scholarly journals Gravity Wave Radiation and Mean Responses to Local Body Forces in the Atmosphere

2001 ◽  
Vol 58 (16) ◽  
pp. 2249-2279 ◽  
Author(s):  
Sharon L. Vadas ◽  
David C. Fritts
Keyword(s):  
Gravity Wave ◽  
Wave Radiation ◽  
Body Forces ◽  
Local Body

scholarly journals Inertia–gravity-wave radiation by a sheared vortex

2008 ◽  
Vol 596 ◽  
pp. 169-189 ◽  
Author(s):  
E. I. ÓLAFSDÓTTIR ◽  
A. B. OLDE DAALHUIS ◽  
J. VANNESTE
Keyword(s):  
Gravity Wave ◽  
Couette Flow ◽  
Gravity Waves ◽  
Dimensional Structure ◽  
Analytic Description ◽  
Wave Radiation ◽  
Rossby Number ◽  
Spontaneous Radiation ◽  
Initial State ◽  
Inertia Gravity Waves

We consider the linear evolution of a localized vortex with Gaussian potential vorticity that is superposed on a horizontal Couette flow in a rapidly rotating strongly stratified fluid. The Rossby number, defined as the ratio of the shear of the Couette flow to the Coriolis frequency, is assumed small. Our focus is on the inertia–gravity waves that are generated spontaneously during the evolution of the vortex. These are exponentially small in the Rossby number and hence are neglected in balanced models such as the quasi-geostrophic model and its higher-order generalizations. We develop an exponential-asymptotic approach, based on an expansion in sheared modes, to give an analytic description of the three-dimensional structure of the inertia–gravity waves emitted by the vortex. This provides an explicit example of the spontaneous radiation of inertia–gravity waves by localized balanced motion in the small-Rossby-number regime.The inertia–gravity waves are emitted as a burst of four wavepackets propagating downstream of the vortex. The approach employed reduces the computation of inertia–gravity-wave fields to a single quadrature, carried out numerically, for each spatial location and each time. This makes it possible to unambiguously define an initial state that is entirely free of inertia–gravity waves, and circumvents the difficulties generally associated with the separation between balanced motion and inertia–gravity waves.

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.

scholarly journals On the Relative Contribution of Inertia–Gravity Wave Radiation to Asymmetric Instabilities in Tropical Cyclone–like Vortices

2016 ◽  
Vol 73 (9) ◽  
pp. 3345-3370 ◽  
Author(s):  
Konstantinos Menelaou ◽  
David A. Schecter ◽  
M. K. Yau
Keyword(s):  
Tropical Cyclone ◽  
Gravity Wave ◽  
Tropical Cyclones ◽  
Potential Vorticity ◽  
Three Dimensional ◽  
Life Cycles ◽  
Wave Radiation ◽  
Ambient Conditions ◽  
Layer Potential ◽  
The Impact

Abstract Intense atmospheric vortices such as tropical cyclones experience various asymmetric instabilities during their life cycles. This study investigates how vortex properties and ambient conditions determine the relative importance of different mechanisms that can simultaneously influence the growth of an asymmetric perturbation. The focus is on three-dimensional disturbances of barotropic vortices with nonmonotonic radial distributions of potential vorticity. The primary modes of instability are examined for Rossby numbers between 10 and 100 and Froude numbers in the broad neighborhood of unity. This parameter regime is deemed appropriate for tropical cyclone perturbations with vertical length scales ranging from the depth of the vortex to moderately smaller scales. At relatively small Froude numbers, the main cause of instability inferred from analysis typically involves the interaction of vortex Rossby waves with each other and/or critical-layer potential vorticity perturbations. As the Froude number increases from its lower bound, the main cause of instability transitions to inertia–gravity wave radiation. In some cases, the transition occurs abruptly at a critical point where a mode whose growth is driven almost entirely by radiation suddenly becomes dominant. In other cases, the transition is gradual and less direct as the fastest-growing mode continuously changes its structure. Examination of the angular pseudomomentum budget helps quantify the impact of radiation. The radiation-driven instabilities examined herein are shown to be quite fast and potentially relevant to real-world tropical cyclones. Their sensitivities to parameterized moisture and outer vorticity skirts are briefly addressed.

scholarly journals The merger of geophysical vortices at finite Rossby and Froude number

2018 ◽  
Vol 848 ◽  
pp. 388-410 ◽  
Author(s):  
Jean N. Reinaud ◽  
David G. Dritschel
Keyword(s):  
Froude Number ◽  
Gravity Wave ◽  
Potential Vorticity ◽  
Initial Conditions ◽  
The Other ◽  
Vertical Shear ◽  
Wave Radiation ◽  
Rossby Number ◽  
Other Hand ◽  
Vorticity Anomaly

We investigate the merger of two co-rotating geophysical vortices at finite Rossby and Froude number. The initial conditions consist of two uniform potential vorticity vortices in near-equilibrium and in a nearly ‘balanced’ state (i.e. with negligible emission of inertia–gravity wave radiation). We determine the critical merger distance between the two vortices. This distance is found to increase with the magnitude of the Rossby number: intense cyclones or intense anticyclones are able to merge from further apart compared to weaker cyclones and anticyclones. Note that the Froude number is proportional to the Rossby number for the near-equilibrium initial conditions considered. The critical merging distance also depends on the sign of the potential vorticity anomaly, which is positive for ‘cyclones’ and negative for ‘anticyclones’. We show that ageostrophic motions occurring at finite Rossby number tend to draw cyclones together but draw anticyclones apart. On the other hand, we show that anticyclones tend to deform more, in particular when subject to vertical shear (as when the vortices are vertically offset). These two effects compete. Overall, nearly aligned cyclones tend to merge from further apart than their anticyclonic counterparts, while vertically offset anticyclones merge from further apart than cyclones.

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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