A fully nonlinear Boussinesq model for surface waves. Part 2. Extension to O(kh)4

2000 ◽  
Vol 405 ◽  
pp. 181-210 ◽  
Author(s):  
MAURÍCIO F. GOBBI ◽  
JAMES T. KIRBY ◽  
GE WEI
Keyword(s):  
Velocity Potential ◽  
Model Performance ◽  
Weighted Average ◽  
Type Model ◽  
Surface Boundary ◽  
Boussinesq Model ◽  
Weakly Nonlinear ◽  
Surface Boundary Condition ◽  
Full Solution ◽  
Model Equations

A Boussinesq-type model is derived which is accurate to O(kh)4 and which retains the full representation of the fluid kinematics in nonlinear surface boundary condition terms, by not assuming weak nonlinearity. The model is derived for a horizontal bottom, and is based explicitly on a fourth-order polynomial representation of the vertical dependence of the velocity potential. In order to achieve a (4,4) Padé representation of the dispersion relationship, a new dependent variable is defined as a weighted average of the velocity potential at two distinct water depths. The representation of internal kinematics is greatly improved over existing O(kh)2 approximations, especially in the intermediate to deep water range. The model equations are first examined for their ability to represent weakly nonlinear wave evolution in intermediate depth. Using a Stokes-like expansion in powers of wave amplitude over water depth, we examine the bound second harmonics in a random sea as well as nonlinear dispersion and stability effects in the nonlinear Schrödinger equation for a narrow-banded sea state. We then examine numerical properties of solitary wave solutions in shallow water, and compare model performance to the full solution of Tanaka (1986) as well as the level 1, 2 and 3 solutions of Shields & Webster (1988).

Calculation of the Streamlines About a Ship Assuming a Linearized Free-Surface Boundary Condition

1973 ◽  
Vol 17 (03) ◽  
pp. 140-146
Author(s):  
Bruce H. Adee
Keyword(s):  
Boundary Condition ◽  
Fluid Flow ◽  
Free Surface ◽  
Boundary Value Problem ◽  
Velocity Potential ◽  
Potential Surface ◽  
Inviscid Fluid ◽  
Surface Boundary ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Condition

The problem of computing the inviscid-fluid flow about a ship hull is investigated. A boundary- value problem, including a linearized free-surface boundary condition, is posed for the velocity potential. Singularities distributed over the hull surface are used to determine this potential. Surface streamlines are computed by numerically integrating a set of differential equations along the hull surface. A sample calculation for a Series 60, block coefficient 0.60 hull at a Froude number of 0.259 is included.

scholarly journals Physics of Traveling Waves in Shallow Water Environment

Water ◽  
2021 ◽  
Vol 13 (21) ◽  
pp. 2990
Author(s):  
Igor Shugan ◽  
Sergey Kuznetsov ◽  
Yana Saprykina ◽  
Yang-Yih Chen
Keyword(s):  
Traveling Waves ◽  
Water Environment ◽  
Stokes Wave ◽  
Type Model ◽  
Intermediate Water ◽  
Boussinesq Model ◽  
Weakly Nonlinear ◽  
Shallow Water Environment ◽  
Fifth Order ◽  
Wave Properties

We present a study of the physical characteristics of traveling waves at shallow and intermediate water depths. The main subject of study is to the influence of nonlinearity on the dispersion properties of waves, their limiting heights and steepness, the shape of solitary waves, etc. A fully nonlinear Serre–Green–Naghdi-type model, a classical weakly nonlinear Boussinesq model and fifth-order Stokes wave solutions were chosen as models for comparison. The analysis showed significant, if not critical, differences in the effect of nonlinearity on the properties of traveling waves for these models. A comparison with experiments was carried out on the basis of the results of a joint Russian–Taiwanese experiment, which was carried out in 2015 at the Tainan Hydraulic Laboratory, and on available experimental data. A comparison with the experimental results confirms the applicability of a completely nonlinear model for calculating traveling waves over the entire range of applicability of the model in contrast to the Boussinesq model, which shows contradictory and unrealistic wave properties for moderate wavelengths.

Optimisation of Nickel Aluminising by CVD

2012 ◽  
Vol 323-325 ◽  
pp. 367-372 ◽  
Author(s):  
Patrick J. Masset ◽  
Agnieszka Bogusz ◽  
Jan Sieniawski ◽  
Bartek Wierzba ◽  
Katarzyna Tkacz-Śmiech
Keyword(s):  
Substrate Surface ◽  
Chemical Vapour ◽  
Aluminium Chloride ◽  
Aluminium Content ◽  
Surface Boundary ◽  
Essential Information ◽  
Nial Phase ◽  
Partial Pressures ◽  
State Diffusion ◽  
Surface Boundary Condition

Results Concerning Nickel Aluminisation with Application of Chemical Vapour Deposition Method Are Presented. Two-Step Processing under Investigation Consists of Al Chloride Formation in the Primary Vessel and Al Deposition in the Secondary One. the Initial Gas Stream Is Composed of Hcl Dissolved in H2at Various Ratios. it Was Shown that the Choice of the [HCl]/[H2] Ratio and the Determination of the Optimum Temperature to Produce Most Preferential β-Nial Phase May Be Done with the Use of Thermodynamic Calculations. the Results Obtained with Application of Factsage Program Confirm Essential Influence of both Initial [HCl]/[H2] Ratio (in the Range between 0,05 and 100) and the Temperature in the Second Vessel (1123 K – 1323 K) on Aluminium Chloride Partial Pressures and Hence Aluminium Content in its Gaseous Donors and at the Substrate Surface (boundary Condition for Interdiffusion in Ni-Al System). it Was Confirmed that β-Nial Growth Is Favoured at Low [HCl]/[H2] Ratios and High Temperatures for which Alcl and AlCl2Partial Pressures Increase with Respect to that of AlCl3. the Thermodynamic Predictions Remain in Agreement with CVD Experiments. the Presented Thermodynamic Data May Be Used as a Source of Essential Information for Designing Further Experiments in this Field as Well as for Modelling of Solid-State Diffusion in Ni-Al System.

The Effect of Journal Bearing Misalignment on Load and Cavitation for Non-Newtonian Lubricants

1986 ◽  
Vol 108 (4) ◽  
pp. 645-654 ◽  
Author(s):  
R. H. Buckholz ◽  
J. F. Lin
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Journal Bearings ◽  
Surface Boundary ◽  
Film Rupture ◽  
Aspect Ratios ◽  
Free Surface Boundary Condition ◽  
Load Carrying ◽  
Boundary Location ◽  
Surface Boundary Condition

An analysis for hydrodynamic, non-Newtonian lubrication of misaligned journal bearings is given. The hydrodynamic load-carrying capacity for partial arc journal bearings lubricated by power-law, non-Newtonian fluids is calculated for small valves of the bearing aspect ratios. These results are compared with: numerical solutions to the non-Newtonian modified Reynolds equation, with Ocvirk’s experimental results for misaligned bearings, and with other numerical simulations. The cavitation (i.e., film rupture) boundary location is calculated using the Reynolds’ free-surface, boundary condition.

SERIES SOLUTION OF TYPHOID FEVER MODEL USING DIFFERENTIAL TRANSFORM METHOD

2018 ◽  
Vol 3 (1) ◽  
pp. 67
Author(s):  
O J Peter ◽  
Oluwaseun B Akinduko ◽  
C Y Ishola ◽  
O A Afolabi ◽  
A B Ganiyu
Keyword(s):  
Typhoid Fever ◽  
Disease Transmission ◽  
Series Solution ◽  
Transformation Method ◽  
Type Model ◽  
Transform Method ◽  
Runge Kutta Method ◽  
Differential Transform ◽  
Model Equations ◽  
Non Linear System

This paper presents an analysis of PSIuIeTR type model, which are used to study the transmission dynamics of typhoid fever diseases in a population. Basic idea of typhoid fever disease transmission using compartmental modeling is discussed. Differential Transformation Method (DTM) is discussed in detail, which is used to compute the series solution of the non-linear system of differential equation governing the model equations. The validity of the (DTM) in solving the proposed model is established by classical fourth-order Runge-Kutta method which is implemented in Maple 18. Graphical results confirm that (DTM) is in good agreement with RK-4 and this produced correctly same behaviour of the model, thus validating the efficiency and accuracy of (DTM) in finding the series solution of an epidemic model.

Natural convection in porous media: effect of weak dispersion on bifurcation

1990 ◽  
Vol 216 ◽  
pp. 285-298 ◽  
Author(s):  
Xiaowei S. He ◽  
John G. Georgiadis
Keyword(s):  
Effective Conductivity ◽  
Horizontal Layer ◽  
Hydrodynamic Dispersion ◽  
The Novel ◽  
Media Effect ◽  
Boussinesq Model ◽  
Weakly Nonlinear ◽  
Volumetric Heating ◽  
Pitchfork Bifurcations ◽  
The Impact

We use weakly nonlinear analysis via a two-parameter expansion to study bifurcation of conduction into cellular convection of an internally heated fluid in a porous medium that forms a horizontal layer between two isothermal walls. The Darcy–Boussinesq model of convection is enhanced by including two nonlinear terms: (i) quadratic (Forchheimer) drag; and (ii) hydrodynamic dispersion enhancement of the thermal conductivity described by a weak linear relationship between effective conductivity and local amplitude of filtration velocity. The impact of the second term on the shape of the bifurcation curve for two-dimensional rolls is profound in the presence of uniform volumetric heating. The resulting bifurcation structure is unlike any pitchfork bifurcations typical of the classical Bénard problem. Although direct experimental validation of the novel bifurcation is not available, we would like to register it as an alternative or a supplement to models of small imperfections, and as an attempt to account for the scatter of observed critical values for the first bifurcation.

scholarly journals Effect of constant collision mean free time on the boundary layer of the active collisional warm plasma

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Mansour Khoram ◽  
S. Farhad Masoudi
Keyword(s):  
Boundary Layer ◽  
Electrical Potential ◽  
Plasma Boundary ◽  
Plasma Pressure ◽  
Ion Temperature ◽  
Ionization Degree ◽  
Solution Approach ◽  
Warm Plasma ◽  
Full Solution ◽  
Model Equations

AbstractThe plasma boundary layer is analyzed for a plasma in contact with a conducting plain surface where the ion temperature is comparable with the electron temperature and the plasma pressure is sufficiently high. The variations of electrical potential from the plasma-presheath boundary to the wall is studied using the fluidal formalism of plasma in three approaches; plasma and sheath asymptotic solutions and full solution. In the full solution approach, fluidal equations lead to a singularity when the ion velocity reaches the ion thermal speed. It is shown that removing the singularity causes a well-defined eigenvalue problem and leads to smooth solutions for the model equations. Some of the applicable aspects such as the floating velocity and density of ions, the floating electrical potential and an estimation of the floating thickness of the boundary layer are obtained. The dependency of these quantities on the ionization degree, the ion temperature and ion-neutral collision is examined too.

scholarly journals Forecasting circulation in the Cilician Basin of the Levantine Sea

2006 ◽  
Vol 3 (5) ◽  
pp. 1481-1514 ◽  
Author(s):  
E. Özsoy ◽  
A. Sözer
Keyword(s):  
Boundary Conditions ◽  
Initial Conditions ◽  
Eastern Mediterranean ◽  
Model Performance ◽  
Surface Flux ◽  
Mediterranean Coast ◽  
Open Boundary ◽  
Surface Boundary ◽  
Open Boundary Conditions ◽  
Levantine Sea

Abstract. The Cilician Basin/Shelf Model is adapted for studying the shelf circulation in the Cilician Basin – Gulf of İskenderun region of the Levantine Basin of the Eastern Mediterranean between the Turkish Mediterranean coast, Syria and the island of Cyprus. The model initial conditions and open boundary conditions are supplied by the ALERMO regional model of the Levantine Sea, while interactive surface flux boundary conditions are specified by an atmospheric boundary layer sub-model using calculated water properties and surface atmospheric variables supplied by the Skiron atmospheric model, within the nested modelling approach of the MFSTEP (Mediterranean Forecasting System: Towards Environmental Predictions) project. Sensitivity tests are performed for alternative surface boundary conditions. Model performance for shelf/meso-scale forecasts is demonstrated.

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