### Abstract

We present a theoretical study of a fundamentally new wave-mean or wave-vortex interaction effect able to force persistent, cumulative change in mean flows in the absence of wave breaking or other kinds of wave dissipation. It is associated with the refraction of non-dissipating waves by inhomogeneous mean (vortical) flows. The effect is studied in detail in the simplest relevant model, the two-dimensional compressible flow equations with a generic polytropic equation of state. This includes the usual shallow-water equations as a special case. The refraction of a narrow, slowly varying wavetrain of small-amplitude gravity or sound waves obliquely incident on a single weak (low Froude or Mach number) vortex is studied in detail. It is shown that, concomitant with the changes in the waves' pseudomomentum due to the refraction, there is an equal and opposite recoil force that is felt, in effect, by the vortex core. This effective force is called a 'remote recoil' to stress that there is no need for the vortex core and wavetrain to overlap in physical space. There is an accompanying 'far-field recoil' that is still more remote, as in classical vortex-impulse problems. The remote-recoil effects are studied perturbatively using the wave amplitude and vortex weakness as small parameters. The nature of the remote recoil is demonstrated in various set-ups with wavetrains of finite or infinite length. The effective recoil force R_{v} on the vortex core is given by an expression resembling the classical Magnus force felt by moving cylinders with circulation. In the case of wavetrains of infinite length, an explicit formula for the scattering angle θ* of waves passing a vortex at a distance is derived correct to second order in Froude or Mach number. To this order R_{v} ∝ θ*. The formula is cross-checked against numerical integrations of the ray-tracing equations. This work is part of an ongoing study of internal-gravity-wave dynamics in the atmosphere and may be important for the development of future gravity-wave parametrization schemes in numerical models of the global atmospheric circulation. At present, all such schemes neglect remote-recoil effects caused by horizontally inhomogeneous mean flows. Taking these effects into account should make the parametrization schemes significantly more accurate.

Original language | English (US) |
---|---|

Pages (from-to) | 207-230 |

Number of pages | 24 |

Journal | Journal of Fluid Mechanics |

Issue number | 492 |

DOIs | |

State | Published - Oct 10 2003 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Fluid Mechanics*, (492), 207-230. https://doi.org/10.1017/S0022112003005639

**Remote recoil : A new wave-mean interaction effect.** / Buhler, Oliver; McIntyre, Michael E.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, no. 492, pp. 207-230. https://doi.org/10.1017/S0022112003005639

}

TY - JOUR

T1 - Remote recoil

T2 - A new wave-mean interaction effect

AU - Buhler, Oliver

AU - McIntyre, Michael E.

PY - 2003/10/10

Y1 - 2003/10/10

N2 - We present a theoretical study of a fundamentally new wave-mean or wave-vortex interaction effect able to force persistent, cumulative change in mean flows in the absence of wave breaking or other kinds of wave dissipation. It is associated with the refraction of non-dissipating waves by inhomogeneous mean (vortical) flows. The effect is studied in detail in the simplest relevant model, the two-dimensional compressible flow equations with a generic polytropic equation of state. This includes the usual shallow-water equations as a special case. The refraction of a narrow, slowly varying wavetrain of small-amplitude gravity or sound waves obliquely incident on a single weak (low Froude or Mach number) vortex is studied in detail. It is shown that, concomitant with the changes in the waves' pseudomomentum due to the refraction, there is an equal and opposite recoil force that is felt, in effect, by the vortex core. This effective force is called a 'remote recoil' to stress that there is no need for the vortex core and wavetrain to overlap in physical space. There is an accompanying 'far-field recoil' that is still more remote, as in classical vortex-impulse problems. The remote-recoil effects are studied perturbatively using the wave amplitude and vortex weakness as small parameters. The nature of the remote recoil is demonstrated in various set-ups with wavetrains of finite or infinite length. The effective recoil force Rv on the vortex core is given by an expression resembling the classical Magnus force felt by moving cylinders with circulation. In the case of wavetrains of infinite length, an explicit formula for the scattering angle θ* of waves passing a vortex at a distance is derived correct to second order in Froude or Mach number. To this order Rv ∝ θ*. The formula is cross-checked against numerical integrations of the ray-tracing equations. This work is part of an ongoing study of internal-gravity-wave dynamics in the atmosphere and may be important for the development of future gravity-wave parametrization schemes in numerical models of the global atmospheric circulation. At present, all such schemes neglect remote-recoil effects caused by horizontally inhomogeneous mean flows. Taking these effects into account should make the parametrization schemes significantly more accurate.

AB - We present a theoretical study of a fundamentally new wave-mean or wave-vortex interaction effect able to force persistent, cumulative change in mean flows in the absence of wave breaking or other kinds of wave dissipation. It is associated with the refraction of non-dissipating waves by inhomogeneous mean (vortical) flows. The effect is studied in detail in the simplest relevant model, the two-dimensional compressible flow equations with a generic polytropic equation of state. This includes the usual shallow-water equations as a special case. The refraction of a narrow, slowly varying wavetrain of small-amplitude gravity or sound waves obliquely incident on a single weak (low Froude or Mach number) vortex is studied in detail. It is shown that, concomitant with the changes in the waves' pseudomomentum due to the refraction, there is an equal and opposite recoil force that is felt, in effect, by the vortex core. This effective force is called a 'remote recoil' to stress that there is no need for the vortex core and wavetrain to overlap in physical space. There is an accompanying 'far-field recoil' that is still more remote, as in classical vortex-impulse problems. The remote-recoil effects are studied perturbatively using the wave amplitude and vortex weakness as small parameters. The nature of the remote recoil is demonstrated in various set-ups with wavetrains of finite or infinite length. The effective recoil force Rv on the vortex core is given by an expression resembling the classical Magnus force felt by moving cylinders with circulation. In the case of wavetrains of infinite length, an explicit formula for the scattering angle θ* of waves passing a vortex at a distance is derived correct to second order in Froude or Mach number. To this order Rv ∝ θ*. The formula is cross-checked against numerical integrations of the ray-tracing equations. This work is part of an ongoing study of internal-gravity-wave dynamics in the atmosphere and may be important for the development of future gravity-wave parametrization schemes in numerical models of the global atmospheric circulation. At present, all such schemes neglect remote-recoil effects caused by horizontally inhomogeneous mean flows. Taking these effects into account should make the parametrization schemes significantly more accurate.

UR - http://www.scopus.com/inward/record.url?scp=0142153779&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0142153779&partnerID=8YFLogxK

U2 - 10.1017/S0022112003005639

DO - 10.1017/S0022112003005639

M3 - Article

SP - 207

EP - 230

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

IS - 492

ER -