Self-consistent theory of turbulent transport in the solar tachocline I. Anisotropic turbulence

We present a self-consistent theory of turbulent transport in the solar tachocline by taking into account the effect of the radial differential rotation on turbulent transport. We show that the shearing by the radial differential rotation leads to reduction in turbulent transport of particles and momentum and the amplitude of turbulent flow via shear stabilization. The degree of reduction depends on the direction as well as the quantity that is transported. Specifically, particle transport in the vertical (radial) direction, orthogonal to the shear flow, is reduced with the scaling ∝A^-2 while it is less reduced in the horizonal plane with the scaling ∝A^-4/3. Here, A is shearing rate, representing the radial differential rotation. A similar, but weaker, anisotropy also develops in the amplitude of turbulent flow. The results suggest that the radial differential rotation in the tachocline can cause anisotropy in turbulence intensity and particle transport with weaker turbulence in the radial direction even in the absence of density stratification and even when the turbulence is mainly driven radially by plumes from the convection zone. We also assess the efficiency of the transport by a meridional circulation by taking into account the interaction with the radial differential rotation. Implications for mixing and angular momentum transport in the solar interior is discussed.