Bernoulli's Theorem in Space Plasmas and Its Applications

The Bernoulli principle, a fundamental concept in fluid dynamics, occupies an important position in the development of the discipline and finds wide application in both theory and engineering practice. In space plasmas, the Bernoulli equation can be derived from the continuity equation and the energy conservation equation. This presentation analyzes and presents the general form of the Bernoulli equation for multicomponent, non-equilibrium, and anisotropic space plasmas. Based on in-situ measurements from spacecraft such as ACE and MMS, this study examines the quantitative relationship between the plasma upstream (solar wind) and downstream (magnetosheath) of the Earth's bow shock. It confirms the applicability of Bernoulli’s theorem across the bow shock under both high-speed and low-speed solar wind conditions, demonstrating the existence of a conserved quantity—the characteristic energy of particles—along plasma streamlines. This indicates that Bernoulli’s theorem serves as an important theoretical tool for analyzing energy conversion processes across the bow shock and reveals a universal invariant—the particle characteristic energy—present in the upstream solar wind and throughout the downstream magnetosheath region. Applying Bernoulli’s theorem to the theoretical analysis of the relationship between solar coronal temperature and planetary magnetosheath temperature yields a quantitative relation that is consistent with statistical analyses of observational data from spacecraft such as MESSENGER, MMS, Voyager 2, and Cassini regarding thermodynamic parameters like the magnetosheath temperatures of planets (Mercury, Earth, Jupiter, and Saturn). These results hold significant value for studying the energy transfer mechanisms from the solar wind to magnetospheres and for understanding space weather in planetary magnetospheres