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

Harada, Masatake; Ishioka, Keiichi

doi:10.2151/sola.2011-029

Cited by 2 publications

(1 citation statement)

References 14 publications

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“…The more relevant parameter regime for synoptic-scale flows would be where the Rossby number is small in the order of unity (Saujani and Shepherd 2002). Future work includes development of a two-layer model in which internal gravity waves are radiated from the baroclinic instability of the jet (Harada and Ishioka 2011), or more realistically, a three-dimensional model in which gravity waves propagate in the vertical direction to study the phenomena of polar night jets and synoptic-scale flows.…”

Section: Summary and Discussionmentioning

confidence: 99%

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: Summary and Discussionmentioning

confidence: 99%

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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Cyclone–anticyclone asymmetry in gravity wave radiation from a co-rotating vortex pair in rotating shallow water

et al. 2015

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Cyclone–anticyclone asymmetry in spontaneous gravity wave radiation from a co-rotating vortex pair is investigated in an $f$-plane shallow water system. The far field of gravity waves is derived analytically by analogy with the theory of aeroacoustic sound wave radiation (Lighthill theory). In the derived form, the Earth’s rotation affects not only the propagation of gravity waves but also their source. While the results correspond to the theory of vortex sound in the limit of $f\rightarrow 0$, there is an asymmetry in gravity wave radiation between cyclone pairs and anticyclone pairs for finite values of $f$. Anticyclone pairs radiate gravity waves more intensely than cyclone pairs due to the effect of the Earth’s rotation. In addition, there is a local maximum of intensity of gravity waves from anticyclone pairs at an intermediate $f$. To verify the analytical solution, a numerical simulation is also performed with a newly developed spectral method in an unbounded domain. The novelty of this method is the absence of wave reflection at the boundary due to a conformal mapping and a pseudo-hyperviscosity that acts like a sponge layer in the far field of waves. The numerical results are in excellent agreement with the analytical results even for finite values of $f$ for both cyclone pairs and anticyclone pairs.

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

Cited by 2 publications

References 14 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

Cyclone–anticyclone asymmetry in gravity wave radiation from a co-rotating vortex pair in rotating shallow water

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