Water waves and conjugate streams

1975 ◽  
Vol 70 (4) ◽  
pp. 663-671 ◽  
Author(s):  
G. Keady ◽  
J. Norbury
Keyword(s):  
Water Waves ◽  
Volume Flow Rate ◽  
Wave Train ◽  
Ideal Liquid ◽  
Volume Flow ◽  
Periodic Waves ◽  
Total Head ◽  
Steady Plane ◽  
Wave Properties ◽  
Horizontal Bottom

Steady plane periodic waves on the surface of an ideal liquid above a horizontal bottom are considered. The flow is irrotational. LetQdenote the volume flow rate,Rthe total head andSthe flow force for the wave train. Bounds on wave properties are obtained in terms of the properties of (i) the conjugate streams with the sameQandR, and (ii) the conjugate streams with the sameQandS.

On the existence theory for irrotational water waves

1978 ◽  
Vol 83 (1) ◽  
pp. 137-157 ◽  
Author(s):  
G. Keady ◽  
J. Norbury
Keyword(s):  
Water Waves ◽  
Volume Flow Rate ◽  
Ideal Liquid ◽  
Flow Speed ◽  
Existence Theory ◽  
Wave Solutions ◽  
Maximum Angle ◽  
Steady Plane ◽  
Image Position ◽  
The Waves

AbstractThis paper concerns steady plane periodic waves on the surface of an ideal liquid flowing above a horizontal bottom. The flow is irrotational. The volume flow rate is denoted by Q, the velocity potential by ø, the period in ø of the waves by 2L, and the maximum angle of inclination between the tangent to the surface and the horizontal by θm.Krasovskii (12) established that, at each fixed Q and L, there exist wave solutions for each value of θm strictly between zero and ⅙π. We establish that, at each fixed Q and L, there exist wave solutions for each value of qc strictly between c and zero. Here qc is the flow speed at the crest, andwhere g is the acceleration due to gravity. Krasovskii's set of solutions is included in the set that we obtain.

Contributions to the theory of stokes waves

1955 ◽  
Vol 51 (4) ◽  
pp. 713-736 ◽  
Author(s):  
S. C. De
Keyword(s):  
Wave Height ◽  
Flow Rate ◽  
Volume Flow Rate ◽  
Wave Theory ◽  
Finite Depth ◽  
Volume Flow ◽  
Steady Flows ◽  
Total Head ◽  
Stokes Waves ◽  
Fifth Order

ABSTRACTThe well-known Stokes theory (9, 10) of waves of permanent form in water of finite depth has been extended to the fifth order of approximation. The solutions have been first obtained in the form of equations for the space coordinates x and y as functions of the velocity potential Φ and stream function ψ. Expressions for the complex potential W in terms of the complex variable z ( = x + iy), the form of the wave profile, and the square of the wave velocity have been obtained to the fifth order.Expressions for the three physical quantities Q, R and S, where Q is the volume flow rate per unit span, R is the energy per unit mass (i.e. g times the total head, measuring heights from the bottom and pressures from atmospheric) and S is the momentum flow rate per unit spaa, corrected for pressure forces and divided by density, have been obtained to the fifth order. The values for the dimensionless quantities r = R/Rc and s = S/Sc, where Rc and Sc refer to the values of R and S for a critical stream of volume flow Q, are tabulated for certain values of the ratios mean depth to wavelength and amplitude to wavelength. The values of r and s thus obtained have been used to calculate the ratios of mean depth to wavelength and of wave height to wavelength according to the cnoidal wave theory as recently presented by Benjamin and Light-hill(1), and the results are found to be in satisfactory agreement with that from Stokes's theory for waves longer than six times the depth.The (r, s) diagram introduced in the recent work of Benjamin and Lighthill(1) has been further considered, and the unshaded part of the diagram referred to in that paper has been mapped with a network of curves for constant values of the ratios of mean depth to wavelength and of wave height to wavelength (Fig. 2). The third barrier to the existence of steady flows, corresponding to ‘waves of greatest height’ referred to in that paper, has also been indicated in Fig. 2.

Peristaltic transport of a conducting Jeffrey fluid in an inclined asymmetric channel

2014 ◽  
Vol 07 (06) ◽  
pp. 1450064 ◽  
Author(s):  
K. Vajravelu ◽  
S. Sreenadh ◽  
G. Sucharitha ◽  
P. Lakshminarayana
Keyword(s):  
Flow Rate ◽  
Magnetic Parameter ◽  
Volume Flow Rate ◽  
Wave Train ◽  
Pressure Rise ◽  
Volume Flow ◽  
Jeffrey Fluid ◽  
Physical Parameters ◽  
Asymmetric Channel ◽  
Inclined Asymmetric Channel

Peristaltic flow of a conducting Jeffrey fluid in an inclined asymmetric channel is investigated. The channel asymmetry is produced by considering a peristaltic wave train on the flexible walls of the channel with different amplitudes and phases. The nonlinear governing equations are solved analytically by a perturbation technique. The expressions for the stream function, axial velocity and the pressure rise per wavelength are determined in terms of the Jeffrey number λ1, the Froude number Fr, the perturbation parameter δ, the angle of inclination θ and the phase difference ϕ. Effects of the physical parameters on the velocity field and the pumping characteristics are discussed. It is observed that the size of the trapping bolus increase with an increase in the magnetic parameter and the volume flow rate. That is, the magnetic parameter and the volume flow rate have strong influence on the trapping bolus phenomenon.

scholarly journals Wind-Driven Waves on the Air-Water Interface

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 122
Author(s):  
Harvey Segur ◽  
Soroush Khadem
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Wave Train ◽  
Periodic Waves ◽  
Water Interface ◽  
Local Dynamics ◽  
Air Water Interface ◽  
The Waves ◽  
Two Fluid ◽  
Insight Into

An ocean swell refers to a train of periodic or nearly periodic waves. The wave train can propagate on the free surface of a body of water over very long distances. A great deal of the current study in the dynamics of water waves is focused on ocean swells. These swells are typically created initially in the neighborhood of an ocean storm, and then the swell propagates away from the storm in all directions. We consider a different kind of wave, called seas, which are created by and driven entirely by wind. These waves typically have no periodicity, and can rise and fall with changes in the wind. Specifically, this is a two-fluid problem, with air above a moveable interface, and water below it. We focus on the local dynamics at the air-water interface. Various properties at this locality have implications on the waves as a whole, such as pressure differentials and velocity profiles. The following analysis provides insight into the dynamics of seas, and some of the features of these intriguing waves, including a process known as white-capping.

The second approximation to cnoidal and solitary waves

1960 ◽  
Vol 9 (3) ◽  
pp. 430-444 ◽  
Author(s):  
E. V. Laitone
Keyword(s):  
Shallow Water ◽  
Solitary Waves ◽  
Water Waves ◽  
Expansion Method ◽  
Finite Amplitude ◽  
Periodic Waves ◽  
Shallow Water Theory ◽  
First Approximation ◽  
Systematic Development ◽  
Horizontal Bottom

The expansion method introduced by Friedrichs (1948) for the systematic development of shallow-water theory for water waves of large wavelength was used by Keller (1948) to obtain the first approximation for the finite-amplitude solitary wave of Boussinesq (1872) and Rayleigh (1876), as well as for periodic waves of permanent type, corresponding to the cnoidal waves of Korteweg & de Vries (1895).The present investigation extends Friedrich's method so as to include terms up to the fourth order from shallow-water theory for a flat horizontal bottom, and thereby obtains the complete second approximations to both cnoidal and solitary waves. These second approximations show that, unlike the first approximation, the vertical motions cannot be considered as negligible, and that the pressure variation is no longer hydrostatic.

Novel epoxy/anhydride alternatives for biological electron microscopy: Physical and performance characteristis of embed 812 and LX 112 in combination with NSA/NMA/DMAE

1989 ◽  
Vol 47 ◽  
pp. 1000-1001
Author(s):  
Joe A. Mascorro ◽  
Gerald S. Kirby
Keyword(s):  
Electron Microscopy ◽  
Flow Rate ◽  
Succinic Anhydride ◽  
Volume Flow Rate ◽  
Mass Density ◽  
Uranyl Acetate ◽  
Volume Flow ◽  
Base Resin ◽  
And Performance ◽  
Acid Anhydrides

Embedding media based upon an epoxy resin of choice and the acid anhydrides dodecenyl succinic anhydride (DDSA), nadic methyl anhydride (NMA), and catalyzed by the tertiary amine 2,4,6-Tri(dimethylaminomethyl) phenol (DMP-30) are widely used in biological electron microscopy. These media possess a viscosity character that can impair tissue infiltration, particularly if original Epon 812 is utilized as the base resin. Other resins that are considerably less viscous than Epon 812 now are available as replacements. Likewise, nonenyl succinic anhydride (NSA) and dimethylaminoethanol (DMAE) are more fluid than their counterparts DDSA and DMP- 30 commonly used in earlier formulations. This work utilizes novel epoxy and anhydride combinations in order to produce embedding media with desirable flow rate and viscosity parameters that, in turn, would allow the medium to optimally infiltrate tissues. Specifically, embeding media based on EmBed 812 or LX 112 with NSA (in place of DDSA) and DMAE (replacing DMP-30), with NMA remaining constant, are formulated and offered as alternatives for routine biological work.Individual epoxy resins (Table I) or complete embedding media (Tables II-III) were tested for flow rate and viscosity. The novel media were further examined for their ability to infilftrate tissues, polymerize, sectioning and staining character, as well as strength and stability to the electron beam and column vacuum. For physical comparisons, a volume (9 ml) of either resin or media was aspirated into a capillary viscocimeter oriented vertically. The material was then allowed to flow out freely under the influence of gravity and the flow time necessary for the volume to exit was recored (Col B,C; Tables). In addition, the volume flow rate (ml flowing/second; Col D, Tables) was measured. Viscosity (n) could then be determined by using the Hagen-Poiseville relation for laminar flow, n = c.p/Q, where c = a geometric constant from an instrument calibration with water, p = mass density, and Q = volume flow rate. Mass weight and density of the materials were determined as well (Col F,G; Tables). Infiltration schedules utilized were short (1/2 hr 1:1, 3 hrs full resin), intermediate (1/2 hr 1:1, 6 hrs full resin) , or long (1/2 hr 1:1, 6 hrs full resin) in total time. Polymerization schedules ranging from 15 hrs (overnight) through 24, 36, or 48 hrs were tested. Sections demonstrating gold interference colors were collected on unsupported 200- 300 mesh grids and stained sequentially with uranyl acetate and lead citrate.

Slip And Hall Effects On The Flow Of A Hyperbolic Tangent Fluid Through Porous Medium In A Planar Channel With Peristalsis

GIS Business ◽  
2020 ◽  
Vol 15 (1) ◽  
pp. 383-394
Author(s):  
K. Shalini ◽  
K.Rajasekhar
Keyword(s):  
Porous Medium ◽  
Pressure Gradient ◽  
Volume Flow Rate ◽  
Perturbation Technique ◽  
Volume Flow ◽  
Planar Channel ◽  
Hyperbolic Tangent ◽  
Closed Form Solutions ◽  
Long Wavelength ◽  
Hall Effects

In this paper, the effect of Slip and Hall effects on the flow of Hyperbolic tangent fluid through a porous medium in a planar channel with peristalsis under the assumption of long wavelength is investigated. A Closed form solutions are obtained for axial velocity and pressure gradient by employing perturbation technique. The effects of various emerging parameters on the pressure gradient, time averaged volume flow rate and frictional force are discussed with the aid of graphs.

Multi-objective optimization of squirrel cage fan for range hood based on Kriging model

2021 ◽  
pp. 095440622199586
Author(s):  
Qianhao Xiao ◽  
Jun Wang ◽  
Boyan Jiang ◽  
Weigang Yang ◽  
Xiaopei Yang
Keyword(s):  
Flow Rate ◽  
Optimization Design ◽  
Volume Flow Rate ◽  
Kriging Model ◽  
Volume Flow ◽  
Design Parameters ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Squirrel Cage

In view of the multi-objective optimization design of the squirrel cage fan for the range hood, a blade parameterization method based on the quadratic non-uniform B-spline (NUBS) determined by four control points was proposed to control the outlet angle, chord length and maximum camber of the blade. Morris-Mitchell criteria were used to obtain the optimal Latin hypercube sample based on the evolutionary operation, and different subsets of sample numbers were created to study the influence of sample numbers on the multi-objective optimization results. The Kriging model, which can accurately reflect the response relationship between design variables and optimization objectives, was established. The second-generation Non-dominated Sorting Genetic algorithm (NSGA-II) was used to optimize the volume flow rate at the best efficiency point (BEP) and the maximum volume flow rate point (MVP). The results show that the design parameters corresponding to the optimization results under different sample numbers are not the same, and the fluctuation range of the optimal design parameters is related to the influence of the design parameters on the optimization objectives. Compared with the prototype, the optimized impeller increases the radial velocity of the impeller outlet, reduces the flow loss in the volute, and increases the diffusion capacity, which improves the volume flow rate, and efficiency of the range hood system under multiple working conditions.

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