scholarly journals Analytical long-profile models of coupled glacier-fluvial systems

2020 ◽  
Author(s):  
Eric Deal ◽  
Günther Prasicek
Keyword(s):  
Steady State ◽  
Steady State Solution ◽  
Climatic Conditions ◽  
Tectonic Geomorphology ◽  
Uplift Rate ◽  
Equilibrium Line Altitude ◽  
Glacial Erosion ◽  
Deep Time ◽  
Fluvial Systems ◽  
Uplift Rates

<p>Glaciers are an effective agent of erosion and landscape evolution, capable of driving high rates of erosion and sediment production. Glacial erosion is therefore an important process mediating the effect of climate on erosion rates and tectonics. Further, as a source of sediment, glacial erosion also has implications for the carbon and silicate cycles, with the potential for longterm feedbacks.  Understanding the interaction of climate, tectonics, glacial erosion and topography will lead to more insight into how glaciers can impact these processes. Simple, analytical long-profile models of fluvial incision are fundamental in tectonic geomorphology and critical for addressing fluvial analogues of problems such as those posed above. The advantage of these simple long-profile models is that they can be applied when information about forcing and boundary conditions is minimal (e.g. in deep time), and they can aid in the development of intuition about how such systems respond in general to different forcing. While models of glacial erosion have existed for quite some time, they tend to be complicated and computationally expensive. Currently, analytical long-profile models do not exist for glacial systems. At the same time, the patterns of glacial erosion and sediment transport, and how these processes respond to climate is fundamentally different than fluvial systems, and cannot be addressed properly with purely fluvial models.</p><p>Building on previous work, we introduce several simplifications to make the equations for coupled glacier-fluvial long-profile models easier to use and show that these simplifications have minimal effect on the steady state solution. We then use these new equations to develop an analytical solution for glacier-fluvial long-profiles at erosional steady state. The solution provides glacier geometry, including length and slope, ice thickness, and overall orogen relief for a given uplift rate, rock erodibility, profile length and climatic conditions. To explore the effect of glaciation on the balance between climate, erosion and orogen geometry, we integrate this solution into a critical wedge orogen theory. We find that the total orogen relief should be closely tied to the equilibrium line altitude (ELA), in line with the glacial buzzsaw theory. In addition, our theory predicts that the geometry and average uplift rate of glaciated critical wedge orogens respond more sensitively to changes in climate than those dominated by fluvial erosion. We suggest that the lowered ELA during glacial maxima over the last few million years could have triggered narrowing of critical orogens, with an associated increase in uplift rates within the active orogen core. </p>

scholarly journals Glacial limitation of tropical mountain height

2019 ◽  
Vol 7 (1) ◽  
pp. 147-169 ◽  
Author(s):  
Maxwell T. Cunningham ◽  
Colin P. Stark ◽  
Michael R. Kaplan ◽  
Joerg M. Schaefer
Keyword(s):  
Steady State ◽  
Mountain Range ◽  
Equilibrium Line Altitude ◽  
Glacial Erosion ◽  
Tropical Mountains ◽  
Base Level ◽  
Snow Line ◽  
Bedrock River Incision ◽  
High Tropical Mountains ◽  
The Tropics

Abstract. Absent glacial erosion, mountain range height is limited by the rate of bedrock river incision and is thought to asymptote to a steady-state elevation as erosion and rock uplift rates converge. For glaciated mountains, there is evidence that range height is limited by glacial erosion rates, which vary cyclically with glaciations. The strongest evidence for glacial limitation is at midlatitudes, where range-scale hypsometric maxima (modal elevations) lie within the bounds of Late Pleistocene snow line variation. In the tropics, where mountain glaciation is sparse, range elevation is generally considered to be fluvially limited and glacial limitation is discounted. Here we present topographic evidence to the contrary. By applying both old and new methods of hypsometric analysis to high mountains in the tropics, we show that (a) the majority are subject to glacial erosion linked to a perched base level set by the snow line or equilibrium line altitude (ELA) and (b) many truncate through glacial erosion towards the cold-phase ELA. Evaluation of the hypsometric analyses at two field sites where glacial limitation is seemingly marginal reveals how glaciofluvial processes act in tandem to accelerate erosion near the cold-phase ELA during warm phases and to reduce their preservation potential. We conclude that glacial erosion truncates high tropical mountains on a cyclic basis: zones of glacial erosion expand during cold periods and contract during warm periods as fluvially driven escarpments encroach and destroy evidence of glacial action. The inherent disequilibrium of this glaciofluvial limitation complicates the concept of time-averaged erosional steady state, making it meaningful only on long timescales far exceeding the interval between major glaciations.

Alpine relief limited by glacial occupation time

Geology ◽  
2021 ◽  
Author(s):  
Bernhard Salcher ◽  
Günther Prasicek ◽  
Sebastian Baumann ◽  
Florian Kober
Keyword(s):  
Feedback Loop ◽  
Occupation Time ◽  
Central Alps ◽  
Key Factors ◽  
Equilibrium Line Altitude ◽  
Glacial Erosion ◽  
Cumulative Impact ◽  
Uplift Rates ◽  
Steep Slopes ◽  
Topographic Relief

Glaciers exert a major control on the shape of mountain topography. They tend to reduce relief above and scour troughs below the equilibrium line altitude (ELA). While many studies report this dichotomy, relief-limiting effects are controversial due to difficulties in quantifying key factors such as the initial topography, the timing of glacial occupancy, or rock uplift counteracting glacial erosion. Consequently, effectivity and degree of glacial erosion remain ambiguous. In geologically and climatically well-investigated parts of the European Central Alps, our calculation of glacial occupation time (GOT) from Quaternary ELA variations allows the quantification of gradual topographic modifications generated by the cumulative impact of cirque erosion over the Quaternary. We show that under low uplift, relief is effectively limited by glacial and periglacial headwall retreat, leading to a decline in topographic relief as GOT increases. Conversely, higher uplift rates seem to induce more persistent valley glaciation, triggering a positive feedback loop in which steep slopes are protected against erosion and relief increases.

scholarly journals Effect of rock uplift and Milankovitch timescale variations in precipitation and vegetation cover on catchment erosion rates

2021 ◽  
Author(s):  
Hemanti Sharma ◽  
Todd A. Ehlers ◽  
Christoph Glotzbach ◽  
Manuel Schmid ◽  
Katja Tielbörger
Keyword(s):  
Vegetation Cover ◽  
Vegetation Change ◽  
Transient State ◽  
Climatic Conditions ◽  
Sediment Flux ◽  
Uplift Rate ◽  
Erosion Rates ◽  
Uplift Rates ◽  
Phase Lags ◽  
Climate Forcings

Abstract. Catchment erosion and sedimentation are influenced by variations in the rates of rock uplift (tectonics), and periodic fluctuations in climate and vegetation cover. In this study we applied the Landlab-SPACE landscape evolution modelling approach. This study focuses on quantifying the effects changing climate and vegetation on erosion and sedimentation over distinct climate-vegetation settings. As catchment evolution is subjected to tectonic and climate forcings at millennial to million-year time-scales, the simulations are performed over different tectonic scenarios and periodicities of climate-vegetation change. We present a series of generalized experiments that explore the sensitivity of catchment hillslope and fluvial erosion and sedimentation for different rock uplift rates (0.05 mm a−1, 0.1 mm a−1, 0.2 mm a−1) and Milankovitch climate periodicities (23 kyr, 41 kyr and 100 kyr). Model inputs were parameterized for two different climate and vegetation conditions at two sites in the Chilean Coastal Cordillera at ~26° S (arid and sparsely vegetated) and ~33° S (mediterranean). For each setting, steady state topographies were produced for each uplift rate before introducing periodic variations in precipitation and vegetation cover. Following this, the sensitivity of these landscapes was analysed for 3 Myr in a transient state. Results suggest that regardless of the uplift rate, transients in precipitation and vegetation cover resulted in transients in erosion rates in the direction of change in precipitation and vegetation. While the transients in sedimentation were observed to be in the opposite direction of change in the precipitation and vegetation cover, with phase lags of ~1.5–2.5 kyr. These phase lags can be attributed to the changes in plant functional type (PFT) distribution induced by the changes in climatic conditions, which is beyond the scope of this study. These effects being most pronounced over longer period changes (100 kyr) and higher rock uplift rates (0.2 mm yr−1). This holds true for both vegetation and climate settings. Furthermore, transient changes in catchment erosion due to varying vegetation and precipitation were between ~35 %–110 % of the background (rock uplift) rate and are measureable with some techniques (e.g. sediment flux histories, cosmogenic nuclides). Taken together, we find that vegetation-dependent erosion and sedimentation are influenced by Milankovitch timescale changes in climate, but that these transient changes are superimposed upon tectonically driven rates of rock uplift.

Compatibility and Uniqueness Analyses of Steady State Solution for Multi-variable Predictive Control Systems

2014 ◽  
Vol 39 (5) ◽  
pp. 519-529 ◽  
Author(s):  
Tao ZOU ◽  
Hai-Qiang LI ◽  
Bao-Cang DING ◽  
Ding-Ding WANG
Keyword(s):  
Steady State ◽  
Control Systems ◽  
Predictive Control ◽  
Steady State Solution ◽  
State Solution

An airfoil theory of bifurcating laminar separation from thin obstacles

1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Steady State ◽  
Steady State Solution ◽  
Equation System ◽  
Branch Points ◽  
Laminar Separation ◽  
Kutta Condition ◽  
Numerical Studies ◽  
Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

Dependency of Unsteady Time-Linearized Flutter Investigations on the Steady State Flow Field

2011 ◽  
Author(s):  
Michael Blocher ◽  
Markus May ◽  
Harald Schoenenborn
Keyword(s):  
Steady State ◽  
Steady State Solution ◽  
Elastic Stability ◽  
Compressor Cascade ◽  
Steady State Flow ◽  
State Flow ◽  
Flow Parameters ◽  
Pressure Distributions ◽  
German Aerospace ◽  
École Polytechnique

The influence of the steady state flow solution on the aero-elastic stability behaviour of an annular compressor cascade shall be studied in order to determine sensitivities of the aero-dynamic damping with respect to characteristic flow parameters. In this context two different flow regimes — a subsonic and a transonic case — are subject to the analysis. The pressure distributions, steady as well as unsteady, on the blade surface of the NACA3506 profile are compared to experimental data that has been gained by the Institute of Aeroelasticity of the German Aerospace Center (DLR) during several wind tunnel tests at the annular compressor cascade facility RGP-400 of the Ecole Polytechnique Fe´de´rale de Lausanne (EPFL). Whereas a certain robustness of the unsteady CFD results can be stated for the subsonic flow regime, the transonic regime proves to be very sensitive with respect to the steady state solution.

On the steady-state solution of the M/G/2 queue

1979 ◽  
Vol 11 (01) ◽  
pp. 240-255 ◽  
Author(s):  
Per Hokstad
Keyword(s):  
Steady State ◽  
General Solution ◽  
Laplace Transform ◽  
Queue Length ◽  
Joint Distribution ◽  
Length Distribution ◽  
Steady State Solution ◽  
Queue Length Distribution ◽  
The Difference ◽  
Number Of Customers

The asymptotic behaviour of the M/G/2 queue is studied. The difference-differential equations for the joint distribution of the number of customers present and of the remaining holding times for services in progress were obtained in Hokstad (1978a) (for M/G/m). In the present paper it is found that the general solution of these equations involves an arbitrary function. In order to decide which of the possible solutions is the answer to the queueing problem one has to consider the singularities of the Laplace transforms involved. When the service time has a rational Laplace transform, a method of obtaining the queue length distribution is outlined. For a couple of examples the explicit form of the generating function of the queue length is obtained.

Observations on the Steady-State Solution of an Extremely Flexible Spinning Disk With a Transverse Load

1983 ◽  
Vol 50 (3) ◽  
pp. 525-530 ◽  
Author(s):  
R. C. Benson
Keyword(s):  
Steady State ◽  
Hybrid System ◽  
Fourth Order ◽  
Steady State Solution ◽  
Transverse Load ◽  
System Of Differential Equations ◽  
Membrane Theory ◽  
Small Disk ◽  
Spinning Disk ◽  
Flexible Disk

The steady deflection of a transversely loaded, extremely flexible, spinning disk is studied. Membrane theory is used to predict the shapes and locations of waves that dominate the response. It is found that waves in disconnected regions are possible. Some results are presented to show how disk stiffness moderates the membrane waves, the most important result being an upper bound on the highest ordered wave of significant amplitude. A hybrid system of differential equations and boundary conditions is developed to replace the pure membrane formulation that is singular, and the full fourth-order plate formulation that is numerically sensitive. The hybrid formulation retains the salient features of the flexible disk response and facilitates calculations for very small disk stiffnesses.

Dynamic Stability of an Impact System Connected With Rock Drilling

1969 ◽  
Vol 36 (4) ◽  
pp. 743-749 ◽  
Author(s):  
C. C. Fu
Keyword(s):  
Computer Simulation ◽  
Exact Solution ◽  
Steady State ◽  
Asymptotic Stability ◽  
Piecewise Linear ◽  
Steady State Solution ◽  
External Excitation ◽  
Rock Drilling ◽  
Impact System ◽  
Number Of Cycles

This paper deals with asymptotic stability of an analytically derived, synchronous as well as nonsynchronous, steady-state solution of an impact system which exhibits piecewise linear characteristics connected with rock drilling. The exact solution, which assumes one impact for a given number of cycles of the external excitation, is derived, its asymptotic stability is examined, and ranges of parameters are determined for which asymptotic stability is assured. The theoretically predicted stability or instability is verified by a digital computer simulation.

scholarly journals Polythermal conditions in arctic glaciers

1991 ◽  
Vol 37 (126) ◽  
pp. 261-269 ◽  
Author(s):  
Heinz Blatter ◽  
Kolumban Hutter
Keyword(s):  
Steady State ◽  
Continuum Hypothesis ◽  
Basal Layer ◽  
Moisture Diffusion ◽  
Moisture Diffusivity ◽  
Climatic Conditions ◽  
Two Dimensions ◽  
Water Mixture ◽  
Plane Flow ◽  
Transition Surface

AbstractEnglacial temperature measurements in Arctic valley glaciers suggest in the ablation zone the existence of a basal layer of temperate ice lying below the bulk of cold ice. For such a polythermal glacier, a mathematical model is presented that calculates the temperature in the cold part and the position of the cold-temperate transition surface (CTS). The model is based on the continuum hypothesis for ice and the ice-water mixture, and on the conservation laws for moisture and energy. Temperate ice is treated as a binary mixture of ice and water at the melting point of pure ice. Boundary and transition conditions are formulated for the free surface, the base and the intraglacial cold-temperate transition surface. The model is reduced to two dimensions (plane flow) and the shallow-ice approximation is invoked. The limit of very small moisture diffusivity is analysed by using a stationary model with further reduction to one dimension (parallel-sided slab), thus providing the means of a consistent formulation of the transition conditions for moisture and heat flux through the CTS at the limit of negligibly small moisture diffusion.The application of the model to the steady-state Laika Glacier, using present-day conditions, results in a wholly cold glacier with a cold sole, in sharp contrast to observations. The present polythermal state of this glacier is suspected to be a remnant of the varying climatic conditions and glacier geometry during the past few centuries. Steady-state solutions representing apolythermalstructure can indeed be found within a range of prescribed conditions which are judged to be realistic for Laika Glacier at the last maximum extent of the glacier.

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