<p>A simplified model of the Earth’s atmosphere is considered, which on the one hand exactly reproduces the real characteristics of the Earth, and on the other hand extremely simplifies the configuration of continents and oceans and completely ignores the topology of the real planet. The aim of this formulation is to analyze the generation of large-scale mid-latitude eddies and waves on a zonally homogeneous flat planet with energy balance and atmospheric properties similar to those of the Earth. It is shown that the preservation of a relatively small equatorial ocean on the background of a flat desert planet is sufficient to reproduce the general atmospheric circulation and the dynamics of mid-latitude wave and vortex structures that are realistic for the Earth. The considered idealized system correctly reproduces not only the spatial structure of the emerging baroclinic waves, but also their seasonal dynamics, including the variability of the spectral composition of the observed waves. The modes with wave numbers 3–8 contain most of the wave energy. The spectra for higher modes are characterized by a power law <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="382_2024_7561_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="TEX">$E_m \sim m^\gamma $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>E</mi> <mi>m</mi> </msub> <mo>∼</mo> <msup> <mi>m</mi> <mi>γ</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> with a slope <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="382_2024_7561_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="69" /> </InlineMediaObject> <EquationSource Format="TEX">$\gamma \approx -3.5$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>γ</mi> <mo>≈</mo> <mo>-</mo> <mn>3.5</mn> </mrow> </math></EquationSource> </InlineEquation> for the winter season and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="382_2024_7561_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="57" /> </InlineMediaObject> <EquationSource Format="TEX">$\gamma \approx -3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>γ</mi> <mo>≈</mo> <mo>-</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation> for the summer season. During the baroclinic season, there is a change in the dominant wave number from 7 to 4. Another particular feature of baroclinic waves in a considered configuration is a significant temporal variation of the phase velocity with two distinct stages of monotonic increase and decrease. There is a time lag between beginning of the gradual increase of the phase velocity for different modes. The higher modes begin to accelerate earlier and as a result lower modes move slower than higher modes. The temporal evolution of the baroclinic wave intensity is well described by the Eady parameter.</p>

Mid-latitude baroclinic waves in a zonally homogeneous Earth-like planet

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发表日期：

2025年1月4日

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Andrei Sukhanovskii,
Rodion Stepanov,
Alexei Bykov,
Andrei Vetrov,
Nikolai Kalinin,
Peter Frick

摘要

A simplified model of the Earth’s atmosphere is considered, which on the one hand exactly reproduces the real characteristics of the Earth, and on the other hand extremely simplifies the configuration of continents and oceans and completely ignores the topology of the real planet. The aim of this formulation is to analyze the generation of large-scale mid-latitude eddies and waves on a zonally homogeneous flat planet with energy balance and atmospheric properties similar to those of the Earth. It is shown that the preservation of a relatively small equatorial ocean on the background of a flat desert planet is sufficient to reproduce the general atmospheric circulation and the dynamics of mid-latitude wave and vortex structures that are realistic for the Earth. The considered idealized system correctly reproduces not only the spatial structure of the emerging baroclinic waves, but also their seasonal dynamics, including the variability of the spectral composition of the observed waves. The modes with wave numbers 3–8 contain most of the wave energy. The spectra for higher modes are characterized by a power law $E_m \sim m^\gamma $ $E_{m} \sim m^{γ}$ with a slope $\gamma \approx -3.5$ $γ \approx - 3.5$ for the winter season and $\gamma \approx -3$ $γ \approx - 3$ for the summer season. During the baroclinic season, there is a change in the dominant wave number from 7 to 4. Another particular feature of baroclinic waves in a considered configuration is a significant temporal variation of the phase velocity with two distinct stages of monotonic increase and decrease. There is a time lag between beginning of the gradual increase of the phase velocity for different modes. The higher modes begin to accelerate earlier and as a result lower modes move slower than higher modes. The temporal evolution of the baroclinic wave intensity is well described by the Eady parameter.