The structure of thermal convection is determined by the spatial distribution of temperature in the mantle. However, in the literature, when modeling various manifestations of convection, little attention is paid to the degree of correspondence of the temperature distribution calculated in the model with the real temperature in the mantle, and often the temperature distribution is not even presented. In this paper, we analyze the effect on the distribution of temperature and heat fluxes of internal heat sources and the sphericity of the mantle, as well as the effects of dissipation and adiabatic compressibility. Using the Cartesian model leads to a large discrepancy between the calculated distribution of the heat flux and temperature with the observational data. It is shown that the effect of sphericity of the mantle can be approximately interpreted as an additional effective negative internal heat source. At the same time, for the parameters of the modern Earth, it turned out by chance that this effective source is approximately equal in modulus (or rather somewhat more) to the real positive internal heat source (due to radioactivity and secular cooling) and compensates for it. Therefore, the numerous literature results of modeling mantle convection in Cartesian coordinates including internal heat sources are poorly consistent with the actual temperature in the mantle. For the convection model in the modern mantle, this discrepancy can be approximately eliminated by simply eliminating real internal heat sources from the convection equations. The depth distribution of temperature in the mantle of the modern Earth is presented, which is optimally consistent with both the available measurement data (reference points) and the results of refined numerical modeling.

中文翻译：

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地球温度和热通量的分布：地幔球度的影响

热对流的结构由地幔中温度的空间分布决定。然而，在文献中，在对对流的各种表现形式进行建模时，很少关注模型中计算出的温度分布与地幔中实际温度的对应程度，往往甚至没有给出温度分布。在本文中，我们分析了对内部热源温度和热通量分布和地幔球形度的影响，以及耗散和绝热压缩性的影响。使用笛卡尔模型导致热通量和温度的计算分布与观测数据之间存在较大差异。结果表明，地幔球度的影响可以近似解释为额外的有效负内热源。同时，对于现代地球的参数，偶然发现这个有效源的模量大约等于（或者更确切地说更多）与真正的正内部热源（由于放射性和长期冷却）并补偿为了它。因此，包括内部热源在内的笛卡尔坐标下地幔对流建模的众多文献结果与地幔中的实际温度不太一致。对于现代地幔中的对流模型，可以通过简单地从对流方程中消除真实的内部热源来近似消除这种差异。