Solitary internal waves in a rotating channel: A numerical study

1987 ◽  
Vol 30 (2) ◽  
pp. 297 ◽  
Author(s):  
C. Katsis ◽  
T. R. Akylas
Keyword(s):  
Internal Waves ◽  
Numerical Study ◽  
Rotating Channel ◽  
Solitary Internal Waves

Numerical study of unsteady MHD Couette flow and heat transfer of nanofluids in a rotating system with convective cooling

2016 ◽  
Vol 26 (5) ◽  
pp. 1567-1579 ◽  
Author(s):  
Ahmada Omar Ali ◽  
Oluwole Daniel Makinde ◽  
Yaw Nkansah-Gyekye
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Couette Flow ◽  
Numerical Study ◽  
Integration Scheme ◽  
Parallel Plates ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Mhd Couette Flow ◽  
Rotating Channel

Purpose – The purpose of this paper is to investigate numerically the unsteady MHD Couette flow and heat transfer of viscous, incompressible and electrically conducting nanofluids between two parallel plates in a rotating channel. Design/methodology/approach – The nanofluid is set in motion by the combined action of moving upper plate, Coriolis force and the constant pressure gradient. The channel rotates in unison about an axis normal to the plates. The nonlinear governing equations for velocity and heat transfer are obtained and solved numerically using semi-discretization, shooting and collocation (bvp4c) techniques together with Runge-Kutta Fehlberg integration scheme. Findings – Results show that both magnetic field and rotation rate demonstrate significant effect on velocity and heat transfer profiles in the system with Cu-water nanofluid demonstrating the highest velocity and heat transfer efficiency. These numerical results are in excellent agreements with the results obtained by other methods. Practical implications – This paper provides a very useful source of information for researchers on the subject of hydromagnetic nanofluid flow in rotating systems. Originality/value – Couette flow of nanofluid in the presence of applied magnetic field in a rotating channel is investigated.

Are Solitary Internal Waves Solitons?

1998 ◽  
Vol 101 (3) ◽  
pp. 289-308 ◽  
Author(s):  
Kevin G. Lamb
Keyword(s):  
Internal Waves ◽  
Solitary Internal Waves

The Generation of Nonlinear Internal Waves in the South China Sea: A Three‐Dimensional, Nonhydrostatic Numerical Study

2019 ◽  
Vol 124 (12) ◽  
pp. 8949-8968 ◽  
Author(s):  
Zhigang Lai ◽  
Guangzhen Jin ◽  
Yongmao Huang ◽  
Haiyun Chen ◽  
Xiaodong Shang ◽  
...  
Keyword(s):  
South China Sea ◽  
Internal Waves ◽  
South China ◽  
Numerical Study ◽  
Three Dimensional ◽  
The South China Sea ◽  
The South ◽  
Nonlinear Internal Waves ◽  
China Sea

scholarly journals Mass and momentum transfer by solitary internal waves in a shelf zone

2012 ◽  
Vol 19 (2) ◽  
pp. 265-272 ◽  
Author(s):  
N. Gavrilov ◽  
V. Liapidevskii ◽  
K. Gavrilova
Keyword(s):  
Mathematical Model ◽  
Internal Waves ◽  
Solitary Waves ◽  
Large Amplitude ◽  
Shelf Zone ◽  
Swash Zone ◽  
Second Mode ◽  
Before And After ◽  
The Mathematical Model ◽  
Solitary Internal Waves

Abstract. The evolution of large amplitude internal waves propagating towards the shore and more specifically the run up phase over the "swash" zone is considered. The mathematical model describing the generation, interaction, and decaying of solitary internal waves of the second mode in the interlayer is proposed. The exact solution specifying the shape of solitary waves symmetric with respect to the unperturbed interface is constructed. It is shown that, taking into account the friction on interfaces in the mathematical model, it is possible to describe adequately the change in the phase and amplitude characteristics of two solitary waves moving towards each other before and after their interaction. It is demonstrated that propagation of large amplitude solitary internal waves of depression over a shelf could be simulated in laboratory experiments by internal symmetric solitary waves of the second mode.

A numerical investigation of solitary internal waves with trapped cores formed via shoaling

2002 ◽  
Vol 451 ◽  
pp. 109-144 ◽  
Author(s):  
KEVIN G. LAMB
Keyword(s):  
Internal Waves ◽  
Mixed Layer ◽  
Propagation Speed ◽  
Horizontal Velocity ◽  
Buoyancy Frequency ◽  
Surface Mixed Layer ◽  
Near Surface ◽  
Flow Limit ◽  
Wave Propagation Speed ◽  
Solitary Internal Waves

The formation of solitary internal waves with trapped cores via shoaling is investigated numerically. For density fields for which the buoyancy frequency increases monotonically towards the surface, sufficiently large solitary waves break as they shoal and form solitary-like waves with trapped fluid cores. Properties of large-amplitude waves are shown to be sensitive to the near-surface stratification. For the monotonic stratifications considered, waves with open streamlines are limited in amplitude by the breaking limit (maximum horizontal velocity equals wave propagation speed). When an exponential density stratification is modified to include a thin surface mixed layer, wave amplitudes are limited by the conjugate flow limit, in which case waves become long and horizontally uniform in the centre. The maximum horizontal velocity in the limiting wave is much less than the wave's propagation speed and as a consequence, waves with trapped cores are not formed in the presence of the surface mixed layer.

Numerical study of internal wave–wave interactions in a stratified fluid

2000 ◽  
Vol 415 ◽  
pp. 65-87 ◽  
Author(s):  
A. JAVAM ◽  
J. IMBERGER ◽  
S. W. ARMFIELD
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Numerical Study ◽  
Experimental Studies ◽  
Interaction Mechanism ◽  
Stratified Fluid ◽  
Interaction Region ◽  
Staggered Grid ◽  
Open Boundary ◽  
Wave Interactions

A finite volume method is used to study the generation, propagation and interaction of internal waves in a linearly stratified fluid. The internal waves were generated using single and multiple momentum sources. The full unsteady equations of motion were solved using a SIMPLE scheme on a non-staggered grid. An open boundary, based on the Sommerfield radiation condition, allowed waves to propagate through the computational boundaries with minimum reflection and distortion. For the case of a single momentum source, the effects of viscosity and nonlinearity on the generation and propagation of internal waves were investigated.Internal wave–wave interactions between two wave rays were studied using two momentum sources. The rays generated travelled out from the sources and intersected in interaction regions where nonlinear interactions caused the waves to break. When two rays had identical properties but opposite horizontal phase velocities (symmetric interaction), the interactions were not described by a triad interaction mechanism. Instead, energy was transferred to smaller wavelengths and, a few periods later, to standing evanescent modes in multiples of the primary frequency (greater than the ambient buoyancy frequencies) in the interaction region. The accumulation of the energy caused by these trapped modes within the interaction region resulted in the overturning of the density field. When the two rays had different properties (apart from the multiples of the forcing frequencies) the divisions of the forcing frequencies as well as the combination of the different frequencies were observed within the interaction region.The model was validated by comparing the results with those from experimental studies. Further, the energy balance was conserved and the dissipation of energy was shown to be related to the degree of nonlinear interaction.

On the three-dimensional internal waves excited by topography in the flow of a stratified fluid

1994 ◽  
Vol 263 ◽  
pp. 293-318 ◽  
Author(s):  
Hideshi Hanazaki
Keyword(s):  
Internal Waves ◽  
Numerical Study ◽  
Mach Reflection ◽  
Three Dimensional ◽  
Stratified Fluid ◽  
Linear Wave ◽  
Kp Equation ◽  
Subcritical Flow ◽  
Boussinesq Fluid ◽  
Upstream Waves

A numerical study of the three-dimensional internal waves excited by topography in the flow of a stratified fluid is described. In the resonant flow of a nearly two-layer fluid, it is found that the time-development of the nonlinearly excited waves agrees qualitatively with the solution of the forced KP equation or the forced extended KP equation. In this case, the upstream-advancing solitary waves become asymptotically straight crested because of abnormal reflection at the sidewall similar to Mach reflection. The same phenomenon also occurs in the subcritical flow of a nearly two-layer fluid. However, in the subcritical flow of a linearly stratified Boussinesq fluid, the two-dimensionalization of the upstream waves can be interpreted as the separation of the lateral modes due to the differences in the group velocity of the linear wave, although this does not mean in general that the generation of upstream waves is describable by the linearized equation.

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