Investigation of the Dependence of Angular Momentum Transport on Spatial Scales for Construction of Differential Rotation

We investigate the dependence of the angular momentum transport (AMT) on the spatial scales with numerical simulation of solar-like stars. It is thought that turbulence has an essential role in constructing solar differential rotation (DR). In a widely used method to analyse the construction mechanism of DR, the flow is divided into two components, `mean flow' and `turbulence', where `turbulence' includes a broad spectrum of spatial scales. The features of the AMT are expected to depend on the scale. In this study, we decompose the angular momentum flux (AMF) to investigate the dependence of the AMF on the spatial scale. We compare the results with anti-solar- (fast pole) and solar-type (fast equator) DR. Our conclusions are summarized as 1. Radially outward AMT is seen on a large scale (60 Mm < L <120 Mm) in rotationally constrained systems. 2. Even when the scale-integrated AMF is negative, we sometimes observe positive AMF on certain scales. 3. Small-scale turbulence tends to transport the angular momentum radially inward and causes the anti-solar DR, indicating that high-resolution simulation is a negative factor for solar-like DR. Our method to decompose the AMF provides a deep understanding of the angular momentum and construction mechanism of DR.