Exponential Growth of Turbulent Cross Helicity in Shear-Flow-Driven Turbulence

Cross helicity, the velocity--magnetic-field correlation, is an ideal invariant of incompressible magnetohydrodynamics and constrains energy cascades and magnetic-field generation. Although cross helicity typically decays via visco-resistive effects, we analytically demonstrate that it grows exponentially in sheared inhomogeneous turbulence. This cross-helical shear instability is confirmed using three-dimensional numerical simulations. Growth requires a nonzero gradient of the Reynolds--Maxwell stress to produce turbulent cross helicity; this production overcomes effective losses when shear exceeds a threshold set by the ratio of turbulent magnetic to momentum diffusivities.