Inertia–Gravity Waves Emitted from Balanced Flow: Observations, Properties, and Consequences

Williams, Paul D.; Haine, Thomas W. N.; Read, P. L.

doi:10.1175/2008jas2480.1

Cited by 76 publications

(63 citation statements)

References 46 publications

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“…This was because U 0 and H 0 are constant for the cases of fixed Fr, and an unsteady jet flow is qualitatively the same for all cases. The shift of the dominant source term, which agrees with a previous laboratory study (Williams et al 2005(Williams et al , 2008, may cause an amplification of the gravity wave flux for smaller Ro. It is probable that there is a lo- cal maximum in the gravity wave flux for the cases of smaller Fr for Ro ∼ 10.…”

Section: Analysis Of the Source Of Gravity Wavessupporting

confidence: 89%

Spontaneous Gravity Wave Radiation in a Shallow Water System on a Rotating Sphere

Sugimoto

Ishii

2012

Journal of the Meteorological Society of Japan

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The effect of the earth's rotation on spontaneous inertial gravity wave radiation from an unsteady rotational flow is investigated numerically using a shallow water system on a rotating sphere, changing three parameters, the Rossby number (1 ≤ Ro ≤ 30), the Froude number (0.1 ≤ Fr ≤ 0.7), and the latitudinal positions of the jet (11.25 • N ≤ θ 0 ≤ 78.75 • N). The spectral-like three-point combined compact difference (sp-CCD) scheme is used for numerical calculation to estimate the amplitude of gravity waves with high accuracy and resolution similar to the spherical harmonics model. The jet, which is initially balanced but evolves with time because of barotropic instability, is maintained by relaxation forcing. The time variations of nearly balanced rotational flows continuously radiate gravity waves. While the amount of gravity wave flux for large Ro (≥ 10) in all positions of the jet is almost constant, that for relatively small Ro (< 10) depends considerably on the positions of the jet and the observational latitude. First, there is almost no gravity wave radiation from the jet positioned at a high latitude. Second, even when gravity waves are radiated from the jet positioned at low latitude, they rarely propagate toward a higher latitude. To discuss the results, the source of gravity waves is introduced as an analogy to the aeroacoustic sound wave radiation theory (Lighthill theory) with an f -plane approximation at the position of the jet. Spectral analysis of the sources reasonably explains the waves. Because the effect of the earth's rotation varies with the latitude, gravity waves are radiated only from an unsteady source with higher frequency than the inertial cut-off frequency at the position of the jet. In a similar way, gravity waves that propagate toward high latitudes should have a higher frequency than the inertial cut-off frequency at that latitude.

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Section: Analysis Of the Source Of Gravity Wavessupporting

confidence: 89%

Spontaneous Gravity Wave Radiation in a Shallow Water System on a Rotating Sphere

Sugimoto

Ishii

2012

Journal of the Meteorological Society of Japan

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“…On the other hand, a recent laboratory experiment (Williams et al 2008) showed that the amplitude changes linearly with Ro for Ro  1. Although the setting and the parameter range of the present paper are different from those of the studies mentioned above and the data shown in Fig.…”

Section: Summary and Discussionmentioning

confidence: 96%

“…Laboratory experiments of a two-layer system have been conducted to examine generation of gravity waves from vortical motions after Lovegrove et al (2000). In a parameter region of Ro  1, Williams et al (2005) and Williams et al (2008) showed that gravity waves are generated during the decay phase of the vacillation motions of the baroclonic wave and the amplitude of the generated gravity waves changes linearly with Ro. On the other hand, theoretical studies with highly idealized settings in this parameter region propose that the wave amplitude increases exponentially with Ro (Vanneste and Yavneh 2004;Plougonven et al 2005).…”

Section: Introductionmentioning

confidence: 99%

Inertia-Gravity Wave Radiation from an Unstable Bickley Jet in Rotating Two-Layer Shallow Water

Harada

Ishioka

2011

SOLA

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Parameter dependence of gravity-wave radiation from an unstable jet is investigated using a two-layer, f-plane shallow-water model. The sweeping parameters are the Rossby number Ro and the Froude number Fr. If Ro/Fr > 0.6, the barotropic instability dominates and gravity waves that are almost independent of the longitudinal direction and have latitudinal wavelengths longer than the jet width are radiated. The radiation occurs when the jet develops into cyclonic and anticyclonic vortex trains. The amplitude of the radiated waves increases monotonically with Ro and Fr. If Ro/Fr < 0.6, the baroclinic instability dominates and gravity waves the latitudinal wavelengths of which are shorter than or the same order of length as the jet width are radiated from cyclonic vortices dominating in the jet region. In this regime, the amplitude of the radiated waves increases with Fr, whereas it decreases with Ro. To understand the different dependences of the wave amplitude on Ro, we adopt the Lagrangian Rossby number R LG , and show that the amplitude increases with R LG .

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“…It can only exist as a modified concept of so called slow quasi-manifold or fuzzy manifold (Lorenz, 1986(Lorenz, , 1987(Lorenz, , 1992Jacobs, 1991;Vautard and Legras, 1986;Vallis, 1996;Vanneste and Yavneh, 2004;Warn and Menard, 1986;Warn et al, 1995;Warn, 1997;Ford, 2000), which means that balanced flow, to some extent, is just an approximation except for some particular cases such as parallel geostrophic flows and axisymmetric gradient flows. There is also now strong experimental evidence that the slow manifold is not an invariant manifold (Williams et al, 2008).…”

Section: Basic State Vortical Flow Balance and Imbalancementioning

confidence: 99%

A possible theory for the interaction between convective activities and vortical flows

Zhao

Shen

Ding

et al. 2011

Nonlin. Processes Geophys.

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Abstract. Theoretical studies usually attribute convections to the developments of instabilities such as the static or symmetric instabilities of the basic flows. However, the following three facts make the validities of these basic theories unconvincing. First, it seems that in most cases the basic flow with balance property cannot exist as the exact solution, so one cannot formulate appropriate problems of stability. Second, neither linear nor nonlinear theories of dynamical instability are able to describe a two-way interaction between convection and its background, because the basic state which must be an exact solution of the nonlinear equations of motion is prescribed in these issues. And third, the dynamical instability needs some extra initial disturbance to trigger it, which is usually another point of uncertainty. The present study suggests that convective activities can be recognized in the perspective of the interaction of convection with vortical flow. It is demonstrated that convective activities can be regarded as the superposition of free modes of convection and the response to the forcing induced by the imbalance of the unstably stratified vortical flow. An imbalanced vortical flow provides not only an initial condition from which unstable free modes of convection can develop but also a forcing on the convection. So, convection is more appropriately to be regarded as a spontaneous phenomenon rather than a disturbance-triggered phenomenon which is indicated by any theory of dynamical instability. Meanwhile, convection, particularly the forced part, has also a reaction on the basic flow by preventing the imbalance of the vortical flow from further increase and maintaining an approximately balanced flow.

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Inertia–Gravity Waves Emitted from Balanced Flow: Observations, Properties, and Consequences

Cited by 76 publications

References 46 publications

Spontaneous Gravity Wave Radiation in a Shallow Water System on a Rotating Sphere

Spontaneous Gravity Wave Radiation in a Shallow Water System on a Rotating Sphere

Inertia-Gravity Wave Radiation from an Unstable Bickley Jet in Rotating Two-Layer Shallow Water

A possible theory for the interaction between convective activities and vortical flows

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