Editorial

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Physical and Mathematical Fluid Mechanics

by

Markus Scholle

Water 2020, 12(8), 2199; https://doi.org/10.3390/w12082199 - 05 Aug 2020

Viewed by 1838

Abstract

Fluid mechanics has emerged as a basic concept for nearly every field of technology. Despite there being a well-developed mathematical theory and available commercial software codes, the computation of solutions of the governing equations of motion is still challenging, especially due to the [...] Read more.

Fluid mechanics has emerged as a basic concept for nearly every field of technology. Despite there being a well-developed mathematical theory and available commercial software codes, the computation of solutions of the governing equations of motion is still challenging, especially due to the nonlinearity involved, and there are still open questions regarding the underlying physics of fluid flow, especially with respect to the continuum hypothesis and thermodynamic local equilibrium. The aim of this Special Issue is to reference recent advances in the field of fluid mechanics both in terms of developing sophisticated mathematical methods for finding solutions of the equations of motion, on the one hand, and on novel approaches to the physical modelling beyond the continuum hypothesis and thermodynamic local equilibrium, on the other. Full article

(This article belongs to the Special Issue Physical and Mathematical Fluid Mechanics)

Research

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Open AccessArticle

Poroacoustic Traveling Waves under the Rubin–Rosenau–Gottlieb Theory of Generalized Continua

by

Pedro M. Jordan

Water 2020, 12(3), 807; https://doi.org/10.3390/w12030807 - 14 Mar 2020

Cited by 2 | Viewed by 1527

Abstract

We investigate linear and nonlinear poroacoustic waveforms under the Rubin–Rosenau– Gottlieb (RRG) theory of generalized continua. Working in the context of the Cauchy problem, on both the real line and the case with periodic boundary conditions, exact and asymptotic expressions are obtained. Numerical [...] Read more.

We investigate linear and nonlinear poroacoustic waveforms under the Rubin–Rosenau– Gottlieb (RRG) theory of generalized continua. Working in the context of the Cauchy problem, on both the real line and the case with periodic boundary conditions, exact and asymptotic expressions are obtained. Numerical simulations are also presented, von Neumann–Richtmyer “artificial” viscosity is used to derive an exact kink-type solution to the poroacoustic piston problem, and possible experimental tests of our findings are noted. The presentation concludes with a discussion of possible follow-on investigations. Full article

(This article belongs to the Special Issue Physical and Mathematical Fluid Mechanics)

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Open AccessArticle

Study on the Characteristic Point Location of Depth Average Velocity in Smooth Open Channels: Applied to Channels with Flat or Concave Boundaries

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Water 2020, 12(2), 430; https://doi.org/10.3390/w12020430 - 05 Feb 2020

Cited by 4 | Viewed by 1600

Abstract

Based on the flow partition theory, we derive a mathematical expression by using the log-law for the characteristic point location (CPL) of depth average velocity in channels with flat or concave boundaries. It can manifest the position of the characteristic points in the [...] Read more.

Based on the flow partition theory, we derive a mathematical expression by using the log-law for the characteristic point location (CPL) of depth average velocity in channels with flat or concave boundaries. It can manifest the position of the characteristic points in the vertical direction relative to the channel side wall or bed. Taking rectangular and semi-circular channels as research objects, we put forward a method to calculate the discharge of channels with CPL. Additionally, we carried out some experiments on rectangular and semi-circular channel sections. CPL’s analytic expression is validated against experimental results through comparison of velocity and discharge. The proposed formulation of characteristic point location could be extensively employed in flow measurements of flat and concave boundary channels, which has practical application value in simplifying the flow measurement steps of open channels. Full article

(This article belongs to the Special Issue Physical and Mathematical Fluid Mechanics)

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Open AccessArticle

Viscosity Controls Rapid Infiltration and Drainage, Not the Macropores

by

Peter Germann

Water 2020, 12(2), 337; https://doi.org/10.3390/w12020337 - 24 Jan 2020

Cited by 3 | Viewed by 2076

Abstract

The paper argues that universal approaches to infiltration and drainage in permeable media pivoting around capillarity and leading to dual porosity, non-equilibrium, or preferential flow need to be replaced by a dual process approach. One process has to account for relatively fast infiltration [...] Read more.

The paper argues that universal approaches to infiltration and drainage in permeable media pivoting around capillarity and leading to dual porosity, non-equilibrium, or preferential flow need to be replaced by a dual process approach. One process has to account for relatively fast infiltration and drainage based on Newton’s viscous shear flow, while the other one draws from capillarity and is responsible for storage and relatively slow redistribution of soil water. Already in the second half of the 19th Century were two separate processes postulated, however, Buckingham’s and Richards’ apparent universal capillarity-based approaches to the flow and storage of water in soils dominated. The paper introduces the basics of Newton’s shear flow in permeable media. It then presents experimental applications, and explores the relationships of Newton’s shear flow with Darcy’s law, Forchheimer’s and Richards’ equations, and finally extends to the transport of solutes and particles. Full article

(This article belongs to the Special Issue Physical and Mathematical Fluid Mechanics)

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Open AccessArticle

Analysis of the Interconnections between Classic Vortex Models of Coherent Structures Based on DNS Data

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Water 2019, 11(10), 2005; https://doi.org/10.3390/w11102005 - 26 Sep 2019

Cited by 4 | Viewed by 2311

Abstract

Low- and high-speed streaks (ejection, Q2, and sweep, Q4, events in quadrant analysis) are significant features of coherent structures in turbulent flow. Streak formation is closely related to turbulent structures in several vortex models, such as attached eddy models, streamwise vortex analysis models, [...] Read more.

Low- and high-speed streaks (ejection, Q2, and sweep, Q4, events in quadrant analysis) are significant features of coherent structures in turbulent flow. Streak formation is closely related to turbulent structures in several vortex models, such as attached eddy models, streamwise vortex analysis models, and hairpin vortex models, which are all standard models. Vortex models are complex, whereby the relationships among the different vortex models are unclear; thus, further studies are still needed to complete our understanding of vortices. In this study, 30 sets of direct numerical simulation (DNS) data were obtained to analyze the mechanics of the formation of coherent structures. Image processing techniques and statistical analysis were used to identify and quantify streak characteristics. We used a method of vortex recognition to extract spanwise vortices in the x–z plane. Analysis of the interactions among coherent structures showed that the three standard vortex models all gave reasonably close results. The attached eddy vortex model provides a good explanation of the linear dimensions of streaky structures with respect to the water depth and Q2 and Q4 events, whereby it can be augmented to form the quasi-streamwise vortex model. The legs of a hairpin vortex envelop low-speed streaky structures and so move in the streamwise direction; lower-velocity vortex legs also gradually accumulate into a streamwise vortex. Statistical analysis allowed us to combine our present results with some previous research results to propose a mechanism for the formation of streaky structures. This study provides a deeper understanding of the interrelationships among different vortex models. Full article

(This article belongs to the Special Issue Physical and Mathematical Fluid Mechanics)

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Review

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Open AccessReview

Potential Fields in Fluid Mechanics: A Review of Two Classical Approaches and Related Recent Advances

by

Markus Scholle

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Florian Marner

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Philip H. Gaskell

Water 2020, 12(5), 1241; https://doi.org/10.3390/w12051241 - 27 Apr 2020

Cited by 7 | Viewed by 2540

Abstract

The use of potential fields in fluid dynamics is retraced, ranging from classical potential theory to recent developments in this evergreen research field. The focus is centred on two major approaches and their advancements: (i) the Clebsch transformation and (ii) the classical complex [...] Read more.

The use of potential fields in fluid dynamics is retraced, ranging from classical potential theory to recent developments in this evergreen research field. The focus is centred on two major approaches and their advancements: (i) the Clebsch transformation and (ii) the classical complex variable method utilising Airy’s stress function, which can be generalised to a first integral methodology based on the introduction of a tensor potential and parallels drawn with Maxwell’s theory. Basic questions relating to the existence and gauge freedoms of the potential fields and the satisfaction of the boundary conditions required for closure are addressed; with respect to (i), the properties of self-adjointness and Galilean invariance are of particular interest. The application and use of both approaches is explored through the solution of four purposely selected problems; three of which are tractable analytically, the fourth requiring a numerical solution. In all cases, the results obtained are found to be in excellent agreement with corresponding solutions available in the open literature. Full article

(This article belongs to the Special Issue Physical and Mathematical Fluid Mechanics)

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Open AccessReview

Stochastic Approaches to Deterministic Fluid Dynamics: A Selective Review

by

Ana Bela Cruzeiro

Water 2020, 12(3), 864; https://doi.org/10.3390/w12030864 - 19 Mar 2020

Cited by 11 | Viewed by 2042

Abstract

We present a stochastic Lagrangian view of fluid dynamics. The velocity solving the deterministic Navier–Stokes equation is regarded as a mean time derivative taken over stochastic Lagrangian paths and the equations of motion are critical points of an associated stochastic action functional involving [...] Read more.

We present a stochastic Lagrangian view of fluid dynamics. The velocity solving the deterministic Navier–Stokes equation is regarded as a mean time derivative taken over stochastic Lagrangian paths and the equations of motion are critical points of an associated stochastic action functional involving the kinetic energy computed over random paths. Thus the deterministic Navier–Stokes equation is obtained via a variational principle. The pressure can be regarded as a Lagrange multiplier. The approach is based on Itô’s stochastic calculus. Different related probabilistic methods to study the Navier–Stokes equation are discussed. We also consider Navier–Stokes equations perturbed by random terms, which we derive by means of a variational principle. Full article

(This article belongs to the Special Issue Physical and Mathematical Fluid Mechanics)

Other

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Open AccessTechnical Note

Damage Characteristics and Mechanism of a 2010 Disastrous Groundwater Inrush Occurred at the Luotuoshan Coalmine in Wuhai, Inner Mongolia, China

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Water 2020, 12(3), 655; https://doi.org/10.3390/w12030655 - 28 Feb 2020

Cited by 4 | Viewed by 1458

Abstract

On 1 March 2010, a disastrous groundwater inrush occurred at the Luotuoshan coalmine in Wuhai (Inner Mongolia, China). Great effort was taken during the post-accident rescue. However, triggered by a large amount of groundwater rushed in from the Ordovician limestone aquifer underlying the [...] Read more.

On 1 March 2010, a disastrous groundwater inrush occurred at the Luotuoshan coalmine in Wuhai (Inner Mongolia, China). Great effort was taken during the post-accident rescue. However, triggered by a large amount of groundwater rushed in from the Ordovician limestone aquifer underlying the No.16 coal seam through the fractured sandy claystone and the karst collapse column, it caused great damage, including 32 deaths and direct economic losses of over 48 million yuan. The groundwater inrush originated from the floor heave in the air return gallery of the No.16 coal seam. The peak inflow rate was 60,036 m³/h. The gallery excavation under conditions caused by the incompletely recognized hydrogeological environment induced the accident. The unidentified spatial distribution of the karst collapse column triggered the accident directly. The high-pressure groundwater accumulated in the collapse column and the gallery excavation, which caused the redistribution of the in situ stress, contributing to progressive fractures in the floor of the No. 16 coal seam. Eventually, an intensive water-conductive passage consisting of the fractured floor and the karst collapse column formed. Administratively/technically, that mandatory regulations on gallery excavation were not carried out which contributed the accident. Moreover, the poor awareness about groundwater inrush recognition and quick remediation also contoirbuted to the disastrous extent of the accident. Full article

(This article belongs to the Special Issue Physical and Mathematical Fluid Mechanics)

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