Some simple analytical solutions to the problem of forced equatorial long waves

Heckley, W. A.; Gill, A. E.

doi:10.1002/qj.49711046314

Cited by 105 publications

(66 citation statements)

References 6 publications

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“…4b). Accordingly, a cyclonic vortex pair appears in the North and southwestern Pacific, quite similar to the Matsuno-Gill model (Gill, 1980) Smagorinsky (1953) and Heckley and Gill (1984). The response of atmospheric circulation to the heating anomaly in the SCS suggests that the Gill dynamics is at work.…”

Section: Influence Of Sst Anomalies In the Meridional Directionsupporting

confidence: 59%

Responses of atmospheric circulation to sea surface temperature anomalies in the South China Sea

Zhou

Wang

2015

Ocean Sci.

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Abstract. The sea surface temperature (SST) anomalies in the South China Sea (SCS) and their influences on global atmospheric circulation were studied. The results of a simple atmospheric model suggested that the SCS SST anomalies can induce several barotropic wave trains from the SCS to other regions such as North America, high latitudes of the Southern Hemisphere and the Mediterranean. The baroclinic stream function anomalies from the simple model showed an anticyclonic vortex pair in the Asian continent and the northern and southern Indian Ocean and a cyclonic vortex in the North Pacific and the southwestern Pacific. It is suggested that the spatial pattern of SST anomalies in the SCS can affect the magnitude of stream function anomalies, although it cannot affect the spatial pattern of atmospheric circulation.

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Section: Influence Of Sst Anomalies In the Meridional Directionsupporting

confidence: 59%

Responses of atmospheric circulation to sea surface temperature anomalies in the South China Sea

Zhou

Wang

2015

Ocean Sci.

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“…Thus, the hydrodynamic nonlinearity of the RSW is preserved in the model, while linearization in one dimension without rotation ͑v =0, f =0͒ gives the equations used in earlier studies 6,7,17,18 upon the change in variables h → −. Note that this change in variables allows us to make connection of our model to the pioneering papers on tropical dynamics by Gill,29,30 where convection effects were parametrized as a mass source in the linear SW equations. This line of argument was pursued under the so-called weak temperature gradient approximation in Refs.…”

Section: A Introducing Moist Convection In Shallow-water Modelsmentioning

confidence: 91%

Fronts and nonlinear waves in a simplified shallow-water model of the atmosphere with moisture and convection

et al. 2009

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We describe a shallow-water type atmospheric model which includes the transport of moisture as well as related precipitation and convection effects. The model combines hydrodynamic nonlinearity of the standard shallow-water model with the intrinsic nonlinearity due to the precipitation threshold. It allows for both theoretical treatment by the method of characteristics and efficient numerical resolution using shock-capturing finite-volume schemes. Linearized in the dynamical sector, the model adequately reproduces the propagation of the edge of precipitation regions ͑precipitation fronts͒ found in earlier studies. Results of numerical experiments on simple wave scattering upon a moisture front are in agreement with analytical results and highlight the role of dissipative reflector played by precipitating zones. We also analyze the evolution of a disturbance propagating in a uniformly saturated region and obtain criteria for precipitation front formation. Finally, we simulate wave breaking as an example of essentially nonlinear phenomenon and show how moist effects modify the classical shock formation scenario.

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“…Similarly, the linear equatorial long-wave equation, (23), has dispersionless equatorial Rossby wave train solutions (Heckley and Gill, 1984;Majda, 2003) …”

Section: Leading Order Asymptotics In a Low Froude Number Expansionmentioning

confidence: 99%

“…The equations in (22) and (23) are simply the linear barotropic long-wave equations and the linear equatorial long-wave equation, respectively, discussed by Heckley and Gill (1984), Majda (2003) and MB. The linear barotropic long-wave equation (22) has the well-known dispersion relation, !…”

Section: Leading Order Asymptotics In a Low Froude Number Expansionmentioning

confidence: 99%

Boundary layer dissipation and the nonlinear interaction of equatorial baroclinic and barotropic rossby waves

Biello

Majda

2004

Geophysical & Astrophysical Fluid Dynamics

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Two-layer equatorial primitive equations for the free troposphere in the presence of a thin atmospheric boundary layer and thermal dissipation are developed here. An asymptotic theory for the resonant nonlinear interaction of long equatorial baroclinic and barotropic Rossby waves is derived in the presence of such dissipation. In this model, a self-consistent asymptotic derivation establishes that boundary layer flows are generated by meridional pressure gradients in the lower troposphere and give rise to degenerate equatorial Ekman friction. That is to say, the asymptotic model has the property that the dissipation matrix has one eigenvalue which is nearly zero: therefore the dynamics rapidly dissipates flows with pressure at the base of the troposphere and creates barotropic/baroclinic spin up/spin down. The simplified asymptotic equations for the amplitudes of the dissipative equatorial barotropic and baroclinic waves are studied by linear theory and integrated numerically. The results indicate that although the dissipation slightly weakens the tropics to midlatitude connection, strong localized wave packets are nonetheless able to exchange energy between barotropic and baroclinic waves on intraseasonal timescales in the presence of baroclinic mean shear. Interesting dissipation balanced wave-mean flow states are discovered through numerical simulations. In general, the boundary layer dissipation is very efficient for flows in which the barotropic and baroclinic components are of the same sign at the base of the free troposphere whereas the boundary layer dissipation is less efficient for flows whose barotropic and baroclinic components are of opposite sign at the base of the free troposphere.

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Some simple analytical solutions to the problem of forced equatorial long waves

Cited by 105 publications

References 6 publications

Responses of atmospheric circulation to sea surface temperature anomalies in the South China Sea

Responses of atmospheric circulation to sea surface temperature anomalies in the South China Sea

Fronts and nonlinear waves in a simplified shallow-water model of the atmosphere with moisture and convection

Boundary layer dissipation and the nonlinear interaction of equatorial baroclinic and barotropic rossby waves

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