## Gravity Waves in a Horizontal Shear Flow. Part II: Interaction between Gravity Waves and Potential Vorticity Perturbations (2007)

Citations: | 2 - 1 self |

### BibTeX

@MISC{Bakas07gravitywaves,

author = {Nikolaos A. Bakas and Brian and F. Farrell},

title = {Gravity Waves in a Horizontal Shear Flow. Part II: Interaction between Gravity Waves and Potential Vorticity Perturbations},

year = {2007}

}

### OpenURL

### Abstract

Interaction among potential vorticity perturbations and propagating internal gravity waves in a horizontally sheared zonal flow is investigated. In the strong stratification limit, an initial vorticity perturbation weakly excites two propagating gravity waves while the density component of the potential vorticity perturbation is significantly amplified, potentially leading to convective collapse. If stratification is sufficiently weak, a strong coupling between vorticity perturbations and gravity waves is found and spontaneous gravity wave generation occurs. This coupling can be traced to the nonnormal interaction between the potential vorticity and gravity wave manifolds in the weak stratification limit. Vorticity perturbations amplify in energy due to downgradient Reynolds stress when their phase lines tilt against the shear and the large growth attained is transferred to propagating gravity waves. When the flow geometry is such that the excited gravity waves are confined in the vicinity of the vorticity perturbation by their trapping levels, an overall convective collapse of this region can be anticipated. On the other hand, when the flow geometry permits wave propagation, significant gravity wave emission occurs. 1.

### Citations

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(Show Context)
Citation Context ...at time t 5 l/k. As in the case of sheared disturbances on the f plane (Vanneste and Yavneh 2004), spontaneous generation of these gravity waves can be analyzed as an instance of a Stokes phenomenon (=-=Olver 1974-=-) in which the subdominant solution (waves) is switched on by the dominant solution (potential vorticity perturbation) when time crosses a Stokes line. To determine the leadingorder approximation to t... |

53 |
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(Show Context)
Citation Context ...ostrophic adjustment of an initially unbalanced flow. Ford et al. (2000) showed that in the small-Froude-number limit, emission of gravity waves is analogous to Lighthill radiation of acoustic waves (=-=Lighthill 1952-=-) and occurs due to frequency matching between the waves and the balanced motion. In the absence of such frequency matching, the emission is very weak, as found by Vanneste and Yavneh (2004), who show... |

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(Show Context)
Citation Context ...nearized, sheared disturbances on an f plane that inertia–gravity waves were spontaneously generated by balanced initial conditions and that this could be analyzed as a Stokes phenomenon (Olver 1974; =-=Berry 1989-=-): the subdominant homogeneous solution was excited by the dominant, oscillation-free, inhomogeneous solution when time t crossed a Stokes line. The Stokes line arose from singularities of the asympto... |

17 |
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(Show Context)
Citation Context ...en intensively studied because the internal wave field is ubiquitous in the ocean and also because of the role of internal wave energy generation and dissipation in the large-scale ocean circulation (=-=Kuhlbrodt et al. 2007-=-). In Part I of this work (Bakas and Farrell 2009, hereafter Part I), we studied the evolution of small perturbations superposed on a stably stratified horizontal shear flow, focusing on the role of t... |

11 |
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Citation Context ...e low frequency compared to the internal wave frequency, the generated waves have an amplitude that is exponentially small in Rossby number. In this work, we perform a generalized stability analysis (=-=Farrell and Ioannou 1996-=-) of a linear threedimensional stably stratified model with a constant Brunt–Väisälä frequency and a meridional shear flow making use of closed-form asymptotic solutions. Our purpose is to clarify the... |

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(Show Context)
Citation Context ...Panepistimiopolis, Zografos, Athens, Greece. E-mail: nikos.bakas@gmail.com Spontaneous generation of gravity waves has been studied previously in theoretical investigations of shallowwater equations (=-=Ford 1994-=-; Ford et al. 2000; Plougonven and Zeitlin 2002), of sheared disturbances on an f plane (McWilliams and Yavneh 1998; Vanneste and Yavneh 2004; Kalashnik et al. 2006), and of Lorenz’s fivecomponent mod... |

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(Show Context)
Citation Context ... Yavneh 1998; Vanneste and Yavneh 2004; Kalashnik et al. 2006), and of Lorenz’s fivecomponent model (Vanneste 2004). Spontaneous emission of gravity waves has also been seen in observational studies (=-=Uccellini and Koch 1987-=-; Guest et al. 2000; Pavelin et al. 2001; Plougonven et al. 2003) and numerical simulations (O’Sullivan and Dunkerton 1995; Zhang 2004; Plougonven and Snyder 2007; Viudez and Dritschel 2006) of barocl... |

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Citation Context ...oscillation-free initial conditions; that is, we choose ^r(0) 5 ^r vort(0). We then follow the analysis in Vanneste and Yavneh (2004) in appendix B and use asymptotic matching in the complex t plane (=-=Hakim 1998-=-) to show that the solution at large times is given by ^r(t) 5 ^r vort(t) 1 ^q(0) pffiffiffi ffiffi S e k ffiffiffi p 1/4 2S 3 [e i pffiffi Ð t pffiffiffiffiffiffi S v(s) ds1 i 0 e p (if0 b) pffiffi Ð... |

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2 | Inertia-gravity wave generation by balanced motion: revisiting the LorenzKrishnamurthy model - Vanneste - 2004 |

1 | 2009: Gravity waves in a barotropic shear flow. Part I: Growth mechanisms in the absence of potential vorticity perturbations - Bakas, Farrell |

1 | 2005: Stokes-multiplier expansion in an inhomogeneous differential equation with a small parameter - Ólafsdóttir, Daalhuis, et al. |

1 | 2006: Spontaneous emission of inertia–gravity wave packets by balanced geophysical wave packets - Viudez, Dritschel |