scholarly journals Parameter Sweep Experiments on Spontaneous Gravity Wave Radiation from Unsteady Rotational Flow in an f-Plane Shallow Water System

2008 ◽  
Vol 65 (1) ◽  
pp. 235-249 ◽  
Author(s):  
Norihiko Sugimoto ◽  
Keiichi Ishioka ◽  
Katsuya Ishii
Keyword(s):  
Shallow Water ◽  
Gravity Wave ◽  
Power Law ◽  
Water System ◽  
Wave Radiation ◽  
Earth’S Rotation ◽  
Rotational Flow ◽  
Earth's Rotation ◽  
Shallow Water System ◽  
Wave Flux

Abstract Inertial gravity wave radiation from an unsteady rotational flow (spontaneous radiation) is investigated numerically in an f-plane shallow water system for a wide range of Rossby numbers, 1 ≤ Ro ≤ 1000, and Froude numbers, 0.1 ≤ Fr ≤ 0.8. A barotropically unstable jet flow is initially balanced and maintained by forcing so that spontaneous gravity wave radiation is generated continuously. The amount of gravity wave flux is proportional to Fr for large Ro(≥30), which is consistent with the power law of the aeroacoustic sound wave radiation theory (the Lighthill theory). In contrast, for small Ro(≤10) this power law does not hold because of the vortex stabilization due to the small deformation radius. In the case of fixed Fr, gravity wave flux is almost constant for larger Ro(>30) and decreases rapidly for smaller Ro(<5). There is a local maximum value between these Ro(∼10). Spectral frequency analysis of the gravity wave source shows that for Ro = 10, while the source term related to the earth’s rotation is larger than that related to unsteady rotational flow, the inertial cutoff frequency is still lower than the peak frequency of the dominant source. The results suggest that the effect of the earth’s rotation may intensify spontaneous gravity wave radiation for Ro ∼ 10.

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.

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

2007 ◽  
Vol 39 (11-12) ◽  
pp. 731-754 ◽  
Author(s):  
Norihiko Sugimoto ◽  
Keiichi Ishioka ◽  
Shigeo Yoden
Keyword(s):  
Shallow Water ◽  
Gravity Wave ◽  
Water System ◽  
Wave Radiation ◽  
Rotational Flow ◽  
Shallow Water System

Ageostrophic instability in rotating shallow water

2012 ◽  
Vol 712 ◽  
pp. 327-353 ◽  
Author(s):  
Peng Wang ◽  
James C. McWilliams ◽  
Ziv Kizner
Keyword(s):  
Shallow Water ◽  
Gravity Wave ◽  
Shear Wave ◽  
Water System ◽  
Wave Mode ◽  
Shear Instability ◽  
Mean Flow ◽  
Shallow Water System ◽  
Rotating Shallow Water ◽  
Wave Modes

AbstractLinear instabilities, both momentum-balanced and unbalanced, in several different $ \overline{u} (y)$ shear profiles are investigated in the rotating shallow water equations. The unbalanced instabilities are strongly ageostrophic and involve inertia–gravity wave motions, occurring only for finite Rossby ($\mathit{Ro}$) and Froude ($\mathit{Fr}$) numbers. They serve as a possible route for the breakdown of balance in a rotating shallow water system, which leads the energy to cascade towards small scales. Unlike previous work, this paper focuses on general shear flows with non-uniform potential vorticity, and without side or equatorial boundaries or vanishing layer depth (frontal outcropping). As well as classical shear instability among balanced shear wave modes (i.e. B–B type), two types of ageostrophic instability (B–G and G–G) are found. The B–G instability has attributes of both a balanced shear wave mode and an inertia–gravity wave mode. The G–G instability occurs as a sharp resonance between two inertia–gravity wave modes. The criterion for the occurrence of the ageostrophic instability is associated with the second stability condition of Ripa (1983), which requires a sufficiently large local Froude number. When $\mathit{Ro}$ and especially $\mathit{Fr}$ increase, the balanced instability is suppressed, while the ageostrophic instabilities are enhanced. The profile of the mean flow also affects the strength of the balanced and ageostrophic instabilities.

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