scholarly journals Modeling internal waves in a two-layer fluid flow

2021 ◽  
Vol 288 ◽  
pp. 01027
Author(s):  
Gulmira Zhanbirova ◽  
Galia Zavyalova ◽  
Elena Muraveva ◽  
Daryn Shabdirov
Keyword(s):  
Mathematical Model ◽  
Fluid Flow ◽  
Internal Waves ◽  
Analytical Approach ◽  
Dimensionless Parameter ◽  
Unsteady Motion ◽  
External Pressure ◽  
Flat Bottom ◽  
Wave Source ◽  
Pressure Application

This study presents mathematical model of the internal waves and examines wave propagation in a two-layer fluid flow. Elements of the functional-analytical approach are used to develop the model. A flat unsteady motion of a two-layer liquid under a cover over a flat bottom is considered. The fluid is assumed to be ideal and incompressible. Internal waves are caused by external pressure application to the interface between the layers, oscillation of the flat bottom and disturbances in the flow. The power of the wave source is characterized by dimensionless parameter ε. The problem is formulated, and its solution is based on asymptotic analysis for 0<ε<1.

scholarly journals Analytical Approach for Solving the Internal Waves Problems Involving the Tidal Force

2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
Jaharuddin ◽  
Hadi Hermansyah
Keyword(s):  
Mathematical Model ◽  
Internal Wave ◽  
Internal Waves ◽  
Analytical Approach ◽  
Nonlinear Partial Differential Equations ◽  
Wave Problem ◽  
Tidal Forces ◽  
Basic Fluid ◽  
Homotopy Analysis ◽  
The Mathematical Model

The mathematical model for describing internal waves of the ocean is derived from the assumption of ideal fluid; i.e., the fluid is incompressible and inviscid. These internal waves are generated through the interaction between the tidal currents and the basic topography of the fluid. Basically the mathematical model of the internal wave problem of the ocean is a system of nonlinear partial differential equations (PDEs). In this paper, the analytical approach used to solve nonlinear PDE is the Homotopy Analysis Method (HAM). HAM can be applied to determine the resolution of almost any internal wave problem involving tidal forces. The use of HAM in the solution to basic fluid equations is efficient and simple, since it involves only modest calculations using the common integral.

Mathematical model of the hydrocyclone based on physics of fluid flow

AIChE Journal ◽  
1991 ◽  
Vol 37 (5) ◽  
pp. 735-746 ◽  
Author(s):  
K. T. Hsieh ◽  
R. K. Rajamani
Keyword(s):  
Mathematical Model ◽  
Fluid Flow

Mathematical Model Establishment and Analysis on the Pipe Deformation under External Pressure with the Ovality

2013 ◽  
Vol 760-762 ◽  
pp. 2263-2266
Author(s):  
Kang Yong ◽  
Wei Chen
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Yield Strength ◽  
Residual Stresses ◽  
Numerical Simulations ◽  
Significant Influence ◽  
External Pressure ◽  
Pipe Diameter ◽  
Axial Loads ◽  
The Stability

Beside the residual stresses and axial loads, other factors of pipe like ovality, moment could also bring a significant influence on pipe deformation under external pressure. The Standard of API-5C3 has discussed the influences of deformation caused by yield strength of pipe, pipe diameter and pipe thickness, but the factor of ovality degree is not included. Experiments and numerical simulations show that with the increasing of pipe ovality degree, the anti-deformation capability under external pressure will become lower, and ovality affecting the stability of pipe shape under external pressure is significant. So it could be a path to find out the mechanics relationship between ovality and pipe deformation under external pressure by the methods of numerical simulations and theoretical analysis.

Tidal Internal Waves in the Bransfield Strait, Antarctica

2021 ◽  
Author(s):  
Eugene Morozov ◽  
Dmitry Frey ◽  
Elizaveta Khimchenko
Keyword(s):  
Internal Waves ◽  
Bottom Topography ◽  
Pressure Sensors ◽  
Internal Tide ◽  
Internal Tides ◽  
South Shetland Islands ◽  
Flat Bottom ◽  
Bransfield Strait ◽  
Vertical Displacements ◽  
Rfbr Grant

&lt;p&gt;Observations of tidal internal waves in the Bransfield Strait, Antarctica, are analyzed. The measurements were carried out for 14 days on a moored station equipped with five autonomous temperature and pressure sensors. The mooring was deployed on the slope of Nelson Island (South Shetland Islands archipelago) over a depth of 70 m at point 62&amp;#176;21&amp;#42892; S, 58&amp;#176;49&amp;#42892; W. Analysis is based on the fluctuations of isotherms. &amp;#160;Vertical displacements of temperature revealed that strong internal vertical oscillations up to 30&amp;#8211;40 m are caused by the diurnal internal tide. Spectral analysis of vertical displacements of the 0.9&amp;#176;C isotherm showed a clear peak at a period of 24 h. It is known that the tides in the Bransfield Strait are mostly mixed diurnal and semidiurnal, but during the Antarctic summer, diurnal tide component may intensify. The velocity ellipses of the barotropic tidal currents were estimated using the global tidal model TPXO9.0. It was found that tidal ellipses rotate clockwise with a period of 24 h and anticlockwise with a period of 12 h. The waves are forced due to the interaction of the barotropic tide with the bottom topography. Diurnal internal tides do not develop at latitudes higher than 30&amp;#186; over flat bottom. The research was supported by RFBR grant 20-08-00246.&lt;/p&gt;

Determination of a Loading Pressure in the Metal Forming by the Given Movements

2013 ◽  
Vol 842 ◽  
pp. 494-499 ◽  
Author(s):  
Evgenii V. Murashkin ◽  
Marina V. Polonik
Keyword(s):  
Mathematical Model ◽  
Metal Forming ◽  
External Pressure ◽  
Stress Changes ◽  
The Given

We propose a mathematical model of large elastocreep deformations. As part of the constructed mathematical model the problem of deformation of the material in the vicinity of microdefect was solved. Integro-differential dependence of external pressure from irreversible deformations and displacements was obtained. The laws of loading material from vector displacements were calculated. We have shown that the monotonous laws of deformation can lead to non-monotonous stress changes.

scholarly journals The dual nature of the dead-water phenomenology: Nansen versus Ekman wave-making drags

2020 ◽  
Vol 117 (29) ◽  
pp. 16770-16775
Author(s):  
Johan Fourdrinoy ◽  
Julien Dambrine ◽  
Madalina Petcu ◽  
Morgan Pierre ◽  
Germain Rousseaux
Keyword(s):  
Internal Waves ◽  
Laboratory Experiments ◽  
Analytical Description ◽  
Unsteady Motion ◽  
Linear Regime ◽  
Dual Nature ◽  
Asymptotic Speed ◽  
Propulsion Force ◽  
Initial Acceleration ◽  
Dead Water

A ship encounters a higher drag in a stratified fluid compared to a homogeneous one. Grouped under the same “dead-water” vocabulary, two wave-making resistance phenomena have been historically reported. The first, the Nansen wave-making drag, generates a stationary internal wake which produces a kinematic drag with a noticeable hysteresis. The second, the Ekman wave-making drag, is characterized by velocity oscillations caused by a dynamical resistance whose origin is still unclear. The latter has been justified previously by a periodic emission of nonlinear internal waves. Here we show that these speed variations are due to the generation of an internal dispersive undulating depression produced during the initial acceleration of the ship within a linear regime. The dispersive undulating depression front and its subsequent whelps act as a bumpy treadmill on which the ship would move back and forth. We provide an analytical description of the coupled dynamics of the ship and the wave, which demonstrates the unsteady motion of the ship. Thanks to dynamic calculations substantiated by laboratory experiments, we prove that this oscillating regime is only temporary: the ship will escape the transient Ekman regime while maintaining its propulsion force, reaching the asymptotic Nansen limit. In addition, we show that the lateral confinement, often imposed by experimental setups or in harbors and locks, exacerbates oscillations and modifies the asymptotic speed.

scholarly journals Pressure-driven flow in a thin pipe with rough boundary

2020 ◽  
Vol 71 (4) ◽  
Author(s):  
Elena Miroshnikova
Keyword(s):  
Fluid Flow ◽  
Longitudinal Direction ◽  
External Pressure ◽  
General Assumption ◽  
Rough Boundary ◽  
Local Behavior ◽  
Sectional Area ◽  
Cross Sectional ◽  
Incompressible Newtonian Fluid ◽  
Pressure Driven Flow

Abstract Stationary incompressible Newtonian fluid flow governed by external force and external pressure is considered in a thin rough pipe. The transversal size of the pipe is assumed to be of the order $$\varepsilon $$ ε , i.e., cross-sectional area is about $$\varepsilon ^{2}$$ ε 2 , and the wavelength in longitudinal direction is modeled by a small parameter $$\mu $$ μ . Under general assumption $$\varepsilon ,\mu \rightarrow 0$$ ε , μ → 0 , the Poiseuille law is obtained. Depending on $$\varepsilon ,\mu $$ ε , μ -relation ($$\varepsilon \ll \mu $$ ε ≪ μ , $$\varepsilon /\mu \sim \mathrm {constant}$$ ε / μ ∼ constant , $$\varepsilon \gg \mu $$ ε ≫ μ ), different cell problems describing the local behavior of the fluid are deduced and analyzed. Error estimates are presented.

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