Gravity wave radiation from unsteady rotational flow in an<i>f</i>-plane shallow water system

Sugimoto, Norihiko; Ishioka, Keiichi; Yoden, Shigeo

doi:10.1016/j.fluiddyn.2007.07.001

Cited by 10 publications

(19 citation statements)

References 26 publications

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“…Thus, gravity waves having high wave number k g are evanescent, which is consistent with the f -plane case (Sugimoto et al 2007b). After these initial phases, forcing makes rotational flows unsteady and continuous gravity wave radiation is observed.…”

Section: Typical Spontaneous Gravity Wave Radiation (Rosupporting

confidence: 80%

“…While source S 1 corresponds to source in the original theory of vortex sound, source S 2 is related to the Coriolis frequency and thus directly depends on the effect of the earth's rotation. Source S 3 is related to surface depression; however, Sugimoto et al (2007b) showed that this term was negligible (S 3 ≈ 0) in the f -plane models. In addition, they also found that the source terms related to zonal forcing and dissipation barely contributed to spontaneous gravity wave radiation (F ≈ 0).…”

Section: Ford-lighthill Equation and Gravity Wave Fluxmentioning

confidence: 93%

“…In the case when gravity waves are radiated mainly from an unsteady rotational flow (Sugimoto et al 2007b) and the source is localized near the jet region (compact assumption), then…”

Section: Ford-lighthill Equation and Gravity Wave Fluxmentioning

confidence: 99%

“…The other way is to use simpler configuration models of an f -plane shallow water system (Ford 1994;Sugimoto et al 2005Sugimoto et al , 2007bSugimoto et al , 2008. This is the simplest system in which both rotational flows and inertial gravity waves exist.…”

Section: Introductionmentioning

confidence: 99%

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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: Typical Spontaneous Gravity Wave Radiation (Rosupporting

confidence: 80%

Section: Ford-lighthill Equation and Gravity Wave Fluxmentioning

confidence: 93%

“…In the case when gravity waves are radiated mainly from an unsteady rotational flow (Sugimoto et al 2007b) and the source is localized near the jet region (compact assumption), then…”

Section: Ford-lighthill Equation and Gravity Wave Fluxmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…5 While gravity wave radiation in a shallow water system is different from that in a continuously stratified one, 6 their fundamental study in geophysical fluid dynamics is nevertheless important. 3 Spontaneous gravity wave radiation from unsteady vortical flows in rotating shallow water has been investigated 5,[7][8][9] and cyclone-anticyclone asymmetry has recently been found. 10 However, it is not evident whether this asymmetry appears in complicated vortical flows, since analysis and numerical verification were performed only for an idealized case of a co-rotating point vortex pair.…”

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confidence: 99%

Inertia-gravity wave radiation from the merging of two co-rotating vortices in the f-plane shallow water system

Sugimoto

2015

Physics of Fluids

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Inertia-gravity wave radiation from the merging of two co-rotating vortices is investigated numerically in a rotating shallow water system in order to focus on cyclone–anticyclone asymmetry at different values of the Rossby number (Ro). A numerical study is conducted on a model using a spectral method in an unbounded domain to estimate the gravity wave flux with high accuracy. Continuous gravity wave radiation is observed in three stages of vortical flows: co-rotating of the vortices, merging of the vortices, and unsteady motion of the merged vortex. A cyclone–anticyclone asymmetry appears at all stages at smaller Ro (≤20). Gravity waves from anticyclones are always larger than those from cyclones and have a local maximum at smaller Ro (∼2) compared with that for an idealized case of a co-rotating vortex pair with a constant rotation rate. The source originating in the Coriolis acceleration has a key role in cyclone–anticyclone asymmetry in gravity waves. An additional important factor is that at later stages, the merged axisymmetric anticyclone rotates faster than the elliptical cyclone due to the effect of the Rossby deformation radius, since a rotation rate higher than the inertial cutoff frequency is required to radiate gravity waves.

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Balance regimes for the stability of a jet in anf-plane shallow water system

2007

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To study a limit of validity of balanced models, stability of a zonal jet is investigated both linearly and nonlinearly in an f-plane shallow water system for a wide range of parameter. It is shown that quasi-geostrophic approximation gives not only a good estimation of maximum growth rate for high Rossby number, Ro, but also is valid even in the nonlinear phase of instability for high Ro as long as Froude number, Fr, is low. While the maximum growth rate of unstable modes is well estimated by the quasi-geostrophic approximation, dominant balance is different between high and low Ro. In the low Ro regime (Ro < 5), geostrophic balance is dominant in the perturbation field, the ratio / of the amplitudes of divergent flow to that of rotational flow is proportional to Fr 2 /Ro, where and are velocity potential and streamfunction, respectively. On the other hand, in the high Ro regime (Ro > 5), cyclostrophic balance with basic shear is dominant, / ∝ Fr 2 . Considering that the barotropic instability is caused by the resonance of neutral Rossby wave modes, we can explain the difference of the ratio in each regime. Using the ratio / being small, different approximation of the linear shallow water equations for each regime is deduced. Properties of the linear unstable modes are explained with these approximations.

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Gravity wave radiation from unsteady rotational flow in anf-plane shallow water system

Cited by 10 publications

References 26 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 the merging of two co-rotating vortices in the f-plane shallow water system

Balance regimes for the stability of a jet in anf-plane shallow water system

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