最小二次螺旋度态

Calculations for the Practical Applications of Quadratic Helicity in MHD

For the quadratic helicity $χ^{(2)}$ we present a generalization of the Arnol'd inequality which relates the magnetic energy to the quadratic helicity, which poses a lower bound. We then introduce the quadratic helicity density using the classical magnetic helicity density and its derivatives along magnetic field lines. For practical purposes we also compute the flow of the quadratic helicity and show that for an $α^2$-dynamo setting it coincides with the flow of the square of the classical helicity. We then show how the quadratic helicity can be extended to obtain an invariant even under comp…

Hall cascade with fractional magnetic helicity in neutron star crusts

The ohmic decay of magnetic fields in the crusts of neutron stars is generally believed to be governed by Hall drift which leads to what is known as a Hall cascade. Here we show that helical and fractionally helical magnetic fields undergo strong inverse cascading like in magnetohydrodynamics (MHD), but the magnetic energy decays more slowly with time $t$: $\propto t^{-2/5}$ instead of $\propto t^{-2/3}$ in MHD. Even for a nonhelical magnetic field there is a certain degree of inverse cascading for sufficiently strong magnetic fields. The inertial range scaling with wavenumber $k$ is compatibl…

将计算流体力学纳入凸二次优化框架

Casting Computational Fluid Mechanics into a Convex Quadratic Optimization Framework

本研究利用最小压力梯度原理将非定常CFD问题转化为带线性约束的凸优化框架，可借助二次规划或KKT条件高效求解，经三个基准算例验证，能准确预测多种流场，为传统CFD提供了简单稳健的变革性替代方案。