Scale-dependent geometric statistics of the Lagrangian and Eulerian accelerations in homogeneous turbulent shear flow

Frank G Jacobitz (1) , Kai Schneider (2)

1 USD - University of San Diego
2 I2M - Institut de Mathématiques de Marseille

The alignment properties of different vector-valued flow quantities, including the Lagrangian, Eulerian, and convective accelerations in homogeneous turbulent shear flow, are quantified through the introduction of scale-dependent geometrical statistics. The vector fields are decomposed into an orthogonal wavelet series and the angles of the scale-wise contributions of different vector-valued flow quantities can be determined. This approach allows us to revisit the random Taylor hypothesis by examining the cancellation properties of Eulerian and convective accelerations at different flow scales. The results for homogeneous turbulent shear flow, computed by direct numerical simulation, show that Taylor's hypothesis holds at small scales of the flow as reflected by the anti-alignment of the Eulerian acceleration and the convective term. Such anti-alignment, however, is not observed at the largest scales of the turbulent motion, indicating that Taylor's hypothesis does not generally hold for homogeneous turbulent shear flow.

Domaines: Mécanique des fluides [physics.class-ph]

Frank G Jacobitz, Kai Schneider. Scale-dependent geometric statistics of the Lagrangian and Eulerian accelerations in homogeneous turbulent shear flow. 12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12), Jul 2022, Osaka, Japan. ⟨hal-03751173⟩