An official website of the United States government
Abstract Vortex Rossby waves (VRWs) affect tropical cyclones’ (TCs’) motion, structure, and intensity. They propagate within annular waveguides defined by a passband between Ω1D, the Doppler-shifted frequency of a one-dimensional VRW, and zero. Wavenumber-1 VRWs cause TC motion directly and have wider waveguides than wavenumbers ≥ 2. VRWs forced with fixed rotation frequency propagate away from the forcing. Initially outward-propagating waves are Doppler shifted to zero at a critical radius, where they are absorbed. Initially inward-propagating waves are Doppler shifted to Ω1D, reflect from a turning point, propagate outward, and are ultimately absorbed at the critical radius. Between the forcing and the turning radii, the VRWs have standing-wave structure; outward from the forcing they are trailing spirals. They carry angular momentum fluxes that act to accelerate the mean flow at the forcing radius and decelerate it at the critical radius. Mean-flow vorticity monopoles are inconsistent with Stokes’s theorem on a spherical Earth, because a contour enclosing the monopole’s antipode would have nonzero circulation but would enclose zero vorticity. The Rossby waveguide paradigm also fits synoptic-scale Rossby waves in a meridionally sheared zonal flow. These waves propagate within a waveguide confined between a poleward turning latitude and an equatorward critical latitude. Forced waves are comma-shaped gyres that resemble observed frontal cyclones, with trailing filaments equatorward of the forcing latitude and standing waves poleward. Even neutral forced Rossby waves converge westerly momentum at the latitude of forcing.
more »
« less
On the nonlinear stability and the existence of selective decay states of 3D quasi‐geostrophic potential vorticity equation
In this article, we study the dynamics of large‐scale motion in atmosphere and ocean governed by the 3D quasi‐geostrophic potential vorticity (QGPV) equation with a constant stratification. It is shown that for a Kolmogorov forcing on the first energy shell, there exist a family of exact solutions that are dissipative Rossby waves. The nonlinear stability of these exact solutions are analyzed based on the assumptions on the growth rate of the forcing. In the absence of forcing, we show the existence of selective decay states for the 3D QGPV equation. The selective decay states are the 3D Rossby waves traveling horizontally at a constant speed. All these results can be regarded as the expansion of that of the 2D QGPV system and in the case of 3D QGPV system with isotropic viscosity. Finally, we present a geometric foundation for the model as a general equation for nonequilibrium reversible‐irreversible coupling.
more »
« less
- Award ID(s):
- 1912715
- PAR ID:
- 10372772
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Mathematical Methods in the Applied Sciences
- Volume:
- 43
- Issue:
- 2
- ISSN:
- 0170-4214
- Page Range / eLocation ID:
- p. 822-846
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
This work discusses modons, or dipolar vortices, propagating along sloping topography. Two different regimes exist, which are studied separately using the surface quasi-geostrophic equations. First, when the modon propagates in the direction opposite to topographic Rossby waves, steady solutions exist and a semi-analytical method is presented for calculating these solutions. Second, when the modon propagates in the same direction as the Rossby waves, a wave wake is generated. This wake removes energy from the modon, causing it to decay slowly. Asymptotic predictions are presented for this decay and found to agree closely with numerical simulations. Over long times, decaying vortices are found to break down due to an asymmetry resulting from the generation of waves inside the vortex. A monopolar vortex moving along a wall is shown to behave in a similar way to a dipole, though the presence of the wall is found to stabilise the vortex and prevent the long-time breakdown. The problem is equivalent mathematically to a dipolar vortex moving along a density front, hence our results apply directly to this case.more » « less
-
Abstract Recent observations of Rossby waves and other more exotic forms of inertial oscillations in the Sun’s convection zone have kindled the hope that such waves might be used as a seismic probe of the Sun's interior. Here, we present a 3D numerical simulation in spherical geometry that models the Sun’s convection zone and upper radiative interior. This model features a wide variety of inertial oscillations, including both sectoral and tesseral equatorial Rossby waves, retrograde mixed inertial modes, prograde thermal Rossby waves, the recently observed high-frequency retrograde (HFR) vorticity modes, and what may be latitudinal overtones of these HFR modes. With this model, we demonstrate that sectoral and tesseral Rossby waves are ubiquitous within the radiative interior as well as within the convection zone. We suggest that there are two different Rossby-wave families in this simulation that live in different wave cavities: one in the radiative interior and one in the convection zone. Finally, we suggest that many of the retrograde inertial waves that appear in the convection zone, including the HFR modes, are in fact all related, being latitudinal overtones that are mixed modes with the prograde thermal Rossby waves.more » « less
-
Abstract Observational evidence of two extratropical pathways to forcing tropical convective disturbances is documented through a statistical analysis of satellite-derived OLR and ERA5 reanalysis. The forcing mechanism and the resulting disturbances are found to strongly depend on the structure of the background zonal wind. Although Rossby wave propagation is prohibited in easterlies, modeling studies have shown that extratropical forcing can still excite equatorial waves through resonance between the tropics and extratropics. Here this “remote” forcing pathway is investigated for the first time in the context of convectively coupled Kelvin waves over the tropical Pacific during northern summer. The extratropical forcing is manifested by eddy momentum flux convergence that arises when extratropical eddies propagate into the subtropics and encounter their critical line. This nonlinear forcing has similar wavenumbers and frequencies with Kelvin waves and excites them by projecting onto their meridional eigenstructure in zonal wind, as a form of resonance. This resonance is also evidenced by a momentum budget analysis, which reveals the nonlinear forcing term is essential for maintenance of the waves, while the remaining linear terms are essential for propagation. In contrast, the “local” pathway of extratropical forcing entails the presence of a westerly duct during northern winter that permits Rossby waves to propagate into the equatorial east Pacific, while precluding any sort of resonance with Kelvin waves due to Doppler shifting effects. The intruding disturbances primarily excite tropical “cloud plumes” through quasigeostrophic forcing, while maintaining their extratropical nature. This study demonstrates the multiple roles of the extratropics in forcing in tropical circulations and illuminates how tropical–extratropical interactions and extratropical basic states can provide be a source of predictability at the S2S time scale. Significance Statement This study seeks to understand how circulations in the midlatitudes excite the weather systems in the tropics. Results show that the mechanisms, as well as the types of tropical weather systems excited, are strongly dependent on the mean large-scale wind structure. In particular, when the large-scale wind blows from east to west, a special type of eastward-moving tropical weather system, the Kelvin wave, is excited owing to its resonance with remote eastward-moving weather systems in the extratropics. On the contrary, when the average wind blows from west to east, midlatitude systems are observed to intrude into the lower latitudes and directly force tropical convection, the cloud plumes, while maintaining their extratropical nature. These results speak to how the midlatitudes can excite distinct types of tropical weather systems under different climatological wind regimes. Understanding these tropical weather systems and their interactions with the midlatitudes may ultimately help to improve predictions of weather beyond 2 weeks.more » « less
-
Abstract Oceanographic observations have revealed that basin‐scale Rossby waves can travel at speeds systematically exceeding values predicted by linear theory based on the flat‐bottom approximation. Using the recently developed parametric “sandpaper” theory of seafloor roughness, we construct a set of analytical solutions for the vertical structure and dispersion relationship of Rossby waves. We then use simulations to confirm these results and show that baroclinic Rossby waves can be accelerated by irregular small‐scale rough topography by up to a factor of 1.6 relative to their flat‐bottom counterparts. This acceleration is most extreme at high latitudes and wavelengths of approximately 600 km. Our investigation demonstrates the importance of relatively small‐scale processes for the large‐scale flow dynamics in general and baroclinic Rossby waves in particular.more » « less
