Wave transformation by a vertical barrier between a single-layer fluid and a two-layer fluid

2000 ◽  
Vol 214 (6) ◽  
pp. 759-769
Author(s):  
M M Lee ◽  
A T Chwang
Keyword(s):  
Water Waves ◽  
Lower Layer ◽  
Wave Transformation ◽  
Linear Wave ◽  
Type I ◽  
Type Ii ◽  
Homogeneous Fluid ◽  
Reflection And Transmission ◽  
Vertical Barrier ◽  
Wave Modes

The reflection and transmission of water waves by a vertical barrier between a homogeneous fluid and a two-layer fluid are investigated for two different types of barrier: type I is a surface-piercing barrier and type II a bottom-standing barrier. For a type I barrier, the lower-layer fluid is the same as the homogeneous fluid and has a higher density than that of the upper-layer fluid. For a type II barrier, the upper layer fluid is the same as the homogeneous fluid and has a lower density than that of the lower-layer fluid. For any given finite thickness of the fluid layers, a hydrostatic equilibrium state exists. Incident progressive waves can then be transmitted through the gap beneath or above the barrier. By using the linear wave theory and eigenfunction expansions, these boundary value problems are solved by a suitable application of the least-squares method. The definitions of the corresponding reflection and transmission coefficients are introduced in each case. For the two-layer fluid, there are two different wave modes: the surface (barotropic) and interfacial (baroclinic) wave modes. It is found that water waves, propagating either from the homogeneous or from the two-layer fluid, are partially reflected or transmitted and produce simultaneously both modes of water waves in the two-layer fluid.

Characteristics of Bragg Reflection of Water Waves by Multiple Vertical Flexible Membranes

2018 ◽  
Author(s):  
Wei-Wei Ding ◽  
Zao-Jian Zou ◽  
Jing-Ping Wu
Keyword(s):  
Water Waves ◽  
Bragg Reflection ◽  
Least Square ◽  
Reflection And Transmission Coefficients ◽  
Effective Bandwidth ◽  
Linear Wave ◽  
Reflection And Transmission ◽  
Flexible Membrane ◽  
Transmission Coefficients ◽  
Flexible Membranes

Bragg reflection of water waves by multiple vertical flexible membranes in water of uniform depth is investigated based on the assumption of linear wave theory and small membrane deflection. The multiple vertical flexible membranes consist of several floating vertical flexible membranes which are installed with both ends fixed. First, a single vertical flexible membrane in water waves is considered, and the reflection and transmission coefficients are obtained based on the eigenfunction expansion method and the least square method. Then the interaction of water waves with the multiple vertical flexible membranes is studied. Using the reflection and transmission coefficients obtained for the single flexible membrane, the reflection and transmission coefficients of the multiple vertical flexible membranes are obtained based on the wide spacing approximation. The proposed method is proved to be efficient by comparing the calculated coefficients with the results published in literature. The characteristics of Bragg reflection, such as the occurring condition, the primary amplitude and the effective bandwidth, are systematically investigated under various factors including the number, the tension, the draft and the spacing of membranes. The results of the present study have certain reference value for design of multiple vertical flexible membranes as effective floating breakwaters.

The influence of surface tension on the reflection of water waves by a plane vertical barrier

1968 ◽  
Vol 64 (3) ◽  
pp. 795-810 ◽  
Author(s):  
D. V. Evans
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Related Problem ◽  
Velocity Potential ◽  
Surface Tension Force ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Reflected Wave ◽  
Vertical Barrier ◽  
Effect Of Surface

AbstractIn this paper the effect of surface tension is included in a well-known problem in the theory of two-dimensional infinitesimal water waves. The problem is that of the reflection of waves from a fixed vertical barrier immersed to a depth a into deep water. It is shown how the solution for the velocity potential may be determined uniquely when simple assumptions are made concerning the behaviour of the free surface near the barrier. In particular, expressions are derived for the reflection coefficient, defined as the ratio of the amplitude of the reflected wave to that of the incident wave, at infinity, and the transmission coefficient, defined similarly. It is shown how these coefficients, for small values of the surface tension force, tend to the values obtained by Ursell (4) when surface tension is ignored. The related problem of a completely immersed vertical barrier extending to a distance a from the surface may be solved in a similar manner. Expressions for the reflection and transmission coefficients for this case are given.

Reflection and transmission from porous structures under oblique wave attack

1991 ◽  
Vol 224 ◽  
pp. 625-644 ◽  
Author(s):  
Robert A. Dalrymple ◽  
Miguel A. Losada ◽  
P. A. Martin
Keyword(s):  
Porous Medium ◽  
Plane Wave ◽  
Water Waves ◽  
Normal Wave ◽  
Eigenfunction Expansions ◽  
Reflection And Transmission ◽  
Oblique Wave ◽  
Water Region ◽  
Wave Incidence ◽  
Wave Modes

The linear theory for water waves impinging obliquely on a vertically sided porous structure is examined. For normal wave incidence, the reflection and transmission from a porous breakwater has been studied many times using eigenfunction expansions in the water region in front of the structure, within the porous medium, and behind the structure in the down-wave water region. For oblique wave incidence, the reflection and transmission coefficients are significantly altered and they are calculated here.Using a plane-wave assumption, which involves neglecting the evanescent eigenmodes that exist near the structure boundaries (to satisfy matching conditions), the problem can be reduced from a matrix problem to one which is analytic. The plane-wave approximation provides an adequate solution for the case where the damping within the structure is not too great.An important parameter in this problem is Γ2= ω2h(s- if)/g, where ω is the wave angular frequency,hthe constant water depth,gthe acceleration due to gravity, andsandfare parameters describing the porous medium. As the friction in the porous medium,f, becomes non-zero, the eigenfunctions differ from those in the fluid regions, largely owing to the change in the modal wavenumbers, which depend on Γ2.For an infinite number of values of ΓF2, there are no eigenfunction expansions in the porous medium, owing to the coalescence of two of the wavenumbers. These cases are shown to result in a non-separable mathematical problem and the appropriate wave modes are determined. As the two wavenumbers approach the critical value of Γ2, it is shown that the wave modes can swap their identity.

Heat-Etching with a Bullivant Type II Simple Freeze-Cleave Device

1970 ◽  
Vol 28 ◽  
pp. 106-107 ◽  
Author(s):  
Ronald S. Weinstein ◽  
N. Scott McNutt
Keyword(s):  
New Zealand ◽  
General Hospital ◽  
Massachusetts General Hospital ◽  
Type I ◽  
Type Ii ◽  
Collaborative Effort ◽  
Temperature And Pressure ◽  
The University

The Type I simple cold block device was described by Bullivant and Ames in 1966 and represented the product of the first successful effort to simplify the equipment required to do sophisticated freeze-cleave techniques. Bullivant, Weinstein and Someda described the Type II device which is a modification of the Type I device and was developed as a collaborative effort at the Massachusetts General Hospital and the University of Auckland, New Zealand. The modifications reduced specimen contamination and provided controlled specimen warming for heat-etching of fracture faces. We have now tested the Mass. General Hospital version of the Type II device (called the “Type II-MGH device”) on a wide variety of biological specimens and have established temperature and pressure curves for routine heat-etching with the device.

Labelling of non-A, non-B hepatitis infected chimpanzee hepatocytes with nuclease-gold conjugates

1984 ◽  
Vol 42 ◽  
pp. 250-251
Author(s):  
G. D. Gagne ◽  
M. F. Miller ◽  
D. A. Peterson
Keyword(s):  
Endoplasmic Reticulum ◽  
Experimental Infection ◽  
Uranyl Acetate ◽  
Type I ◽  
Cellular Injury ◽  
Type Ii ◽  
Tubular Structures ◽  
Type Iii ◽  
Type Iv ◽  
Infected Chimpanzee

Experimental infection of chimpanzees with non-A, non-B hepatitis (NANB) or with delta agent hepatitis results in the appearance of characteristic cytoplasmic alterations in the hepatocytes. These alterations include spongelike inclusions (Type I), attached convoluted membranes (Type II), tubular structures (Type III), and microtubular aggregates (Type IV) (Fig. 1). Type I, II and III structures are, by association, believed to be derived from endoplasmic reticulum and may be morphogenetically related. Type IV structures are generally observed free in the cytoplasm but sometimes in the vicinity of type III structures. It is not known whether these structures are somehow involved in the replication and/or assembly of the putative NANB virus or whether they are simply nonspecific responses to cellular injury. When treated with uranyl acetate, type I, II and III structures stain intensely as if they might contain nucleic acids. If these structures do correspond to intermediates in the replication of a virus, one might expect them to contain DNA or RNA and the present study was undertaken to explore this possibility.

Comparative surface and ultrastructural views of methylotrophic bacteria by TEM, STEM, SE, and freeze-etch electron microscopy.

1987 ◽  
Vol 45 ◽  
pp. 792-793
Author(s):  
T.A. Fassel ◽  
M.J. Schaller ◽  
M.E. Lidstrom ◽  
C.C. Remsen
Keyword(s):  
Cytoplasmic Membrane ◽  
Structural Features ◽  
Methylotrophic Bacteria ◽  
Type I ◽  
Type Ii ◽  
Membrane Complex ◽  
Oxidation Of Methane ◽  
Methane Oxidizing Bacteria ◽  
Wall Structures ◽  
Methylomonas Albus

Methylotrophic bacteria play an Important role in the environment in the oxidation of methane and methanol. Extensive intracytoplasmic membranes (ICM) have been associated with the oxidation processes in methylotrophs and chemolithotrophic bacteria. Classification on the basis of ICM arrangement distinguishes 2 types of methylotrophs. Bundles or vesicular stacks of ICM located away from the cytoplasmic membrane and extending into the cytoplasm are present in Type I methylotrophs. In Type II methylotrophs, the ICM form pairs of peripheral membranes located parallel to the cytoplasmic membrane. Complex cell wall structures of tightly packed cup-shaped subunits have been described in strains of marine and freshwater phototrophic sulfur bacteria and several strains of methane oxidizing bacteria. We examined the ultrastructure of the methylotrophs with particular view of the ICM and surface structural features, between representatives of the Type I Methylomonas albus (BG8), and Type II Methylosinus trichosporium (OB-36).

OPTICAL STUDIES OF TYPE I AND TYPE II RECOMBINATION IN GaAs-AlAs QUANTUM WELLS

1987 ◽  
Vol 48 (C5) ◽  
pp. C5-525-C5-528 ◽  
Author(s):  
K. J. MOORE ◽  
P. DAWSON ◽  
C. T. FOXON
Keyword(s):  
Quantum Wells ◽  
Type I ◽  
Type Ii ◽  
Optical Studies

An old friend is better than two new ones? Approaches to market research in the context of digital transformation for the antitrust laws enforcement

2020 ◽  
pp. 37-55 ◽  
Author(s):  
A. E. Shastitko ◽  
O. A. Markova
Keyword(s):  
Business Models ◽  
Rapid Development ◽  
Digital Transformation ◽  
Market Definition ◽  
Type I ◽  
Type Ii ◽  
Digital Platforms ◽  
Advantages And Disadvantages ◽  
Pass Through ◽  
Type Ii Errors

Digital transformation has led to changes in business models of traditional players in the existing markets. What is more, new entrants and new markets appeared, in particular platforms and multisided markets. The emergence and rapid development of platforms are caused primarily by the existence of so called indirect network externalities. Regarding to this, a question arises of whether the existing instruments of competition law enforcement and market analysis are still relevant when analyzing markets with digital platforms? This paper aims at discussing advantages and disadvantages of using various tools to define markets with platforms. In particular, we define the features of the SSNIP test when being applyed to markets with platforms. Furthermore, we analyze adjustment in tests for platform market definition in terms of possible type I and type II errors. All in all, it turns out that to reduce the likelihood of type I and type II errors while applying market definition technique to markets with platforms one should consider the type of platform analyzed: transaction platforms without pass-through and non-transaction matching platforms should be tackled as players in a multisided market, whereas non-transaction platforms should be analyzed as players in several interrelated markets. However, if the platform is allowed to adjust prices, there emerges additional challenge that the regulator and companies may manipulate the results of SSNIP test by applying different models of competition.

Sign in / Sign up

Export Citation Format

Share Document