scholarly journals The Magnetohydrodynamic Kelvin‐Helmholtz Instability: A Three‐dimensional Study of Nonlinear Evolution

2000 ◽  
Vol 545 (1) ◽  
pp. 475-493 ◽  
Author(s):  
Dongsu Ryu ◽  
T. W. Jones ◽  
Adam Frank
Keyword(s):  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Helmholtz Instability

scholarly journals Lump Solutions, Multi Lump Solutions and More Soliton Solutions of a Novel (2+1)-dimensional Nonlinear Evolution Equation

2021 ◽  
Author(s):  
Hongcai Ma ◽  
Shupan Yue ◽  
Yidan Gao ◽  
Aiping Deng
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Bilinear Method ◽  
Test Function ◽  
Lump Solutions ◽  
Hirota Bilinear ◽  
Test Function Method

Abstract Exact solutions of a new (2+1)-dimensional nonlinear evolution equation are studied. Through the Hirota bilinear method, the test function method and the improved tanh-coth and tah-cot method, with the assisstance of symbolic operations, one can obtain the lump solutions, multi lump solutions and more soliton solutions. Finally, by determining different parameters, we draw the three-dimensional plots and density plots at different times.

scholarly journals Numerical Investigation of Kelvin-Helmholtz Instability in a Centrifugal Compressor Operating Near Stall

2015 ◽  
Author(s):  
Y. Bousquet ◽  
X. Carbonneau ◽  
I. Trebinjac ◽  
N. Binder ◽  
G. Dufour
Keyword(s):  
Centrifugal Compressor ◽  
Vortex Shedding ◽  
Three Dimensional ◽  
Flow Region ◽  
Main Flow ◽  
Helmholtz Instability ◽  
Vaned Diffuser ◽  
Leakage Flows ◽  
Rotor Stator Interaction ◽  
Three Dimensional Simulations

The present works details the occurrence of the Kelvin–Helmholtz instability in a centrifugal compressor operating near stall. The analysis are based on unsteady three dimensional simulations performed on a calculation domain covering the full annulus for the impeller and the vaned diffuser. A detailed investigation of the flow structure is presented, together with its evolution consequent to the mass flow reduction. It is demonstrated that this reduction leads to an enlargement of the low momentum flow region initially induced by the combination of the secondary and leakage flows. When the compressor operates near stall, the shear layer at the interface between the main flow and this low momentum flow becomes unstable and induces a periodic vortex shedding. The frequency of such an unsteady phenomenon is not correlated with the blade passing frequency. Its signature is thus easily isolated from the deterministic rotor/stator interaction. Its detection requires full-annulus simulations with an accurate resolution in time and space, which explains why it has never been previously observed in centrifugal compressors.

NONLINEAR EVOLUTION OF TURBULENT COHERENT STRUCTURES IN CHANNEL FLOWS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1539-1542
Author(s):  
ZHANG LI ◽  
DENGBIN TANG ◽  
LINLIN GUO
Keyword(s):  
Coherent Structures ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Channel Flows ◽  
Navier Stokes ◽  
Theoretic Model ◽  
Compact Difference Scheme ◽  
Navier Stokes Equation ◽  
Turbulent Coherent Structures ◽  
Dimensional Coupling

The generation and the development of turbulent coherent structures in channel flows are investigated by using numerical simulation of Navier-Stokes equation and the theoretic model of turbulent coherent structures built up by the flow stability theories. The three-dimensional coupling compact difference scheme with high accuracy and resolution developed can be applied to the calculative region including points near the boundary. The results computed show nonlinear evolution process and characteristics of Reynolds stress, stream-wise vortices and span-wise vorticities, especially the nonlinear interactions between different coherent structures.

Nonlinear evolution of the Kelvin-Helmholtz instability in the high-latitude ionosphere

1988 ◽  
Vol 93 (A1) ◽  
pp. 137 ◽  
Author(s):  
M. J. Keskinen ◽  
H. G. Mitchell ◽  
J. A. Fedder ◽  
P. Satyanarayana ◽  
S. T. Zalesak ◽  
...  
Keyword(s):  
High Latitude ◽  
Nonlinear Evolution ◽  
Helmholtz Instability ◽  
High Latitude Ionosphere

scholarly journals Nonlinear evolution of interacting oblique waves on two-dimensional shear layers

1989 ◽  
Vol 207 ◽  
pp. 97-120 ◽  
Author(s):  
M. E. Goldstein ◽  
S.-W. Choi
Keyword(s):  
Wave Amplitude ◽  
Numerical Solutions ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Shear Layers ◽  
Instability Wave ◽  
Two Dimensional ◽  
Instability Waves ◽  
Downstream Distance ◽  
Parallel Streams

We consider the effects of critical-layer nonlinearity on spatially growing oblique instability waves on nominally two-dimensional shear layers between parallel streams. The analysis shows that three-dimensional effects cause nonlinearity to occur at much smaller amplitudes than it does in two-dimensional flows. The nonlinear instability wave amplitude is determined by an integro-differential equation with cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. We show that they always end in a singularity at a finite downstream distance.

Sign in / Sign up

Export Citation Format

Share Document