scholarly journals Hortonian Overland Flow, Hillslope Morphology and Stream Power I: Spatial Energy Distributions and Steady-state Power Maxima

2021 ◽  
Author(s):  
Samuel Schroers ◽  
Olivier Eiff ◽  
Axel Kleidon ◽  
Jan Wienhöfer ◽  
Erwin Zehe
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Energy Dissipation ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Overland Flow ◽  
Slope Angle ◽  
Order Estimate ◽  
Energy Fluxes ◽  
Stream Power

Abstract. Recent developments in hydrology have led to a new perspective on runoff processes, extending beyond the classical mass dynamics of water in a catchment. For instance, stream flow has been analyzed in a thermodynamic framework, which allows the incorporation of two additional physical laws and enhances our understanding of catchments as open environmental systems. Related investigations suggested that energetic extremal principles might constrain hydrological processes, because the latter are associated with conversions and dissipation of free energy. Here we expand this thermodynamic perspective by exploring how macro and micro hillslope structures control the free energy balance of Hortonian overland flow. This may ultimately help understanding why these structures have evolved to their present shape. To this end, we develop a general theory of surface runoff and of the related conversion of geopotential energy gradients into other forms of energy, particularly kinetic energy as driver of erosion and sediment transport. We then use this framework to analyze how combinations of typical hillslopes profiles and width distributions control the spatial patterns of steady state stream power and energy dissipation along the flow path. Additionally, we provide a first order estimate whether and when rills reduce the overall energy dissipation compared to sheet flow. Finally, we relate accumulated stream power of linear hillslopes to slope angles, closing the loop to Horton's original formulation of erosion force. The analytical analysis of stream power reveals that the common formulation, a function of the depth-discharge product is a reduced version of the more general equations if we neglect changes in velocity and discharge in space. The full equations of stream power result in maximum energy fluxes in space for sinusoidal and exponential hillslope profiles, while linear and negative exponential forms unlimitedly increase these fluxes in the downstream direction. Depending on geometry, rill flow increases or decreases kinetic energy fluxes downslope, effectively counteracting or increasing the dissipation of potential energy. For accumulated power in space for steady state runoff, we find that on linear hillslopes a slope angle of 45° maximizes the conversion of potential energy into dissipation and an angle of 35° maximizes the conversion of potential energy into kinetic energy.

Extracting Substantial Free Energy From Static Ambient Potential Energy Using Distance, Time-Lapse Chaos, and Coriolis Principles

2018 ◽  
Author(s):  
Jim B. Surjaatmadja
Keyword(s):  
Free Energy ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Time Lapse ◽  
Gas Wells ◽  
Direct Path ◽  
Natural Processes ◽  
Perpetual Motion ◽  
Financial Costs ◽  
Save Energy

Extracting free energy has long been a goal of science but is mostly considered impossible to achieve. Natural processes having independent movement, such as rivers and wind, are often used but provide varied effectiveness. However, coordinated instability within a statically pressurized ambience can be used to extract a significant percentage of the ambient potential energy. This method creates two pathways between two adjacent points, one being a chaotic or Coriolis swirling path and the other being a direct path, thereby creating a pressure difference between the two adjacent points, which can be harvested to reduce the kinetic energy input required to perform the process. While some refer to the proposed benefits as “perpetual motion,” it is necessary to understand that 55 to 80% of the required kinetic energy would still be mechanically generated; therefore, they could be better referred to as “coordinated chaos” or a “Coriolis energy extractor” to save energy [1]. This paper studies direct returns—extracting energy directly from a static (not dynamic) ambient energy. While such returns might not be substantial in normal activities, in deepwater or underground applications (e.g., oil or gas wells), they can be significant, often equating to a 20–45% reduction in fuel use or pollutant generation. In operations that use 20,000 horsepower, this could represent a savings of 4,000 horsepower or 10,000,000 Btu/hr with no associated financial costs.

scholarly journals Numerical Simulation of Katabatic Flow with Changing Slope Angle

2005 ◽  
Vol 133 (11) ◽  
pp. 3065-3080 ◽  
Author(s):  
Craig M. Smith ◽  
Eric D. Skyllingstad
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Slope Angle ◽  
Gravitational Potential Energy ◽  
Flow Profile ◽  
Advanced Regional Prediction System ◽  
Regional Prediction ◽  
Les Model ◽  
Lower Slope ◽  
Upper Slope

Abstract A large eddy simulation (LES) model and the Advanced Regional Prediction System (ARPS) model, which does not resolve turbulent eddies, are used to study the effect of a slope angle decrease on the structure of katabatic slope flows. For a simple, uniform angle slope, simulations from both models produce turbulence kinetic energy and momentum budgets that are in good overall agreement. Simulations of a compound angle slope are compared to a uniform angle slope to demonstrate how a changing slope angle can strongly affect the strength of katabatic flows. Both ARPS and the LES model show that slopes with a steep upper slope followed by a shallower lower slope (concave shape) generate a rapid acceleration on the upper slope followed by a transition to a slower evolving structure characterized by an elevated jet over the lower slope. In contrast, the case with uniform slope (having the same total height change) yields a more uniform flow profile with stronger winds at the slope bottom. Higher average slope in the uniform slope angle case generates greater gravitational potential energy, which is converted to kinetic energy at the bottom of the slope. Analysis of the total energy budget of slope flows indicates a consistent structure where potential energy generated at the top of the slope is transported downslope and converted into kinetic energy near the slope base.

scholarly journals Morphological controls on Hortonian surface runoff: An interpretation of steady-state energy patterns, maximum power states and dissipation regimes within a thermodynamic framework

2021 ◽  
Author(s):  
Samuel Schroers ◽  
Olivier Eiff ◽  
Axel Kleidon ◽  
Ulrike Scherer ◽  
Jan Wienhöfer ◽  
...  
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Surface Runoff ◽  
Overland Flow ◽  
Dynamic Equilibrium ◽  
Flow Path ◽  
Maximum Power ◽  
Rainfall Simulation ◽  
Sheet Flow ◽  
Thermodynamic Framework

Abstract. Recent developments in hydrology have led to a new perspective on runoff processes, extending beyond the classical mass dynamics of water in a catchment. For instance, stream flow has been analysed in a thermodynamic framework, which allows the incorporation of two additional physical laws and enhances our understanding of catchments as open environmental systems. Related investigations suggested that energetic extremal principles might constrain hydrological processes, because the latter are associated with conversions and dissipation of free energy. Here we expand this thermodynamic perspective by exploring how hillslope structures at the macro- and microscale control the free energy balance of Hortonian overland flow. We put special emphasis on the transitions of surface runoff processes at the hillslope scale, as hillslopes energetically behave distinctly different in comparison to fluvial systems. To this end, we develop a general theory of surface runoff and of the related conversion of geopotential energy gradients into other forms of energy, particularly kinetic energy as the driver of erosion and sediment transport. We then use this framework at a macroscopic scale to analyse how combinations of typical hillslopes profiles and width distributions control the spatial patterns of steady-state stream power and energy dissipation along the flow path. At the microscale, we analyse flow concentration in rills and its influence on the distribution of energy and dissipation in space. Therefore, we develop a new numerical method for the Catflow model, which allows a dynamical separation of Hortonian surface runoff between a rill- and a sheet flow domain. We calibrated the new Catflow-Rill model to rainfall simulation experiments and observed overland flow in the Weiherbach catchment and found evidence that flow accumulation in rills serves as a means to redistribute energy gradients in space, therefore minimizing energy expenditure along the flow path, while also maximizing overall power of the system. Our results indicate that laminar sheet flow and turbulent rill flow on hillslopes develop to a dynamic equilibrium that corresponds to a maximum power state, and that the transition of flow from one domain into the other is marked by an energy maximum in space.

scholarly journals Spray and Cooling Dynamics of Cryogen Sprays Impinging on a Human Skin Model

2007 ◽  
Author(s):  
Walfre Franco ◽  
Henry Vu ◽  
Wangcun Jia ◽  
J. Stuart Nelson ◽  
Guillermo Aguilar
Keyword(s):  
Heat Flux ◽  
Steady State ◽  
Kinetic Energy ◽  
Surface Temperature ◽  
Human Skin ◽  
Surface Heat ◽  
Large Temperature ◽  
Skin Model ◽  
Energy Fluxes ◽  
Spray Cone

The objective of the present work is to correlate the time-dependent flow characteristics of cryogen sprays to the induced thermal dynamics at the surface of a human skin model. First, a numerical analysis to evaluate our skin model is carried out. Next, diameter and axial velocity of droplets impinging onto the skin model are measured. Diameter, velocity and surface temperature are acquired simultaneously at the center of the spray cone close to and at the skin model surface, respectively. Spurt durations of 10, 30 and 50 ms are investigated. Finally, measurements are used to compute spray number, mass and kinetic energy fluxes and surface heat flux. Numerical modeling shows that, subject to the same heat flux, the thermal response of our model and human skin is qualitatively similar but the total temperature drop in skin is about 50% less than that of the model. A simple transformation can be used to map the temperature response of the model to that of skin. Experimental measurements show that during the initial spray transient, fast and small droplets (respect to steady state values) induce large temperature drops and the highest heat flux because the temperature difference between liquid and substrate is the largest; during the spray steady state, surface temperature remains at its lowest value; during the final transient, droplets are fast and small again, although their impact on the surface heat transfer is negligible due to decreasing mass and kinetic energy fluxes and reduced temperature differences between liquid and substrate.

scholarly journals Correlation between Buoyancy Flux, Dissipation and Potential Vorticity in Rotating Stratified Turbulence

Atmosphere ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 157
Author(s):  
Duane Rosenberg ◽  
Annick Pouquet ◽  
Raffaele Marino
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Potential Vorticity ◽  
Isotropic Turbulence ◽  
Joint Probability ◽  
Buoyancy Flux ◽  
Turbulent Regime ◽  
Stratified Turbulence ◽  
Low Dissipation ◽  
Linear And Nonlinear

We study in this paper the correlation between the buoyancy flux, the efficiency of energy dissipation and the linear and nonlinear components of potential vorticity, PV, a point-wise invariant of the Boussinesq equations, contrasting the three identified regimes of rotating stratified turbulence, namely wave-dominated, wave–eddy interactions and eddy-dominated. After recalling some of the main novel features of these flows compared to homogeneous isotropic turbulence, we specifically analyze three direct numerical simulations in the absence of forcing and performed on grids of 10243 points, one in each of these physical regimes. We focus in particular on the link between the point-wise buoyancy flux and the amount of kinetic energy dissipation and of linear and nonlinear PV. For flows dominated by waves, we find that the highest joint probability is for minimal kinetic energy dissipation (compared to the buoyancy flux), low dissipation efficiency and low nonlinear PV, whereas for flows dominated by nonlinear eddies, the highest correlation between dissipation and buoyancy flux occurs for weak flux and high localized nonlinear PV. We also show that the nonlinear potential vorticity is strongly correlated with high dissipation efficiency in the turbulent regime, corresponding to intermittent events, as observed in the atmosphere and oceans.

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