### Abstract

The properties of reflection, refraction and absorption of a gravity wave incident upon a shear layer are investigated. It is shown that one must expect these properties to be very different depending upon the parameters (such as the Richardson number Ri, the wavelength normalized by the length scale of the shear and the ratio of the flow speed to the phase speed of the wave) characterizing the interaction of a gravity wave with a shear layer. In particular, it is shown that for all Richardson numbers there is a discontinuity in the net wave-action flux across the critical level, i. e. at a height where the flow speed matches the horizontal phase speed of the wave. When Ri greater than one quarter , this is accompanied by absorption of part of the energy of the incident wave into the mean flow. In addition, it is shown that the phenomenon of wave amplification (over-reflection) can arise provided that the ultimate shear flow speed exceeds the horizontal phase speed of the wave and Ri is less than a certain critical value Ri//c congruent 0. 1129, in which case the reflected wave extracts energy from the streaming motion. It is also pointed out that wave amplification can lead to instability if the boundary conditions are altered in such a way that the system can behave like an 'amplifier'.

Original language | English |
---|---|

Pages (from-to) | 661-671 |

Number of pages | 11 |

Journal | Journal of Fluid Mechanics |

Volume | 72 |

Issue number | pt 4 |

Publication status | Published - Jan 1 1975 |

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### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Journal of Fluid Mechanics*,

*72*(pt 4), 661-671.

**CRITICAL-LEVEL BEHAVIOUR AND WAVE AMPLIFICATION OF A GRAVITY WAVE INCIDENT UPON A SHEAR LAYER.** / Eltayeb, I. A.; McKenzie, J. F.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, vol. 72, no. pt 4, pp. 661-671.

}

TY - JOUR

T1 - CRITICAL-LEVEL BEHAVIOUR AND WAVE AMPLIFICATION OF A GRAVITY WAVE INCIDENT UPON A SHEAR LAYER.

AU - Eltayeb, I. A.

AU - McKenzie, J. F.

PY - 1975/1/1

Y1 - 1975/1/1

N2 - The properties of reflection, refraction and absorption of a gravity wave incident upon a shear layer are investigated. It is shown that one must expect these properties to be very different depending upon the parameters (such as the Richardson number Ri, the wavelength normalized by the length scale of the shear and the ratio of the flow speed to the phase speed of the wave) characterizing the interaction of a gravity wave with a shear layer. In particular, it is shown that for all Richardson numbers there is a discontinuity in the net wave-action flux across the critical level, i. e. at a height where the flow speed matches the horizontal phase speed of the wave. When Ri greater than one quarter , this is accompanied by absorption of part of the energy of the incident wave into the mean flow. In addition, it is shown that the phenomenon of wave amplification (over-reflection) can arise provided that the ultimate shear flow speed exceeds the horizontal phase speed of the wave and Ri is less than a certain critical value Ri//c congruent 0. 1129, in which case the reflected wave extracts energy from the streaming motion. It is also pointed out that wave amplification can lead to instability if the boundary conditions are altered in such a way that the system can behave like an 'amplifier'.

AB - The properties of reflection, refraction and absorption of a gravity wave incident upon a shear layer are investigated. It is shown that one must expect these properties to be very different depending upon the parameters (such as the Richardson number Ri, the wavelength normalized by the length scale of the shear and the ratio of the flow speed to the phase speed of the wave) characterizing the interaction of a gravity wave with a shear layer. In particular, it is shown that for all Richardson numbers there is a discontinuity in the net wave-action flux across the critical level, i. e. at a height where the flow speed matches the horizontal phase speed of the wave. When Ri greater than one quarter , this is accompanied by absorption of part of the energy of the incident wave into the mean flow. In addition, it is shown that the phenomenon of wave amplification (over-reflection) can arise provided that the ultimate shear flow speed exceeds the horizontal phase speed of the wave and Ri is less than a certain critical value Ri//c congruent 0. 1129, in which case the reflected wave extracts energy from the streaming motion. It is also pointed out that wave amplification can lead to instability if the boundary conditions are altered in such a way that the system can behave like an 'amplifier'.

UR - http://www.scopus.com/inward/record.url?scp=0016655633&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0016655633&partnerID=8YFLogxK

M3 - Article

VL - 72

SP - 661

EP - 671

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

IS - pt 4

ER -