Non-dimensional Wave Amplitude Research Articles

Effect of the Magnetic Field and Rotation on Peristaltic Flow of A Bingham Fluid in Asymmetric Channel with Porous Medium

In this paper, we investigate the influence of the rotation and magnetic field on the peristaltic flow of the Bingham fluid in an asymmetric channel with a porous medium under the long wavelength and low Reynolds number approximation assumptions. The perturbation method and the Mathematica program for solving nonlinear partial differential equations are used to couple the momentum equations with the rotational and magnetic field equations. The fluid is considered to be subject to a magnetic field and to flow within a porous medium. Graphs are used to display expressions for speed, stress gradient, magnetic subject, current density, rotation impact, and drift function. The findings reveal that the rotation, density, permeability, coupling diversity, and non-dimensional wave amplitude all play significant roles in the phenomenon. The quantities flow has been tested for variant parameters. The impact of the Bingham, Hartman and Darcy numbers are also tested for different values to indicate the effect on the movement of flow fluid. The applications can be seen through many graphics.

Effect of the Rotation and Inclined Magnetic Field on Peristaltic Slip Flow of a Bingham Fluid in Asymmetric Channel and Porous medium

This essay aims to describe the peristaltic behavior of Bingham's fluid in an asymmetric channel and porous material. The liquid is thought to flow in a porous media and be susceptible to a powerfully inclined magnetic field. The long wavelength dependency and low Reynolds number result in a major simplification of the nonlinear equations. The pressure gradient, pressure rise per wavelength, axial velocity, spin velocity, volume flow rate, and tilted magnetic number are all given specific attention. The findings reveal that rotation, density, permeability, coupling diversity, and non-dimensional wave amplitude all play significant roles in the phenomenon. With rising slip coefficient values and falling magnetic field strengths, permeability, and yield stress coefficients the trapped bolus grows in size

Estimate of energy loss from internal solitary waves breaking on slopes

Abstract. Internal solitary waves (ISWs) emerge in the ocean and seas in various forms and break on the shelf zones in a variety of ways. This results in intensive mixing that affects processes such as biological productivity and sediment transport. As ISWs of depression propagate in a two-layer ocean, from the deep part onto a shelf, two mechanisms are significant: (1) the breaking of internal waves over bottom topography when fluid velocities exceed the wave phase speed that causes overturning of the rear face of the wave, and (2) the changing of polarity at the turning point where the depths of the upper and lower layers are equal. We assume that the parameters that describe the process of the interaction of ISWs in a two-layer fluid with an idealized shelf-slope topography are (1) the nondimensional wave amplitude, normalized on the upper-layer thickness; (2) the ratio of the height of the bottom layer on the shelf to the incident wave amplitude; and (3) the angle of the bottom inclination. Based on a proposed three-dimensional classification diagram, four types of wave propagation over the slopes are distinguished: the ISW propagates over the slope without changing polarity and wave breaking, the ISW changes polarity over the slope without wave breaking, the ISW breaks over the slope without changing polarity, and the ISW both breaks and changes polarity over the slope. The energy loss during ISW transformation over slopes with various angles was estimated using the results of 85 numerical experiments. “Hot spots” of high levels of energy loss were highlighted for an idealized bottom configuration that mimics the continental shelf in the Lufeng region in the South China Sea.

The Influence of Magnetic Fields and Heat and Mass Transfer on Peristaltic Flow Through a Porous Channel

This paper discusses the effects of both magnetic fields and heat and mass transfer on the flows of a peristaltic nature with incompressible Newtonian fluid mechanics in a channel. The study was conducted under the assumption of a low Reynolds number and a long wavelength. The analytical solution was deduced from velocity and temperature. The outcomes for velocity and temperature, presented analytically, were evaluated in a numerical form and discussed briefly. Non-dimensional wave amplitude impact, the magnetic field, Grashof number, and the volume rate of flow in the waveform were analyzed theoretically and computed numerically. The expressions for velocity, pressure gradient, pressure rise, temperature, fractional force of the internal and outer channels, and shear stress were sketched for various embedded parameters; afterward, they were accordingly interpreted. Results of a numerical nature were given and illustrated graphically in every case. The results acquired in the presence and lack of magnetic field were compared against each other. The outcomes imply that the effects of the magnetic field and heat and mass transfer were evident in the phenomena. The effects of various involved criteria manifesting in the solutions were meticulously assayed.

Peristaltic flow of a Jeffrey fluid under the effect of radially varying magnetic field in a tube with an endoscope

The influence of an endoscope on peristaltic flow of a Jeffrey fluid through the cylindrical cavity between concentric tubes with variable magnetic field has been investigated. The governing equations of two dimensional fluid have been simplified under the consideration of long wavelength and low Reynolds number approximation. Exact analytical calculations are carried out for the pressure gradient, velocity, pressure rise, friction force on the inner and outer tubes and shear stress. The effect of the non-dimensional wave amplitude, the variable magnetic field, the ratio of relaxation of retardation time, the radius ratio and the non-dimensional volume flow are analyzed theoretically and computed numerically. Comparison was made with the results obtained in the presence and absence of variable magnetic field and an endoscope. The results indicate that the effect of the non-dimensional wave amplitude, variable magnetic field, ratio of relaxation to retardation time, radius ratio and non-dimensional volume flow on peristaltic flow are very pronounced.

A numerical study on the energy transfer from surface waves to interfacial waves in a two-layer fluid system

AbstractInteraction between surface and interfacial waves with continuous energy spectra in a two-layer density stratified fluid system is investigated numerically. For an initial wave field which consists only of the surface waves all propagating in the same direction, it is confirmed that the spectra $S_{s}(k)$ of the surface waves and $S_{i}(k)$ of the interfacial waves change significantly due to the recently found class 3 triad resonance. When the bulk of the surface wave spectrum $S_{s}(k)$ is initially located well above the critical wavenumber $k_{crit}$, below which the class 3 triad resonance is prohibited, $S_{s}(k)$ downshifts gradually toward the lower wavenumber during the initial stage of evolution. However, this downshift halts when the peak of $S_{s}(k)$ reaches around $k_{crit}$, and after that a steep peak forms in $S_{s}(k)$ around $k_{crit}$. It is confirmed that the timescale of the spectral evolution is of $O(1/{\it\epsilon}^{2})$ (${\it\epsilon}$ is a characteristic non-dimensional wave amplitude) in most of the $k$ space, consistent with the prediction of the wave turbulence theory for a system with a decay-type dispersion relation. However, it is also found that the timescale of the formation and growth of the sharp peak in $S_{s}(k)$ around $k_{crit}$ is of $O(1/{\it\epsilon})$, i.e. the timescale of the deterministic three-wave resonance.

Effect of an endoscope and rotation on the peristaltic flow involving a Jeffrey fluid with magnetic field

This paper deals with the influence of an endoscope and rotation on peristaltic flow of a Jeffrey fluid through the cylindrical cavity between concentric tubes with magnetic field. The two-dimensional equations of Jeffrey fluid are simplified by making the assumptions of long wave length and low Reynolds number. The expressions for pressure gradient, velocity, pressure rise, friction force on the inner and outer tubes and shear stress are sketched for various embedded parameters and interpreted. The effect of the non-dimensional wave amplitude, magnetic field, rotation, ratio of relaxation to retardation time, radius ratio and non-dimensional volume flow are analyzed theoretically and computed numerically. The features of the flow characteristics are analyzed by plotting graphs and discussed in detail. Comparison was made with the results obtained in the presence and absence of rotation, an endoscope and magnetic field. The results indicate that the effect of the non-dimensional wave amplitude, rotation, ratio of relaxation to retardation time, radius ratio and non-dimensional volume flow on peristaltic flow is highly pronounced.

Effects of an Endoscope and Rotation on Peristaltic Flow in a Tube with Long Wavelength

The objective of this project is to study examines the problem of peristaltic flow in a tube with an endoscope subjected to rotation. The effect of an endoscope and rotation of the peristaltic flow of a Jeffrey fluid through the cylindrical cavity between concentric tubes is investigated. The analytical expressions for the pressure gradient, velocity, pressure rise, friction force on the inner and outer tubes and shear stress are obtained in the physical domain. Effect of the non-dimensional wave amplitude, the rotation, the ratio of relaxation to retardation time, the radius ratio and the nondimensional volume flow is analyzed theoretically and computed numerically. Comparison is made with the results obtained in the presence of rotation and an endoscope.

Influence of heat and mass transfer, initial stress and radially varying magnetic field on the peristaltic flow in an annulus with gravity field

In this paper, the effects of both initial stress, radially varying and gravity field on the peristaltic flow of an incompressible MHD Newtonian fluid in a vertical annulus have been studied under the assumption of long wavelength and low-Reynolds number. The analytical solution has been derived for the temperature, concentration and velocity. The results for velocity, concentration and temperature obtained in the analytical form have been evaluated numerically and discussed briefly. The effect of the non-dimensional wave amplitude, the coefficient of viscosity, Sort number, Schmidt number, initial stress, gravitational field and the dimensionless time-mean flow in the wave frame are analyzed theoretically and computed numerically. The expressions for pressure rise, temperature, concentration field, velocity and pressure gradient are sketched for various embedded parameters and interpreted. Numerical results are given and illustrated graphically in each case considered. Comparison was made with the results obtained in the presence and absence of initial stress and gravitational field.

Effect of rotation on peristaltic flow of a micropolar fluid through a porous medium with an external magnetic field

In this paper, the effects of both rotation and magnetic field of a micropolar fluid through a porous medium induced by sinusoidal peristaltic waves traveling down the channel walls are studied analytically and computed numerically. Closed-form solutions under the consideration of long wavelength and low-Reynolds number is presented. The analytical expressions for axial velocity, pressure rise per wavelength, mechanical efficiency, spin velocity, stream function and pressure gradient are obtained in the physical domain. The effect of the rotation, density, Hartmann number, permeability, coupling number, micropolar parameter and the non-dimensional wave amplitude in the wave frame is analyzed theoretically and computed numerically. Numerical results are given and illustrated graphically in each case considered. Comparison was made with the results obtained in the presence and absence of rotation and magnetic field. The results indicate that the effect of rotation, density, Hartmann number, permeability, coupling number, micropolar parameter and the non-dimensional wave amplitude are very pronounced in the phenomena.

Effects of rotation and magnetic field on the nonlinear peristaltic flow of a second-order fluid in an asymmetric channel through a porous medium

In this paper, the effects of both rotation and magnetic field of the peristaltic transport of a second-order fluid through a porous medium in a channel are studied analytically and computed numerically. The material is represented by the constitutive equations for a second-order fluid. Closed-form solutions under the consideration of long wavelength and low Reynolds number is presented. The analytical expressions for the pressure gradient, pressure rise, friction force, stream function, shear stress, and velocity are obtained in the physical domain. The effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow in the wave frame are analyzed theoretically and computed numerically. Numerical results are given and illustrated graphically in each case considered. Comparison was made with the results obtained in the presence and absence of rotation, magnetic field, and porosity. The results indicate that the effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow are very pronounced in the phenomena.

Long wavelength peristaltic flow in a tubes with an endoscope subjected to magnetic field

In this paper, this study examines problem of peristaltic flow in a tubes with an endoscope subjected to magnetic field. Effect of an endoscope and magnetic field on the peristaltic flow of a Jeffrey fluid through the cylindrical cavity between concentric tubes has been investigated. The analytical expressions for the pressure gradient, velocity, pressure rise, friction force on the inner and outer tubes and shear stress are obtained in the physical domain. Effect of the non-dimensional wave amplitude, the magnetic field, the ratio of relaxation to retardation time, the radius ratio and the non-dimensional volume flow are analyzed theoretically and computed numerically. Comparison were made with the results obtained in the presence and absence of magnetic field and an endoscope. The results indicate that the effect of the non-dimensional wave amplitude, magnetic field, ratio of relaxation to retardation time, radius ratio and non-dimensional volume flow on peristaltic flow are very pronounced.

Wave diffraction on arc-shaped floating perforated breakwaters

An analytical method is developed to study the sheltering effects on arc-shaped floating perforated breakwaters. In the process of analysis, the floating breakwater is assumed to be rigid, thin, vertical, and immovable and located in water with constant depth. The fluid domain is divided into two regions by imaginary interface. The velocity potential in each region is expanded by eigenfunction in the context of linear theory. By satisfying continuity of pressure and normal velocity across the imaginary fluid interface, a set of linear algebraic equations can be obtained to determine the unknown coefficients for eigenfunction expansions. The accuracy of the present model was verified by a comparison with existing results for the case of arc-shaped floating breakwater. Numerical results, in the form of contour maps of the non-dimensional wave amplitude around the breakwater and diffracted wave amplitude at typical sections, are presented for a range of wave and breakwater parameters. Results show that the sheltering effects on the arc-shaped floating perforated breakwater are closely related to the incident wavelength, the draft and the porosity of the breakwater.

Feasibility of Using Tsunami Coda and Envelope for Forecasting Far-field Tsunami - Their Definitions and Application to 2006 Kuril Island Earthquake Tsunami -

As the first step toward forecasting the decay process of far-field tsunamis, we have introduced the concept of using and codas as measures in this paper. We applied these measures to the tsunami waveform data of the 2006 Kuril Island earthquake tsunami observed using tide gauges located in Japan. Analytical results indicate that the tsunami coda envelopes decayed exponentially with time and that the fluctuation in the nondimensional wave amplitude was interpreted by the Rayleigh distribution. Further, we found that these characteristics were commonly observed in the region facing the Pacific Ocean. Thus, the two measures can be used to reveal the characteristics of the tsunami decay process, and applying them to tsunami waveforms in realtime might realize appropriate cancelation of tsunami warnings.

Solitary wave transformation, breaking and run-up at a beach

A validated one-dimensional Boussinesq–non-linear shallow water equations numerical model was used to investigate the interaction of solitary waves with beaches. The numerical model requires two adjustable parameters: the bed friction coefficient and a wave breaking parameter. Excellent agreement was achieved between the numerical predictions of solitary wave transformation and run-up at a plane beach with two sets of high-quality laboratory measurements: one a large number of experiments in a wave flume by Synolakis, the other in the UK Coastal Research Facility. A parameter study investigated the effect of uniform offshore water depth, bed friction and bed slope on solitary wave run-up. A uniform water depth may be associated with a continental shelf region. The non-dimensional run-up was found to be an asymptotic function of non-dimensional wave amplitude at high and low values of initial wave steepness. Both asymptotes scale as (R/ho)∼α(Ao/ho)β where R is run-up (defined as the vertical elevation reached by the wave uprush above still water level), Ao is the offshore wave amplitude and ho is the uniform depth offshore of the beach. The empirical coefficients α and β depend on the beach characteristics. The model is then used to simulate the interaction of a full-scale tsunami event with an idealised beach profile representative of a beach in Eastern Kamchatka.

Numerical Experiments on the Breaking of Solitary Internal Wavesover a Slope–Shelf Topography

A theoretical study of the transformation of large amplitude internal solitary waves (ISW) of permanent form over a slope–shelf topography is considered using as basis the Reynolds equations. The vertical fluid stratification, amplitudes of the propagating ISWs, and the bottom parameters were taken close to those observed in the Andaman and Sulu Seas. The problem was solved numerically. It was found that, when an intense ISW of depression propagates from a deep part of a basin onto the shelf with water depth Hs, a breaking event will arise whenever the wave amplitude am is larger than 0.4(Hs − Hm), where Hm is the undisturbed depth of the isopycnal of maximum depression. The cumulative effect of nonlinearity in a propagating ISW leads to a steepening and overturning of a rear wave face over the inclined bottom. Immediately before breaking the horizontal orbital velocity at the site of instability exceeds the phase speed of the ISW. So, the strong breaking is caused by a kinematic instability of the propagating wave. At the latest stages of the evolution the overturned hydraulic jump transforms into a horizontal density intrusion (turbulent pulsating wall jet) propagating onto the shelf. The breaking criterion of the ISW over the slope was found. Over the range of examined parameters (0.52° < γ < 21.8°, where γ is the slope angle) the breaking event arises at the position with depth Hb, when the nondimensional wave amplitude a = am/(Hb − Hm) satisfies the condition a ≅ 0.8°/γ + 0.4. If the water depth Hs on a shelf is less than Hb, a solitary wave breaks down before it penetrates into a shallow water zone; otherwise (at Hs > Hb) it passes as a dispersive wave tail onto the shelf without breaking.

The generation and propagation of internal gravity waves in a rotating fluid

On the basis of a series of experiments in a 2×5 m tank containing a two‐layer salt‐stratified fluid mounted on the large rotating table at the University of Grenoble, we observe and attempt to explain the internal wave motions created by a moving bottom topography, which is oscillated to simulate barotropic tidal flow. We have found that when the flow over the obstacle is very supercritical, the initial wave field is quite asymmetric in plan form but evolves toward a more symmetric shape as time progresses. Large velocities are created along the crests of the waves, and these appear to scale with 2ΩAλ, where Ω is the rotation rate, A the nondimensional wave amplitude, and λ the wave width. When the flow is only slightly supercritical, the transverse velocities are correspondingly smaller, and the wave field approaches the symmetric plan form found by Maxworthy (1979) for the nonrotating case. For our particular combination of stratification and obstacle shape, two major wave systems evolve from two initial pulses created by the obstacle motion. There are of solitary wave type and during the course of the experiments are seen to evolve, combine, and form a series of finite amplitute waves ordered by amplitude. Rotation appears to have little effect on this evolutionary process but does initially affect the wave plan form and amplitude distributions.