scholarly journals Limits of Predictability of a Global Self-Similar Routing Model in a Local Self-Similar Environment

Atmosphere ◽  
2020 ◽  
Vol 11 (8) ◽  
pp. 791
Author(s):  
Nicolas Velasquez ◽  
Ricardo Mantilla
Keyword(s):  
Scaling Laws ◽  
Hydraulic Geometry ◽  
Distributed Hydrological Model ◽  
Self Similarity ◽  
Cross Sectional ◽  
Actual Observation ◽  
Scaling Parameters ◽  
Self Similar ◽  
Distributed Hydrological Models ◽  
Similarity Laws

Regional Distributed Hydrological models are being adopted around the world for prediction of streamflow fluctuations and floods. However, the details of the hydraulic geometry of the channels in the river network (cross sectional geometry, slope, drag coefficients, etc.) are not always known, which imposes the need for simplifications based on scaling laws and their prescription. We use a distributed hydrological model forced with radar-derived rainfall fields to test the effect of spatial variations in the scaling parameters of Hydraulic Geometric (HG) relationships used to simplify routing equations. For our experimental setup, we create a virtual watershed that obeys local self-similarity laws for HG and attempt to predict the resulting hydrographs using a global self-similar HG parameterization. We find that the errors in the peak flow value and timing are consistent with the errors that are observed when trying to replicate actual observation of streamflow. Our results provide evidence that local self-similarity can be a more appropriate simplification of HG scaling laws than global self-similarity.

SCALING LAWS IN A TURBULENT BAROCLINIC INSTABILITY

Fractals ◽  
1995 ◽  
Vol 03 (02) ◽  
pp. 297-314 ◽  
Author(s):  
C. SERIO ◽  
V. TRAMUTOLI
Keyword(s):  
Power Law ◽  
Scaling Laws ◽  
Spatial Scales ◽  
Baroclinic Instability ◽  
Satellite Image ◽  
Horizontal Resolution ◽  
Turbulent Motion ◽  
Self Similarity ◽  
Wavelet Transform Analysis ◽  
Self Similar

This work provides an empirical investigation of scaling laws in a cloud system generated and advected by a strong baroclinic instability. An infrared satellite image with a spatial (horizontal) resolution of about 1 km has been analyzed. The presence of two sizeable and unmistakable scaling regions, one extending from 1 to 15 km and characterized by a power law with an exponent close to 1, the other stretching from 20 km up to 100 km and characterized by a power law with exponent close to 1/3, have been revealed by variogram analysis. These two scaling laws are in agreement with the idea of scale invariance of the turbulent motion and also suggest the presence of a self-similar structure. To explore this possibility, wavelet transform analysis at different spatial scales has been used. Our findings are that self-similarity is present at the smallest scales, but this universal characteristic may be masked by non-universal effects which influence the homogeneity of the underlying turbulent motion. The implications of the two scaling exponents, 1 and 1/3, are also discussed.

Self-focusing of thin liquid jets

2007 ◽  
Vol 464 (2089) ◽  
pp. 197-206 ◽  
Author(s):  
Laurent Duchemin
Keyword(s):  
Free Surface ◽  
Time Evolution ◽  
Scaling Laws ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Liquid Jets ◽  
Self Similarity ◽  
Long Time ◽  
Self Similar ◽  
Long Time Evolution

The nonlinear evolution of an initially perturbed free surface perpendicularly accelerated, or of an initially flat free surface subject to a perturbed velocity profile, gives rise to the emergence of thin spikes of fluid. We are investigating the long-time evolution of a thin inviscid jet of this kind, subject or not to a body force acting in the direction of the jet itself. A fully nonlinear theory for the long-time evolution of the jet is given. In two dimensions, the curvature of the tip scales like t 3 , where t is time, and the peak undergoes an overshoot in acceleration which evolves like t −5 . In three dimensions, the jet evolves towards an axisymmetric shape, and the curvature and the overshoot in acceleration obey asymptotic laws in t 2 and t −4 , respectively. The asymptotic self-similar shape of the spike is found to be a hyperbola in two dimensions, a hyperboloid in three dimensions. Scaling laws and self-similarity are confronted with two-dimensional computations of the Richtmyer–Meshkov instability.

A WAVELET METHOD COUPLED WITH QUASI-SELF-SIMILAR STOCHASTIC PROCESSES FOR TIME SERIES APPROXIMATION

2011 ◽  
Vol 09 (05) ◽  
pp. 685-711 ◽  
Author(s):  
MOHAMED ESSAIED HAMRITA ◽  
NIDHAL BEN ABDALLAH ◽  
ANOUAR BEN MABROUK
Keyword(s):  
Time Series ◽  
Stochastic Processes ◽  
Scaling Laws ◽  
Financial Time Series ◽  
Wavelet Theory ◽  
Self Similarity ◽  
Wavelet Method ◽  
Financial Time ◽  
Functional Methods ◽  
Self Similar

Scaling laws and generally self-similar structures are now well known facts in financial time series. Furthermore, these signals are characterized by the presence of stochastic behavior allowing their analysis with pure functional methods being incomplete. In the present paper, some existing models are reviewed and modified, based on wavelet theory and self-similarity, to recover multi-scaling cases for approximating financial signals. The resulting models are then tested on some empirical examples and analyzed for error estimates.

scholarly journals Hydrology without dimensions

2021 ◽  
Author(s):  
Amilcare Porporato
Keyword(s):  
Scaling Laws ◽  
Self Similarity ◽  
Environmental Controls ◽  
Dryness Index ◽  
Self Similar ◽  
Pi Theorem ◽  
Physical Laws ◽  
Process Complexity ◽  
Dimensional Homogeneity

Abstract. By rigorously accounting for dimensional homogeneity in physical laws, the Pi theorem and the related self-similarity hypotheses allow us to achieve a dimensionless reformulation of scientific hypotheses in a lower dimensional context. This paper presents applications of these concepts to the partitioning of water and soil on terrestrial landscapes, for which the process complexity and lack of first principle formulation make dimensional analysis an excellent tool to formulate theories that are amenable to empirical testing and analytical developments. The resulting scaling laws help reveal the dominant environmental controls for these partitionings. In particular, we discuss how the dryness index and the storage index affect the long term rainfall partitioning, the key nonlinear control of the dryness index in global datasets of weathering rates, and the existence of new macroscopic relations among average variables in landscape evolution statistics. The scaling laws for the partitioning of sediments, the elevation profile, and the spectral scaling of self-similar topographies also unveil tantalizing analogies with turbulent fluctuations.

Self-similarity of the large-scale motions in turbulent pipe flow

2016 ◽  
Vol 792 ◽  
Author(s):  
Leo H. O. Hellström ◽  
Ivan Marusic ◽  
Alexander J. Smits
Keyword(s):  
Turbulent Flows ◽  
Pipe Flow ◽  
Large Scale ◽  
Decomposition Analysis ◽  
Turbulent Pipe Flow ◽  
Self Similarity ◽  
Cross Sectional ◽  
Self Similar ◽  
Logarithmic Layer ◽  
Sectional Shape

Townsend’s attached eddy hypothesis assumes the existence of a set of energetic and geometrically self-similar eddies in the logarithmic layer in wall-bounded turbulent flows, which can be scaled with their distance to the wall. To examine the possible self-similarity of the energetic eddies in fully developed turbulent pipe flow, we performed stereo particle image velocimetry measurements together with a proper orthogonal decomposition analysis. For two Reynolds numbers, $Re_{{\it\tau}}=1330$ and 2460, the resulting modes/eddies were shown to exhibit self-similar behaviour for eddies with wall-normal length scales spanning a decade. This single length scale provides a complete description of the cross-sectional shape of the self-similar eddies.

scholarly journals Onset of the Mach Reflection of Zel’dovich–von Neumann–Döring Detonations

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 314
Author(s):  
Tianyu Jing ◽  
Huilan Ren ◽  
Jian Li
Keyword(s):  
Hot Spot ◽  
Mach Reflection ◽  
Near Field ◽  
The Self ◽  
Small Scale ◽  
Mach Stem ◽  
Self Similarity ◽  
Von Neumann ◽  
Similarity Problem ◽  
Self Similar

The present study investigates the similarity problem associated with the onset of the Mach reflection of Zel’dovich–von Neumann–Döring (ZND) detonations in the near field. The results reveal that the self-similarity in the frozen-limit regime is strictly valid only within a small scale, i.e., of the order of the induction length. The Mach reflection becomes non-self-similar during the transition of the Mach stem from “frozen” to “reactive” by coupling with the reaction zone. The triple-point trajectory first rises from the self-similar result due to compressive waves generated by the “hot spot”, and then decays after establishment of the reactive Mach stem. It is also found, by removing the restriction, that the frozen limit can be extended to a much larger distance than expected. The obtained results elucidate the physical origin of the onset of Mach reflection with chemical reactions, which has previously been observed in both experiments and numerical simulations.

scholarly journals Depressurization-Induced Nucleation in the “Polylactide-Carbon Dioxide” System: Self-Similarity of the Bubble Embryos Expansion

Polymers ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1115
Author(s):  
Dmitry Zimnyakov ◽  
Marina Alonova ◽  
Ekaterina Ushakova
Keyword(s):  
Initial Rate ◽  
Initial Pressure ◽  
External Pressure ◽  
Self Similarity ◽  
Embryo Formation ◽  
Linear Behavior ◽  
Joint Influence ◽  
External Pressures ◽  
Adiabatic Cooling ◽  
Self Similar

Self-similar expansion of bubble embryos in a plasticized polymer under quasi-isothermal depressurization is examined using the experimental data on expansion rates of embryos in the CO2-plasticized d,l-polylactide and modeling the results. The CO2 initial pressure varied from 5 to 14 MPa, and the depressurization rate was 5 × 10−3 MPa/s. The constant temperature in experiments was in a range from 310 to 338 K. The initial rate of embryos expansion varied from ≈0.1 to ≈10 µm/s, with a decrease in the current external pressure. While modeling, a non-linear behavior of CO2 isotherms near the critical point was taken into account. The modeled data agree satisfactorily with the experimental results. The effect of a remarkable increase in the expansion rate at a decreasing external pressure is interpreted in terms of competing effects, including a decrease in the internal pressure, an increase in the polymer viscosity, and an increase in the embryo radius at the time of embryo formation. The vanishing probability of finding the steadily expanding embryos for external pressures around the CO2 critical pressure is interpreted in terms of a joint influence of the quasi-adiabatic cooling and high compressibility of CO2 in the embryos.

scholarly journals Self-similar resistive circuits as fractal-like structures

2017 ◽  
Vol 40 (1) ◽  
Author(s):  
Claudio Xavier Mendes dos Santos ◽  
Carlos Molina Mendes ◽  
Marcelo Ventura Freire
Keyword(s):  
Scale Invariance ◽  
Self Similarity ◽  
General Properties ◽  
Modern Physics ◽  
Resistive Networks ◽  
Self Similar ◽  
And Mathematics ◽  
Definition Of ◽  
The Individual

Fractals play a central role in several areas of modern physics and mathematics. In the present work we explore resistive circuits where the individual resistors are arranged in fractal-like patterns. These circuits have some of the characteristics typically found in geometric fractals, namely self-similarity and scale invariance. Considering resistive circuits as graphs, we propose a definition of self-similar circuits which mimics a self-similar fractal. General properties of the resistive circuits generated by this approach are investigated, and interesting examples are commented in detail. Specifically, we consider self-similar resistive series, tree-like resistive networks and Sierpinski’s configurations with resistors.

TUBE FORMULAS FOR GRAPH-DIRECTED FRACTALS

Fractals ◽  
2010 ◽  
Vol 18 (03) ◽  
pp. 349-361 ◽  
Author(s):  
BÜNYAMIN DEMÍR ◽  
ALI DENÍZ ◽  
ŞAHIN KOÇAK ◽  
A. ERSIN ÜREYEN
Keyword(s):  
The Self ◽  
Self Similarity ◽  
Complex Dimensions ◽  
Tubular Neighborhoods ◽  
Self Similar ◽  
Tube Formulas

Lapidus and Pearse proved recently an interesting formula about the volume of tubular neighborhoods of fractal sprays, including the self-similar fractals. We consider the graph-directed fractals in the sense of graph self-similarity of Mauldin-Williams within this framework of Lapidus-Pearse. Extending the notion of complex dimensions to the graph-directed fractals we compute the volumes of tubular neighborhoods of their associated tilings and give a simplified and pointwise proof of a version of Lapidus-Pearse formula, which can be applied to both self-similar and graph-directed fractals.

scholarly journals On the scaling of shear-driven entrainment: a DNS study

2013 ◽  
Vol 732 ◽  
pp. 150-165 ◽  
Author(s):  
Harm J. J. Jonker ◽  
Maarten van Reeuwijk ◽  
Peter P. Sullivan ◽  
Edward G. Patton
Keyword(s):  
Reynolds Number ◽  
Lower Boundary ◽  
Square Root ◽  
Simulation Design ◽  
Self Similarity ◽  
Original Experiment ◽  
Turbulent Layer ◽  
Entrainment Velocity ◽  
Constant Shear Stress ◽  
Self Similar

AbstractThe deepening of a shear-driven turbulent layer penetrating into a stably stratified quiescent layer is studied using direct numerical simulation (DNS). The simulation design mimics the classical laboratory experiments by Kato & Phillips (J. Fluid Mech., vol. 37, 1969, pp. 643–655) in that it starts with linear stratification and applies a constant shear stress at the lower boundary, but avoids sidewall and rotation effects inherent in the original experiment. It is found that the layers universally deepen as a function of the square root of time, independent of the initial stratification and the Reynolds number of the simulations, provided that the Reynolds number is large enough. Consistent with this finding, the dimensionless entrainment velocity varies with the bulk Richardson number as$R{i}^{- 1/ 2} $. In addition, it is observed that all cases evolve in a self-similar fashion. A self-similarity analysis of the conservation equations shows that only a square root growth law is consistent with self-similar behaviour.

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