scholarly journals Theoretical Foundation of Rapid Distortion Theory on Transversely Sheared Mean Flows

Fluids ◽  
2020 ◽  
Vol 5 (2) ◽  
pp. 62
Author(s):  
Marvin E. Goldstein
Keyword(s):  
Boundary Condition ◽  
General Theory ◽  
Fluid Mechanics ◽  
Theoretical Foundation ◽  
Surface Interactions ◽  
Velocity Fluctuations ◽  
Rapid Distortion Theory ◽  
Secondary Purpose ◽  
Physical Variables ◽  
General Conservation

The focus of this paper is on Rapid Distortion Theory on transversely sheared mean flows, which is often used to investigate turbulence-solid surface interactions. The main purpose of the paper is to bring together and present in a consistent fashion a general theory that has been developed in several different papers that have been published in the Journal of Fluid Mechanics. The equations for the unsteady pressure and velocity flections (which decouple from the entropy fluctuations) are rewritten in terms of a gauge function in order to obtain expressions that involve two arbitrarily convected quantities. A pair of very general conservation laws are used to derive upstream boundary conditions that relate these quantities to the actual physical variables. The entropy fluctuations can be determined after the fact once the solutions for the pressure and velocity fluctuations are known. The result involves a third arbitrary convected quantity that is equal to the entropy fluctuations at upstream infinity and can, therefore, be specified as an additional upstream boundary condition. A secondary purpose of the paper is to summarize a number of applications of the theory that have also appeared in the literature and show how they compare with an experiment.

Fundamentals concerning wave loading on offshore structures

1986 ◽  
Vol 173 ◽  
pp. 667-681 ◽  
Author(s):  
James Lighthill
Keyword(s):  
Fluid Mechanics ◽  
Natural Frequency ◽  
Potential Flow ◽  
Vortex Flow ◽  
Offshore Structures ◽  
Second Order ◽  
Mechanics Of Solids ◽  
Wave Loading ◽  
Velocity Fluctuations ◽  
Substantial Body

This article is aimed at relating a certain substantial body of established material concerning wave loading on offshore structures to fundamental principles of mechanics of solids and of fluids and to important results by G. I. Taylor (1928a,b). The object is to make some key parts within a rather specialised field accessible to the general fluid-mechanics reader.The article is concerned primarily to develop the ideas which validate a separation of hydrodynamic loadings into vortex-flow forces and potential-flow forces; and to clarify, as Taylor (1928b) first did, the major role played by components of the potential-flow forces which are of the second order in the amplitude of ambient velocity fluctuations. Recent methods for calculating these forces have proved increasingly important for modes of motion of structures (such as tension-leg platforms) of very low natural frequency.

Local fluid and heat flow near contact lines

1998 ◽  
Vol 371 ◽  
pp. 377-378
Author(s):  
D. M. Anderson ◽  
S. H. Davis
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Heat Flow ◽  
Fluid Mechanics ◽  
Contact Line ◽  
Thermal Boundary Condition ◽  
The Other ◽  
Private Communication ◽  
Contact Lines ◽  
Rigid Plane

Journal of Fluid Mechanics, vol. 268 (1994), pp. 231–265It has recently come to our attention that our paper, which describes Marangoni-driven flow near a contact line, overlooks solutions involving a general thermal boundary condition on the free surface (private communication, S. J. Tavener 1997). These new solutions are applicable for non-isothermal flows in a corner region where one boundary is a rigid plane (and either perfectly insulating or perfectly conducting) and the other is a free surface upon which a general thermal boundary condition is applied. We describe these additional solutions below.

scholarly journals General theory of legal design in law and economics framework of commercial contracting

2022 ◽  
pp. 205556362110616
Author(s):  
Katri Nousiainen
Keyword(s):  
Economic Theory ◽  
General Theory ◽  
Economic Analysis ◽  
Theoretical Foundation ◽  
Law And Economics ◽  
Real Life ◽  
Conventional Wisdom ◽  
Standard Theory ◽  
Microeconomic Theory ◽  
Economic Analysis Of Law

We need law and economics to do the scientific measurement necessary for legal design to be seen as on the stage of science. Law and economics—which is the application of economic theory, especially microeconomic theory, to the analysis and the practice of law--is a valid tool and approach to reflect on what should be empirically investigated in the practice of legal design. The neoclassical (mainstream) theoretical foundation of economic analysis of law is, however, at times far from reality as it often predicts uncooperative and even selfish behaviour. In real life people do cooperate, have empathy, emotions and even behave in an altruistic way. For those reasons, behavioural law and economics and conventional wisdom are needed to complement the teachings from standard theory in the field of commercial contracting.

scholarly journals Some possible legal approaches about ‘efficacy’ as research category of alternative methods for conflict solution (AMCS)

2018 ◽  
Vol 37 (75) ◽  
pp. 130-153
Author(s):  
Martha Eugenia Lezcano Miranda ◽  
Jorge Eduardo Vásquez-Santamaría
Keyword(s):  
General Theory ◽  
Metropolitan Area ◽  
General Principle ◽  
Theoretical Foundation ◽  
Alternative Methods ◽  
Research Approach ◽  
Methodological Development ◽  
Public Contracts ◽  
Conflict Solution ◽  
Analytical Category

By questioning the applicability of Alternative Methods for Conflict Solution (AMCS) in public contracts of working, consulting and concession in the Metropolitan Area of Valle de Aburrá in the light of Law 80 of 1993, itwas showed the absence of previous methodological construction on efcacy as analytical category of juridical setting and sociojuridical objects. So it is valid to ask which juridical approaches allow the category ‘efcacy’ tointermediate the object of some juridical research? This work is centered  in showing some possible implications of efcacy as category for juridicalresearch, by a theoretical foundation of its methodological development,from contributions of Law General Theory and statements about efcacy  as general principle in the practice of administrative function and public deals. From two proposed dimensions, in the conclusions is stated thatefcacy is a category that allows a particular research approach, resulting both in a defnite searching criterion and in the validation of juridical and sociojuridical objects, such as conflict resolution in public contracts.

The no-slip boundary condition in fluid mechanics

Resonance ◽  
2004 ◽  
Vol 9 (4) ◽  
pp. 50-60 ◽  
Author(s):  
Sandeep Prabhakara ◽  
M. D. Deshpande
Keyword(s):  
Boundary Condition ◽  
Fluid Mechanics ◽  
Slip Boundary Condition ◽  
Slip Boundary

The no-slip boundary condition in fluid mechanics

Resonance ◽  
2004 ◽  
Vol 9 (5) ◽  
pp. 61-71 ◽  
Author(s):  
Sandeep Prabhakara ◽  
M. D. Deshpande
Keyword(s):  
Boundary Condition ◽  
Fluid Mechanics ◽  
Slip Boundary Condition ◽  
Slip Boundary

scholarly journals Coherent structure of the convective boundary layer derived from large-eddy simulations

1989 ◽  
Vol 200 ◽  
pp. 511-562 ◽  
Author(s):  
Helmut Schmidt ◽  
Ulrich Schumann
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Large Scale ◽  
Three Dimensional ◽  
Large Eddy Simulations ◽  
Stable Layer ◽  
Convective Boundary ◽  
Velocity Fluctuations ◽  
Large Eddy ◽  
The Mean

Turbulence in the convective boundary layer (CBL) uniformly heated from below and topped by a layer of uniformly stratified fluid is investigated for zero mean horizontal flow using large-eddy simulations (LES). The Rayleigh number is effectively infinite, the Froude number of the stable layer is 0.09 and the surface roughness height relative to the height of the convective layer is varied between 10−6 and 10−2. The LES uses a finite-difference method to integrate the three-dimensional grid-volume-averaged Navier–Stokes equations for a Boussinesq fluid. Subgrid-scale (SGS) fluxes are determined from algebraically approximated second-order closure (SOC) transport equations for which all essential coefficients are determined from the inertial-range theory. The surface boundary condition uses the Monin–Obukhov relationships. A radiation boundary condition at the top of the computational domain prevents spurious reflections of gravity waves. The simulation uses 160 × 160 × 48 grid cells. In the asymptotic state, the results in terms of vertical mean profiles of turbulence statistics generally agree very well with results available from laboratory and atmospheric field experiments. We found less agreement with respect to horizontal velocity fluctuations, pressure fluctuations and dissipation rates, which previous investigations tend to overestimate. Horizontal spectra exhibit an inertial subrange. The entrainment heat flux at the top of the CBL is carried by cold updraughts and warm downdraughts in the form of wisps at scales comparable with the height of the boundary layer. Plots of instantaneous flow fields show a spoke pattern in the lower quarter of the CBL which feeds large-scale updraughts penetrating into the stable layer aloft. The spoke pattern has also been found in a few previous investigations. Small-scale plumes near the surface and remote from strong updraughts do not merge together but decay while rising through large-scale downdraughts. The structure of updraughts and downdraughts is identified by three-dimensional correlation functions and conditionally averaged fields. The mean circulation extends vertically over the whole boundary layer. We find that updraughts are composed of quasi-steady large-scale plumes together with transient rising thermals which grow in size by lateral entrainment. The skewness of the vertical velocity fluctuations is generally positive but becomes negative in the lowest mesh cells when the dissipation rate exceeds the production rate due to buoyancy near the surface, as is the case for very rough surfaces. The LES results are used to determine the root-mean-square value of the surface friction velocity and the mean temperature difference between the surface and the mixed layer as a function of the roughness height. The results corroborate a simple model of the heat transfer in the surface layer.

scholarly journals A theory of higher-order subtyping with type intervals

2021 ◽  
Vol 5 (ICFP) ◽  
pp. 1-30
Author(s):  
Sandro Stucki ◽  
Paolo G. Giarrusso
Keyword(s):  
General Theory ◽  
Theoretical Foundation ◽  
Bounded Operator ◽  
Higher Order ◽  
Important Type ◽  
Robust Implementation ◽  
Syntactic Approach

The calculus of Dependent Object Types (DOT) has enabled a more principled and robust implementation of Scala, but its support for type-level computation has proven insufficient. As a remedy, we propose F ·· ω , a rigorous theoretical foundation for Scala’s higher-kinded types. F ·· ω extends F <: ω with interval kinds , which afford a unified treatment of important type- and kind-level abstraction mechanisms found in Scala, such as bounded quantification, bounded operator abstractions, translucent type definitions and first-class subtyping constraints. The result is a flexible and general theory of higher-order subtyping. We prove type and kind safety of F ·· ω , as well as weak normalization of types and undecidability of subtyping. All our proofs are mechanized in Agda using a fully syntactic approach based on hereditary substitution.

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