Planar ideal-MHD Bernoulli invariant
= Planar ideal-MHD Bernoulli invariant
{title2=$Q=u^2/2+\Phi+w-UB_z/(\mu_0k)$}
Under the hypotheses of <steady planar ideal-MHD field-line invariants>, the <specific enthalpy> relation and the velocity projection of momentum give $\mathbf B\cdot\nabla Q=0$. The horizontal total energy flux, including the <Poynting vector>, is $k\mathbf B_h Q$. The magnetic correction accounts for work exchanged between the fluid and the field.