Nonlinear shallow-water solutions using the weak temperature gradient approximation

Zhou, Bo; Sobel, Adam H.

doi:10.1007/s00162-006-0028-8

Cited by 2 publications

(10 citation statements)

References 27 publications

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“…For sufficiently small values of the hyperdiffusion coefficient and U Ͻ 0, there is a regime in which the forced vortex periodically separates from the forcing and moves away to the northwest where it disperses and dissipates as a new vortex is generated at the forcing location, resulting in a periodic or quasiperiodic cycle. Similar behavior is documented, for a stationary forcing, in Zhou and Sobel (2006). This behavior is likely to be of little relevance to the observed phenomena of TD-type disturbances and multiple cyclone events, as in observations the secondary vortices appear to the east or southeast of the TC.…”

Section: Nonlinear Regime Ro ͼsupporting

confidence: 72%

On the Wavelength of the Rossby Waves Radiated by Tropical Cyclones

Krouse

Sobel

Polvani

2008

Journal of the Atmospheric Sciences

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The authors present a theory for the zonal wavelength of tropical depression-type disturbances, which occur as a result of Rossby wave radiation from a preexisting tropical cyclone (TC). In some cases, such disturbances undergo tropical cyclogenesis, resulting in a pair of tropical cyclones; the theory then predicts the zonal separation distance of such tropical cyclone pairs.Numerical experiments are presented in which a thermally forced vortex, superimposed on an initial state of rest, is moved at different velocities in a shallow-water model on a sphere. Vortices moving westward generate coherent wave trains to the east or southeast (depending on the amplitude of the vortex), resembling those in observations. The zonal wavelengths of these wave trains in each case are well described by the linear stationary solution in the frame comoving with the vortex. Vortices moving eastward or remaining stationary do not generate such trains, also consistent with linear theory, which admits no stationary solutions in such cases. It is hypothesized that the wavelengths of observed disturbances are set by the properties of the relevant stationary solution. The environmental flow velocity that determines this wavelength is not the translation velocity of the tropical cyclone, but the difference between the steering flow of the radiated Rossby waves and that of the TC. The authors argue that either horizontal or vertical shear in the environment of the TC can generate differences between these steering flows of the necessary magnitude and sign to generate the observed wavelengths.

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Section: Nonlinear Regime Ro ͼsupporting

confidence: 72%

On the Wavelength of the Rossby Waves Radiated by Tropical Cyclones

Krouse

Sobel

Polvani

2008

Journal of the Atmospheric Sciences

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“…Eq. (11)] is not formally consistent with the WTG scaling (Zhou and Sobel 2006). On the other hand, it is not an issue for the nonlinear longwave balance model considered here as we make no formal assumption regarding the scale of the height perturbation (i.e., we take Fr 5 1).…”

Section: Comparison With the Charney Balance/weak Temperature Gradienmentioning

confidence: 88%

“…This truncation of the continuity equation filters out fast inertia-gravity waves (IGW) while retaining the slow, advective, balanced dynamics. Although the scaling underlying the WTG model is formally valid only on the mesoscale (Sobel et al 2001;Majda and Klein 2003), the model has been used to study synoptic-and planetary-scale dynamics (e.g., Polvani and Sobel 2002;Bretherton and Sobel 2003;Zhou and Sobel 2006), and has been shown to be in qualitative agreement with previous work on the Gill model (Gill 1980) and Hadley circulation (e.g., Hsu and Plumb 2000). The WTG model can be considered to be a diabatic generalization of the Charney (1963) model.…”

Section: Introductionmentioning

confidence: 89%

“…Another view of balance dynamics in the tropics is exemplified by the theory of Charney (1963), which was subsequently generalized by Sobel et al (2001) to result in the WTG model, and extended to the equatorial b plane by Zhou and Sobel (2006). While the WTG model is a balance model (as pointed out in the introduction), it filters out Kelvin waves, which our balance model retains.…”

Section: Comparison With the Charney Balance/weak Temperature Gradienmentioning

confidence: 97%

“…The computational domain is [213.3, 13.3] in the zonal direction, which corresponds roughly to the circumference of the earth. Following Zhou and Sobel (2006), we choose a 5 0.1 and b 5 1/8.64, respectively, which approximately correspond to a Rayleigh damping time scale of 3.5 days and a Newtonian relaxation time scale of 3 days.…”

Section: A Numerical Modelmentioning

confidence: 99%

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Diabatic Balance Model for the Equatorial Atmosphere

Chan

Shepherd

2014

Journal of the Atmospheric Sciences

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Using an asymptotic expansion, a balance model is derived for the shallow-water equations (SWE) on the equatorial b plane that is valid for planetary-scale equatorial dynamics and includes Kelvin waves. In contrast to many theories of tropical dynamics, neither a strict balance between diabatic heating and vertical motion nor a small Froude number is required. Instead, the expansion is based on the smallness of the ratio of meridional to zonal length scales, which can also be interpreted as a separation in time scale. The leading-order model is characterized by a semigeostrophic balance between the zonal wind and meridional pressure gradient, while the meridional wind y vanishes; the model is thus asymptotically nondivergent, and the nonzero correction to y can be found at the next order. Importantly for applications, the diagnostic balance relations are linear for winds when inferring the wind field from mass observations and the winds can be diagnosed without direct observations of diabatic heating. The accuracy of the model is investigated through a set of numerical examples. These examples show that the diagnostic balance relations can remain valid even when the dynamics do not, and the balance dynamics can capture the slow behavior of a rapidly varying solution.

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Nonlinear shallow-water solutions using the weak temperature gradient approximation

Cited by 2 publications

References 27 publications

On the Wavelength of the Rossby Waves Radiated by Tropical Cyclones

On the Wavelength of the Rossby Waves Radiated by Tropical Cyclones

Diabatic Balance Model for the Equatorial Atmosphere

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