Non-linear wave interactions from transient growth in plane-parallel shear flows

2009 ◽  
Vol 28 (3) ◽  
pp. 420-429 ◽  
Author(s):  
L. Håkan Gustavsson
Keyword(s):  
Shear Flows ◽  
Linear Wave ◽  
Transient Growth ◽  
Wave Interactions ◽  
Plane Parallel ◽  
Non Linear ◽  
Parallel Shear Flows

Lagrangian approach to non-linear wave interactions in a warm plasma

1971 ◽  
Vol 6 (1) ◽  
pp. 53-72 ◽  
Author(s):  
J. J. Galloway ◽  
H. Kim
Keyword(s):  
Linear Equations ◽  
Wave Interaction ◽  
Lagrangian Approach ◽  
Linear Wave ◽  
Coupling Coefficients ◽  
Direct Expansion ◽  
Wave Interactions ◽  
Electrostatic Waves ◽  
Non Linear ◽  
Warm Plasma

In this paper, the coupled-mode equations and coupling coefficients for three-wave interaction are derived by a Lagrangian approach for a general medium. A derivation of the Low Lagrangian for a warm plasma is then given, which avoids certain problems associated with the original analysis. An application of the Lagrangian method is made to interaction between collinearly-propagating electrostatic waves, and a coupling coefficient is derived which agrees with a previous result obtained by direct expansion of the non-linear equations. The paper serves primarily to present and demonstrate a conceptually useful and efficient theoretical approach to non-linear wave interactions.

Transition in Homogeneously Heated Inclined Plane Parallel Shear Flows

2003 ◽  
Vol 125 (5) ◽  
pp. 795-803 ◽  
Author(s):  
S. Generalis ◽  
M. Nagata
Keyword(s):  
Shear Flows ◽  
Numerical Study ◽  
Fluid Layer ◽  
Travelling Wave ◽  
Inclined Plane ◽  
Vertical Orientation ◽  
Plane Parallel ◽  
Wide Range ◽  
Parallel Shear Flows ◽  
Roll Type

The transition of internally heated inclined plane parallel shear flows is examined numerically for the case of finite values of the Prandtl number Pr. We show that as the strength of the homogeneously distributed heat source is increased the basic flow loses stability to two-dimensional perturbations of the transverse roll type in a Hopf bifurcation for the vertical orientation of the fluid layer, whereas perturbations of the longitudinal roll type are most dangerous for a wide range of the value of the angle of inclination. In the case of the horizontal inclination transverse roll and longitudinal roll perturbations share the responsibility for the prime instability. Following the linear stability analysis for the general inclination of the fluid layer our attention is focused on a numerical study of the finite amplitude secondary travelling-wave solutions (TW) that develop from the perturbations of the transverse roll type for the vertical inclination of the fluid layer. The stability of the secondary TW against three-dimensional perturbations is also examined and our study shows that for Pr=0.71 the secondary instability sets in as a quasi-periodic mode, while for Pr=7 it is phase-locked to the secondary TW. The present study complements and extends the recent study by Nagata and Generalis (2002) in the case of vertical inclination for Pr=0.

Generation of surf beat by non-linear wave interactions

1971 ◽  
Vol 49 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Brent Gallagher
Keyword(s):  
Gravity Waves ◽  
Numerical Evaluation ◽  
Low Frequency ◽  
Linear Wave ◽  
Transfer Energy ◽  
Wave Interactions ◽  
Frequency Spectra ◽  
Non Linear ◽  
Linear Interactions ◽  
Low Frequency Waves

Non-linear interactions among wind-generated gravity waves transfer energy to low frequency waves in a coastal zone. A transfer function is derived for a straight coastline of constant bottom slope. This model is applied to three actual cases, and numerical evaluation of the energy transfer produces low frequency spectra which are compared with observations.

Transition in plane parallel shear flows heated internally

2004 ◽  
Vol 332 (1) ◽  
pp. 9-16 ◽  
Author(s):  
Masato Nagata ◽  
Sotos Generalis
Keyword(s):  
Shear Flows ◽  
Plane Parallel ◽  
Parallel Shear Flows
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