scholarly journals Analogy between electro-magnetic waves in cold unmagnetized plasma and shallow water inertio-gravity waves in geophysical systems

2021 ◽  
Author(s):  
E. Heifetz ◽  
L. R. M. Maas ◽  
J. Mak ◽  
I. Pomerantz
Keyword(s):  
Dispersion Relation ◽  
Shallow Water ◽  
Gravity Waves ◽  
Collisionless Plasma ◽  
Water System ◽  
Phase Speed ◽  
Rotating Shallow Water ◽  
Unmagnetized Plasma ◽  
Electro Magnetic ◽  
Magnetic Waves

Abstract The fundamental dispersion relation of transverse electro-magnetic waves in a cold collisionless plasma is formally equivalent to the two-dimensional dispersion relation of inertio-gravity waves in a rotating shallow water system, where the Coriolis frequency can be identified with the plasma frequency, and the shallow water gravity wave phase speed plays the role of the speed of light. Here we examine this equivalence and compare between the propagation wave mechanisms in these seemingly unrelated physical systems.

Existence and properties of ageostrophic modons and coherent tripoles in the two-layer rotating shallow water model on the -plane

2012 ◽  
Vol 706 ◽  
pp. 71-107 ◽  
Author(s):  
Noé Lahaye ◽  
Vladimir Zeitlin
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Coherent Structures ◽  
Water Model ◽  
Shallow Water Model ◽  
Scatter Plot ◽  
Weak Stratification ◽  
Rotating Shallow Water ◽  
Frontal Collisions ◽  
Inertia Gravity Waves

AbstractWe study formation and properties of new coherent structures: ageostrophic modons in the two-layer rotating shallow water model. The ageostrophic modons are obtained by ‘ageostrophic adjustment’ of the exact modon solutions of the two-layer quasi-geostrophic equations with the free surface, which are used to initialize the full two-layer shallow water model. Numerical simulations are performed using a well-balanced high-resolution finite volume numerical scheme. For large enough Rossby numbers, the initial configurations undergo ageostrophic adjustment towards asymmetric ageostrophic quasi-stationary coherent dipoles. This process is accompanied by substantial emission of inertia–gravity waves. The resulting dipole is shown to be robust and survives frontal collisions. It contains captured inertia–gravity waves and, for higher Rossby numbers and weak stratification, carries a (baroclinic) hydraulic jump at its axis. For stronger stratifications and high enough Rossby numbers, ‘rider’ coherent structures appear as a result of adjustment, with a monopole in one layer and a dipole in another. Other ageostrophic coherent structures, such as two-layer tripoles and two-layer modons with nonlinear scatter plot, result from the collisions of ageostrophic modons. They are shown to be long-living and robust, and to capture waves.

Waves in parallel or swirling stratified shear flows

1979 ◽  
Vol 93 (3) ◽  
pp. 401-412 ◽  
Author(s):  
S. Leibovich
Keyword(s):  
Dispersion Relation ◽  
Gravity Waves ◽  
Wave Energy ◽  
Richardson Number ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Maximum Speed ◽  
Meridian Plane ◽  
Finite Rate ◽  
Critical Richardson Number

The dispersion relations for infinitesimal internal gravity waves (A) and axisymmetric waves in swirling streams (B) are considered. In both cases the mainstream may be sheared and density stratified in the transverse (vertical in case A, radial in case B) direction. The following results are proved for either case: If the maximum speed Wmax (or minimum speed Wmin) (in a meridian plane in case B) of the mainstream occurs at an interior point in the fluid, then the phase speed of any mode takes all values from the Wmax (or Wmin) to +∞ ( —∞) as the overall Richardson number λ2 varies from 0 to ∞. If Wmax(Wmin) is attained at a boundary point with finite rate of strain, there is a positive non-zero critical Richardson number below which one or both branches of the dispersion relation terminate. These results employ variational methods and correct erroneous results concerning problem B stated in Chandrasekhar's treatise on hydrodynamic stability. Furthermore, bounds are given on the group velocity for both branches of the dispersion relation. From these bounds it is shown that in the absence of reversals of the mainstream (Wmin > 0) upstream propagation of wave energy is impossible whenever upstream propagation of constant phase surfaces is impossible.

Modulation of Shallow-Water Equatorial Waves due to a Varying Equivalent Height Background

2013 ◽  
Vol 70 (9) ◽  
pp. 2726-2750 ◽  
Author(s):  
Juliana Dias ◽  
Pedro L. Silva Dias ◽  
George N. Kiladis ◽  
Maria Gehne
Keyword(s):  
Shallow Water ◽  
Large Scale ◽  
Water System ◽  
Phase Speed ◽  
Asymptotic Solutions ◽  
Height Anomaly ◽  
Equatorial Waves ◽  
Moist Convection ◽  
Horizontal Structure ◽  
Shallow Water System

Abstract The dynamics of convectively coupled equatorial waves (CCEWs) is analyzed in an idealized model of the large-scale atmospheric circulation. The model is composed of a linear rotating shallow-water system with a variable equivalent height, or equivalent gravity wave speed, which varies in space. This model is based on the hypothesis that moist convection acts to remove convective instability, therefore modulating the equivalent height of a shallow-water system. Asymptotic solutions are derived in the case of a small perturbation around a constant coefficient, which is assumed to be a mean moist equivalent height derived from satellite observations. The first-order solutions correspond to the free normal modes of the linear shallow-water system and the second-order flow is derived solving a perturbation eigenvalue problem. The asymptotic solutions are documented in the case of a zonally varying equivalent height and for wavenumbers and frequencies that are consistent with observations of CCEWs. This analysis shows that the dynamics of the secondary divergence and its impact on the full divergence varies mode by mode. For instance, for a negative equivalent height anomaly, which is interpreted as a moister background, the secondary divergence is nearly in phase with the primary divergence in the case of Kelvin waves—in contrast to mixed Rossby–gravity waves where the secondary divergence acts to attenuate the primary divergence. While highly idealized, the modeled waves share some features with observations, providing a mechanism for the relationship between CCEWs phase speed, amplitude, and horizontal structure.

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

2015 ◽  
Vol 772 ◽  
pp. 80-106 ◽  
Author(s):  
Norihiko Sugimoto ◽  
K. Ishioka ◽  
H. Kobayashi ◽  
Y. Shimomura
Keyword(s):  
Shallow Water ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Water System ◽  
Local Maximum ◽  
Vortex Pair ◽  
Wave Radiation ◽  
Earth’S Rotation ◽  
Far Field ◽  
Earth's Rotation

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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