Scaling and Self-Similarity of One-Dimensional Unsteady Suspended Sediment Transport with Emphasis on Unscaled Sediment Material Properties

Carr, K. J.; Ercan, Ali; Kavvas, M. L.

doi:10.1061/(asce)hy.1943-7900.0000994

Cited by 17 publications

(11 citation statements)

References 18 publications

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“…The research of Fischer and Holley stated that simple transposition of concentration profiles from model to prototype is not valid and models may magnify or reduce longitudinal dispersion [8]. Current methods used in scaling sediment transport result in a number of scale effects, decreasing the accuracy and applicability of scale models [9]. The kinematics of suspended sediment is inversely proportional to the distortion ratio of the physical model but proportional to the width-depth ratio and curvature ratio [10].…”

Section: Introductionmentioning

confidence: 99%

Prediction and correction of scaling effects on velocity profile in hydraulic laboratory experiments

Zhang¹,

Wang²,

Chen³

et al. 2019

Desalination and Water Treatment

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Due to the geometric distortion in distorted hydraulic laboratory experiments, velocity profile cannot maintain as constant as required by the traditional criteria. Scaling effects, which lack quantitative researches, cannot be avoided even if the Froude and drag coefficient similitude criteria were satisfied. Prediction formulas of scaling effect rate are established in this research to theoretically reveal the quantitative relations between velocity profile distortion and experimental parameters. They are directly related to three parameters, distorted ratio, relative water depth, and relative bed roughness. In vertical direction, most effects happen near the bed and the deviation increases with distortion ratio. The similarity of secondary flow is worse and more complicated than that of stream-wise flow. The correction method, which is the improvement of traditional similitude criteria, can effectively reduce scaling effects when converting experimental results into their corresponding values in the prototype. Three dimensional numerical models are built to verify the accuracy of the prediction formulas and correction method.

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Section: Introductionmentioning

confidence: 99%

Prediction and correction of scaling effects on velocity profile in hydraulic laboratory experiments

Zhang¹,

Wang²,

Chen³

et al. 2019

Desalination and Water Treatment

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“…Yung et al (1994) used the Lie group method to classify symmetries in Richard's equation for heterogeneous flow in the vadose zone. Scaling of sediment transport problems using the Lie group method was done by Carr et al (2015). Lie scaling was applied to a variety of hydrological problems in Haltas and Kavvas (2011a).…”

Section: Introductionmentioning

confidence: 99%

A comparison of the modern Lie scaling method to classical scaling techniques

Polsinelli¹,

Kavvas²

2016

Hydrol. Earth Syst. Sci.

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Abstract. In the past 2 decades a new modern scaling technique has emerged from the highly developed theory on the Lie group of transformations. This new method has been applied by engineers to several problems in hydrology and hydraulics, including but not limited to overland flow, groundwater dynamics, sediment transport, and open channel hydraulics. This study attempts to clarify the relationship this new technology has with the classical scaling method based on dimensional analysis, non-dimensionalization, and the Vaschy-Buckingham-theorem. Key points of the Lie group theory, and the application of the Lie scaling transformation, are outlined and a comparison is made with two classical scaling models through two examples: unconfined groundwater flow and contaminant transport. The Lie scaling method produces an invariant scaling transformation of the prototype variables, which ensures the dynamics between the model and prototype systems will be preserved. Lie scaling can also be used to determine the conditions under which a complete model is dynamically, kinematically, and geometrically similar to the prototype phenomenon. Similarities between the Lie and classical scaling methods are explained, and the relative strengths and weaknesses of the techniques are discussed.

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“…Scaling transforms have been the subject of numerous other studies, both within and outside the context of groundwater problems. Notable examples of scaling studies are the following: Carr et al (2015) in which scaling techniques were applied to sediment transport; Ercan et al (2014) in which scaling techniques were applied to one-dimensional open channel flow; Haltas and Kavvas (2011) which derived scale invariance conditions for numerous 1D groundwater problems, including the one-dimensional unconfined and confined groundwater equations under various boundary conditions ;and Yung et al (1994) which characterized scaling transformations for the one-dimensional homogeneous unsaturated equations using common functional forms for the hydraulicparameter functions. Experimental studies have indicated that the hydraulic head exhibits temporal scaling (Zhang and Schilling, 2004).…”

Section: Introductionmentioning

confidence: 99%

Scaling procedures for heterogeneous unconfined aquifers

Polsinelli

Kavvas

2016

Hydrol. Process.

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Abstract:Complex flows in heterogeneous confined and unconfined aquifers is a phenomenon that continues to present difficulties in flow mapping and modelling in the field, laboratory, and through numerical simulations. It is often the case with complicated phenomena that transformative scaling and reduction of the problem through symmetry is of great efficacy in the formation of predictive models in both the laboratory and computational settings. A detailed a study of the application of a broad class of Lie scaling transformations on a set of equations representing the groundwater flows in heterogeneous confined and unconfined aquifers has produced a set of scaling relationships between the spatial variables, hydrologic variables, and parameters. The set of scaling transformations preserve the structure of the equations in the sense that the scaling transformations leave the initialboundary value system representing the invariant groundwater flows. This theoretical approach elucidates not only the scaling relationships but also the properties that hydrologic variables and parameters must satisfy in order for calling to be possible. Validation of the theory developed is carried out through a series of four numerical simulations using the USGS MODFLOW-2005 software package. The results of these experiments demonstrate that the derived scaling transformations can effectively form predictive models of large-scale phenomena at small scales with negligible error in many cases. Comments on the limitations of the approach and directions for future research are made in the closing sections.

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Scaling and Self-Similarity of One-Dimensional Unsteady Suspended Sediment Transport with Emphasis on Unscaled Sediment Material Properties

Cited by 17 publications

References 18 publications

Prediction and correction of scaling effects on velocity profile in hydraulic laboratory experiments

Prediction and correction of scaling effects on velocity profile in hydraulic laboratory experiments

A comparison of the modern Lie scaling method to classical scaling techniques

Scaling procedures for heterogeneous unconfined aquifers

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