scholarly journals An application of Nwogu’s Boussinesq model to analyze the head-on collision process between hydroelastic solitary waves

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 177-191 ◽  
Author(s):  
Muhammad Mubashir Bhatti ◽  
Dong-Qiang Lu
Keyword(s):  
Phase Shift ◽  
Solitary Waves ◽  
Free Parameter ◽  
Wave Speed ◽  
Physical Parameters ◽  
Beam Model ◽  
Boussinesq Model ◽  
Highly Nonlinear ◽  
Run Up ◽  
The Impact

AbstractThis article deals with the nonlinear head-on collision between two hydroelastic solitary waves in plate–covered water with Nwogou’s Boussinesq model for the nonlinear fluid motion. This model contains a parameter α that is associated with horizontal velocities according to the chosen level of horizontal velocity variables. A thin elastic cover is considered as the Euler–Bernoulli beam model. To derive the series solution, we apply the Poincaré–Lighthill–Kuo (PLK) method to solve analytically the highly nonlinear coupled partial differential equations. The impact of all the physical parameters is discussed with the help of the asymptotic solutions and graphic representations. In particular, the authors address the behavior of plate deflection, maximum run-up during a collision, phase shift, distortion profile, and wave speed. It is found that the variation of the free parameter α and plate terms dramatically change the amplitude of a solitary wave. It is noticed that a very small tilting occurs due to the distortion in wave profile. The maximum run-up amplitude and the wave speed rise due to a greater influence of the free parameter. The phase shift tends to diminish due to an increment in the free parameter and plate terms. The novelty of the present methodology is compared with previously published results.

scholarly journals Analytical Study of the Head-On Collision Process between Hydroelastic Solitary Waves in the Presence of a Uniform Current

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 333 ◽  
Author(s):  
Muhammad Bhatti ◽  
Dong Lu
Keyword(s):  
Solitary Waves ◽  
Elastic Plate ◽  
Wave Speed ◽  
Nonlinear Partial Differential Equations ◽  
Thin Elastic Plate ◽  
Beam Model ◽  
Singular Perturbation Method ◽  
Highly Nonlinear ◽  
Uniform Current ◽  
Run Up

The present study discusses an analytical simulation of the head-on collision between a pair of hydroelastic solitary waves propagating in the opposite directions in the presence of a uniform current. An infinite thin elastic plate is floating on the surface of water. The mathematical modeling of the thin elastic plate is based on the Euler–Bernoulli beam model. The resulting kinematic and dynamic boundary conditions are highly nonlinear, which are solved analytically with the help of a singular perturbation method. The Poincaré–Lighthill–Kuo method is applied to obtain the solution of the nonlinear partial differential equations. The resulting solutions are presented separately for the left- and right-going waves. The behavior of all the emerging parameters are presented mathematically and discussed graphically for the phase shift, maximum run-up amplitude, distortion profile, wave speed, and solitary wave profile. It is found that the presence of a current strongly affects the wavelength and wave speed of both solitary waves. A graphical comparison with pure-gravity waves is also presented as a particular case of our study.

scholarly journals Head-on collision between capillary–gravity solitary waves

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Marin Marin ◽  
M. M. Bhatti
Keyword(s):  
Surface Tension ◽  
Solitary Waves ◽  
Water Waves ◽  
Free Parameter ◽  
Order Approximation ◽  
Third Order ◽  
Boussinesq Model ◽  
Run Up ◽  
Physical Features ◽  
Third Order Approximation

AbstractThe present study deals with the head-on collision process between capillary–gravity solitary waves in a finite channel. The present mathematical modeling is based on Nwogu’s Boussinesq model. This model is suitable for both shallow and deep water waves. We have considered the surface tension effects. To examine the asymptotic behavior, we employed the Poincaré–Lighthill–Kuo method. The resulting series solutions are given up to third-order approximation. The physical features are discussed for wave speed, head-on collision profile, maximum run-up, distortion profile, the velocity at the bottom, and phase shift profile, etc. A comparison is also given as a particular case in our study. According to the results, it is noticed that the free parameter and the surface tension tend to decline the solitary-wave profile significantly. However, the maximum run-up amplitude was affected in great measure due to the surface tension and the free parameter.

Numerical simulations of large-amplitude internal solitary waves

1998 ◽  
Vol 362 ◽  
pp. 53-82 ◽  
Author(s):  
DMITRY E. TEREZ ◽  
OMAR M. KNIO
Keyword(s):  
Phase Shift ◽  
Solitary Waves ◽  
Numerical Experiments ◽  
Wave Speed ◽  
Wave Amplitude ◽  
Stokes Equations ◽  
Fluid Model ◽  
Internal Solitary Waves ◽  
Highly Nonlinear ◽  
The Waves

A numerical model based on the incompressible two-dimensional Navier–Stokes equations in the Boussinesq approximation is used to study mode-2 internal solitary waves propagating on a pycnocline between two deep layers of different densities. Numerical experiments on the collapse of an initially mixed region reveal a train of solitary waves with the largest leading wave enclosing an intrusional ‘bulge’. The waves gradually decay as they propagate along the horizontal direction, with a corresponding reduction in the size of the bulge. When the normalized wave amplitude, a, falls below the critical value ac=1.18, the wave is no longer able to transport mixed fluid as it propagates away from the mixed region, and a sharp-nosed intrusion is left behind. The wave structure is studied using a Lagrangian particle tracking scheme which shows that for small amplitudes the bulges have a well-defined elliptic shape. At larger amplitudes, the bulge entrains and mixes fluid from the outside while instabilities develop in the rear part of the bulge. Results are obtained for different wave amplitudes ranging from small-amplitude ‘regular’ waves with a=0.7 to highly nonlinear unstable waves with a=3.8. The dependence of the wave speed and wavelength on amplitude is measured and compared with available experimental data and theoretical predictions. Consistent with experiments, the wave speed increases almost linearly with amplitude at small values of a. As a becomes large, the wave speed increases with amplitude at a smaller rate, which gradually approaches the asymptotic limit for a two-fluid model. Results show that in the parameter range considered the wave amplitude decreases linearly with time at a rate inversely proportional to the Reynolds number. Numerical experiments are also conducted on the head-on collision of solitary waves. The simulations indicate that the waves experience a negative phase shift during the collision, in accordance with experimental observations. Computations are used to determine the dependence of the phase shift on the wave amplitude.

scholarly journals On Mixed Convection Squeezing Flow of Nanofluids

Energies ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 3138 ◽  
Author(s):  
Sheikh Irfan Ullah Khan ◽  
Ebraheem Alzahrani ◽  
Umar Khan ◽  
Noreena Zeb ◽  
Anwar Zeb
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Mixed Convection ◽  
Ordinary Differential Equations ◽  
Volume Fraction ◽  
Squeezing Flow ◽  
Physical Parameters ◽  
Gamma Alumina ◽  
Highly Nonlinear ◽  
The Impact

In this article, the impact of effective Prandtl number model on 3D incompressible flow in a rotating channel is proposed under the influence of mixed convection. The coupled nonlinear system of partial differential equations is decomposed into a highly nonlinear system of ordinary differential equations with aid of suitable similarity transforms. Then, the solution of a nonlinear system of ordinary differential equations is obtained numerically by using Runge–Kutta–Fehlberg (RKF) method. Furthermore, the surface drag force C f and the rate of heat transfer N u are portrayed numerically. The effects of different emerging physical parameters such as Hartmann number (M), Reynold’s number (Re), squeezing parameter ( β ), mixed convection parameter λ , and volume fraction ( φ ) are also incorporated graphically for γ — alumina. Due to the higher viscosity and thermal conductivity ethylene-based nanofluids, it is observed to be an effective common base fluid as compared to water. These observations portrayed the temperature of gamma-alumina ethylene-based nanofluids rising on gamma-alumina water based nanofluids.

scholarly journals Run-Up of Solitary Waves on Twin Conical Islands Using a Boussinesq Model

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Dongfang Liang ◽  
Alistair G. L. Borthwick ◽  
Jonathan K. Romer-Lee
Keyword(s):  
Numerical Model ◽  
Solitary Waves ◽  
Laboratory Data ◽  
Boussinesq Model ◽  
Reflected Waves ◽  
Wave Refraction ◽  
Local Wave ◽  
Run Up ◽  
Gap Spacing ◽  
Incident Waves

This paper investigates the interaction of solitary waves (representative of tsunamis) with idealized flat-topped conical islands. The investigation is based on simulations produced by a numerical model that solves the two-dimensional Boussinesq-type equations of Madsen and Sørensen using a total variation diminishing Lax–Wendroff scheme. After verification against published laboratory data on solitary wave run-up at a single island, the numerical model is applied to study the maximum run-up at a pair of identical conical islands located at different spacings apart for various angles of wave attack. The predicted results indicate that the maximum run-up can be attenuated or enhanced according to the position of the second island because of wave refraction, diffraction, and reflection. It is also observed that the local wave height and hence run-up can be amplified at certain gap spacing between the islands, owing to the interference between the incident waves and the reflected waves between islands.

scholarly journals Damage Evolution of Granodiorite after Heating and Cooling Treatments

Minerals ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 779
Author(s):  
Mohamed Gomah ◽  
Guichen Li ◽  
Salah Bader ◽  
Mohamed Elkarmoty ◽  
Mohamed Ismael
Keyword(s):  
Mechanical Properties ◽  
Tensile Strength ◽  
Failure Mode ◽  
Physical And Mechanical Properties ◽  
P Wave ◽  
Physical Parameters ◽  
Slow Cooling ◽  
Heating And Cooling ◽  
Natural Rock ◽  
The Impact

The awareness of the impact of high temperatures on rock properties is essential to the design of deep geotechnical applications. The purpose of this research is to assess the influence of heating and cooling treatments on the physical and mechanical properties of Egyptian granodiorite as a degrading factor. The samples were heated to various temperatures (200, 400, 600, and 800 °C) and then cooled at different rates, either slowly cooled in the oven and air or quickly cooled in water. The porosity, water absorption, P-wave velocity, tensile strength, failure mode, and associated microstructural alterations due to thermal effect have been studied. The study revealed that the granodiorite has a slight drop in tensile strength, up to 400 °C, for slow cooling routes and that most of the physical attributes are comparable to natural rock. Despite this, granodiorite thermal deterioration is substantially higher for quick cooling than for slow cooling. Between 400:600 °C is ‘the transitional stage’, where the physical and mechanical characteristics degraded exponentially for all cooling pathways. Independent of the cooling method, the granodiorite showed a ductile failure mode associated with reduced peak tensile strengths. Additionally, the microstructure altered from predominantly intergranular cracking to more trans-granular cracking at 600 °C. The integrity of the granodiorite structure was compromised at 800 °C, the physical parameters deteriorated, and the rock tensile strength was negligible. In this research, the temperatures of 400, 600, and 800 °C were remarked to be typical of three divergent phases of granodiorite mechanical and physical properties evolution. Furthermore, 400 °C could be considered as the threshold limit for Egyptian granodiorite physical and mechanical properties for typical thermal underground applications.

scholarly journals A Review of Photocatalytic Materials for Urban NOx Remediation

Catalysts ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 675
Author(s):  
Hugo Savill Russell ◽  
Louise Bøge Frederickson ◽  
Ole Hertel ◽  
Thomas Ellermann ◽  
Steen Solvang Jensen
Keyword(s):  
Photocatalytic Oxidation ◽  
Urban Air Pollution ◽  
Field Trials ◽  
Urban Environments ◽  
Physical Parameters ◽  
Nox Removal ◽  
Removal Efficiencies ◽  
The Impact ◽  
By Products ◽  
Photocatalytic Materials

NOx is a pervasive pollutant in urban environments. This review assesses the current state of the art of photocatalytic oxidation materials, designed for the abatement of nitrogen oxides (NOx) in the urban environment, and typically, but not exclusively based on titanium dioxide (TiO2). Field trials with existing commercial materials, such as paints, asphalt and concrete, in a range of environments including street canyons, car parks, tunnels, highways and open streets, are considered in-depth. Lab studies containing the most recent developments in the photocatalytic materials are also summarised, as well as studies investigating the impact of physical parameters on their efficiency. It is concluded that this technology may be useful as a part of the measures used to lower urban air pollution levels, yielding ∼2% NOx removal in the immediate area around the surface, for optimised TiO2, in some cases, but is not capable of the reported high NOx removal efficiencies >20% in outdoor urban environments, and can in some cases lower air quality by releasing hazardous by-products. However, research into new material is ongoing. The reason for the mixed results in the studies reviewed, and massive range of removal efficiencies reported (from negligible and up to >80%) is mainly the large range of testing practices used. Before deployment in individual environments site-specific testing should be performed, and new standards for lab and field testing should be developed. The longevity of the materials and their potential for producing hazardous by-products should also be considered.

scholarly journals Crossbreed impact of double-diffusivity convection on peristaltic pumping of magneto Sisko nanofluids in non-uniform inclined channel: A bio-nanoengineering model

2021 ◽  
Vol 104 (3) ◽  
pp. 003685042110336
Author(s):  
Safia Akram ◽  
Maria Athar ◽  
Khalid Saeed ◽  
Alia Razia
Keyword(s):  
Mathematical Modeling ◽  
Magnetic Field ◽  
Physical Parameters ◽  
Induced Magnetic Field ◽  
Long Wavelength ◽  
Inclined Channel ◽  
Graphical Data ◽  
Peristaltic Pumping ◽  
Highly Nonlinear ◽  
Linear Pdes

The consequences of double-diffusivity convection on the peristaltic transport of Sisko nanofluids in the non-uniform inclined channel and induced magnetic field are discussed in this article. The mathematical modeling of Sisko nanofluids with induced magnetic field and double-diffusivity convection is given. To simplify PDEs that are highly nonlinear in nature, the low but finite Reynolds number, and long wavelength estimation are used. The Numerical solution is calculated for the non-linear PDEs. The exact solution of concentration, temperature and nanoparticle are obtained. The effect of various physical parameters of flow quantities is shown in numerical and graphical data. The outcomes show that as the thermophoresis and Dufour parameters are raised, the profiles of temperature, concentration, and nanoparticle fraction all significantly increase.

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