, je hitrost kondenzacije in posledično korozije do 1μm na leto. Teoretične rezultate uporabimo tudi za izračun korozije kapnikov in tipa škrapelj (röhrenkarren), ki jih opisuje Simms (2003). Za pretvorbo hitrosti kondenzacije v hitrost korozije, potrebujemo...
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