Viscous gravity currents over flat inclined surfaces

2021 ◽  
Vol 931 ◽  
Author(s):  
Herbert E. Huppert ◽  
Vitaly A. Kuzkin ◽  
Svetlana O. Kraeva
Keyword(s):  
Boundary Conditions ◽  
Pressure Gradient ◽  
Direct Action ◽  
Gravity Currents ◽  
Analytic Solutions ◽  
High Accuracy ◽  
Square Root ◽  
Inclined Surfaces ◽  
Inclined Planes ◽  
Short Times

Previous analyses of the flow of low-Reynolds-number, viscous gravity currents down inclined planes are investigated further and extended. Particular emphasis is on the motion of the fluid front and tail, which previous analyses treated somewhat cavalierly. We obtain reliable, approximate, analytic solutions in these regions, the accuracies of which are satisfactorily tested against our numerical evaluations. The solutions show that the flow has several time scales determined by the inclination angle, $\alpha$ . At short times, the influence of initial and boundary conditions is important and the flow is governed by both the pressure gradient and the direct action of gravity due to inclination. Later on, the areas where the boundary conditions are important shrink. This fact explains why previous solutions, being inaccurate near the front and the tail, described experimental data with high accuracy. At larger times, of the order of $\alpha ^{-5/2}$ , the influence of the pressure gradient may be neglected and the fluid profile converges to the square-root shape predicted in previous works. Important extensions of our approach are also outlined.

Analytic solutions of the scattering by two multilayered dielectric spheres

1992 ◽  
Vol 70 (9) ◽  
pp. 696-705 ◽  
Author(s):  
A-K. Hamid ◽  
I. R. Ciric ◽  
M. Hamid
Keyword(s):  
Boundary Conditions ◽  
Cross Sections ◽  
Plane Electromagnetic Wave ◽  
Expansion Method ◽  
Analytic Solutions ◽  
Addition Theorem ◽  
Modal Expansion ◽  
Modal Expansion Method ◽  
Dielectric Spheres ◽  
Scattered Fields

The problem of plane electromagnetic wave scattering by two concentrically layered dielectric spheres is investigated analytically using the modal expansion method. Two different solutions to this problem are obtained. In the first solution the boundary conditions are satisfied simultaneously at all spherical interfaces, while in the second solution an iterative approach is used and the boundary conditions are satisfied successively for each iteration. To impose the boundary conditions at the outer surface of the spheres, the translation addition theorem of the spherical vector wave functions is employed to express the scattered fields by one sphere in the coordiante system of the other sphere. Numerical results for the bistatic and back-scattering cross sections are presented graphically for various sphere sizes, layer thicknesses and permittivities, and angles of incidence.

scholarly journals Direct Action of Light in Naturally Pigmented Muscle Fibers

1962 ◽  
Vol 46 (2) ◽  
pp. 333-342 ◽  
Author(s):  
Howard H. Seliger
Keyword(s):  
Visual Pigment ◽  
Absorption Maximum ◽  
Pupil Diameter ◽  
Direct Action ◽  
Pigment Epithelium ◽  
Action Spectrum ◽  
Square Root ◽  
Light Reaction ◽  
First Order ◽  
Iris Sphincter

Contraction due to light in excised eel irises appears to follow a simple first order law. The action spectrum for contraction has a maximum which agrees with the eel rhodopsin absorption maximum. Inasmuch as rhodopsin is the rod pigment-opsin complex and the iris sphincter pupillae evolves from the pigment epithelium of the retina in the region of the iris, the muscle pigment might be the same as the visual pigment. In the human eye the contraction of the iris sphincter is activated only by light incident on the retina and the pupil diameter varies inversely with the square root of the light intensity. The inverse first power relation observed in the present experiments suggests a more primitive origin for the light reaction in eel irises. Relaxation is a much slower process and can be approximated as the sum of two first order processes.

scholarly journals Application of the successive approximation method to the analysis of bending plates

2018 ◽  
Vol 251 ◽  
pp. 04058
Author(s):  
Radek Gabbasov ◽  
Vladimir Filatov ◽  
Nikita Ryasny
Keyword(s):  
Boundary Conditions ◽  
Successive Approximation ◽  
Approximation Method ◽  
High Accuracy ◽  
Numerical Results ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Successive Approximation Method ◽  
Medium Thickness ◽  
Bending Plates

This work presents an algorithm for calculating the bending plates of medium thickness according to the Reissner’. To obtain numerical results, the method of successive approximations (MSA) is used. This method has high accuracy and fast convergence, which was confirmed by the solution of a range of tasks. Publication of the results of the calculation of plates of medium thickness with the boundary conditions revised here is supposed to be in the following articles.

scholarly journals High Accuracy Buoyancy for Underwater Gliders: The Uncertainty in the Depth Control

Sensors ◽  
2019 ◽  
Vol 19 (8) ◽  
pp. 1831 ◽  
Author(s):  
Enrico Petritoli ◽  
Fabio Leccese ◽  
Marco Cagnetti
Keyword(s):  
Boundary Conditions ◽  
High Accuracy ◽  
Science Department ◽  
Underwater Gliders ◽  
Depth Control

This paper is a section of several preliminary studies of the Underwater Drones Group of the Università degli Studi “Roma Tre” Science Department: We describe the study philosophy, the theoretical technological considerations for sizing and the development of a technological demonstrator of a high accuracy buoyancy and depth control. We develop the main requirements and the boundary conditions that design the buoyancy system and develop the mathematical conditions that define the main parameters.

scholarly journals The square root problem for second-order, divergence form operators with mixed boundary conditions on L p

2014 ◽  
Vol 15 (1) ◽  
pp. 165-208 ◽  
Author(s):  
Pascal Auscher ◽  
Nadine Badr ◽  
Robert Haller-Dintelmann ◽  
Joachim Rehberg
Keyword(s):  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Divergence Form ◽  
Second Order ◽  
Square Root

Cellular‐automaton fluids: A model for flow in porous media

Geophysics ◽  
1988 ◽  
Vol 53 (4) ◽  
pp. 509-518 ◽  
Author(s):  
Daniel H. Rothman
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Numerical Methods ◽  
Boundary Conditions ◽  
Pressure Gradient ◽  
Cellular Automaton ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Cellular Automaton Fluids

Numerical models of fluid flow through porous media can be developed from either microscopic or macroscopic properties. The large‐scale viewpoint is perhaps the most prevalent. Darcy’s law relates the chief macroscopic parameters of interest—flow rate, permeability, viscosity, and pressure gradient—and may be invoked to solve for any of these parameters when the others are known. In practical situations, however, this solution may not be possible. Attention is then typically focused on the estimation of permeability, and numerous numerical methods based on knowledge of the microscopic pore‐space geometry have been proposed. Because the intrinsic inhomogeneity of porous media makes the application of proper boundary conditions difficult, microscopic flow calculations have typically been achieved with idealized arrays of geometrically simple pores, throats, and cracks. I propose here an attractive alternative which can freely and accurately model fluid flow in grossly irregular geometries. This new method solves the Navier‐Stokes equations numerically using the cellular‐automaton fluid model introduced by Frisch, Hasslacher, and Pomeau. The cellular‐ automaton fluid is extraordinarily simple—particles of unit mass traveling with unit velocity reside on a triangular lattice and obey elementary collision rules—but is capable of modeling much of the rich complexity of real fluid flow. Cellular‐automaton fluids are applicable to the study of porous media. In particular, numerical methods can be used to apply the appropriate boundary conditions, create a pressure gradient, and measure the permeability. Scale of the cellular‐automaton lattice is an important issue; the linear dimension of a void region must be approximately twice the mean free path of a lattice gas particle. Finally, an example of flow in a 2-D porous medium demonstrates not only the numerical solution of the Navier‐Stokes equations in a highly irregular geometry, but also numerical estimation of permeability and a verification of Darcy’s law.

scholarly journals Rayleigh-Bѐnard Convection in a Second-Order Fluid with Maxwell-Cattaneo Law

2012 ◽  
Vol 2 ◽  
pp. 24-32 ◽  
Author(s):  
Smita Saklesh Nagouda ◽  
Subbarama Pranesh
Keyword(s):  
Boundary Conditions ◽  
Critical Rayleigh Number ◽  
Propagation Speed ◽  
Heat Propagation ◽  
Second Order ◽  
Onset Of Convection ◽  
Eigen Value ◽  
Eigen Values ◽  
Heat Flux Law ◽  
Short Times

The objective of the paper is to study the Rayleigh-Bѐnard convection in second order fluid by replacing the classical Fourier heat law by non-classical Maxwell-Cattaneo law using Galerkin technique. The eigen value of the problem is obtained using the general boundary conditions on velocity and third type of boundary conditions on temperature. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analyzed. The classical Fourier flux law over predicts the critical Rayleigh number compared to that predicted by the non-classical law. The present non-classical Maxwell-Cattaneo heat flux law involves a wave type heat transport (SECOND SOUND) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. It is found that the results are noteworthy at short times and the critical eigen values are less than the classical ones. Over stability is the preferred mode of convection.

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