Geometrical structure and topology of pressure Hessian in the turbulent boundary layer

Pressure Hessian $H_{ij} = P_{,ij}$ plays an important role in the evolution equations for the invariants of the deformation tensor $A_{ij} = u_{i,j}$ and its symmertic part $S_{ij}$. The properties of $H_{ij}$ need to be understood in order to develop a mathematical model for the evolution of invariant quantities. In order to develop a full dynamical model for $H_{ij}$, there is a need to study and understand the full e ffect of the $H_{ij}$ tensor on the Lagrangian dynamics of the invariants. This type of study requires well-resolved data to evaluate all the right-hand side terms in the evolution equations. Attempts to study the properties of $H_{ij}$ via its invariants for the case of decaying isotropic turbulence and a temporally evolving plane wake can be found in the current literature. We present the a priori study of properties of $H_{ij}$ based on the results from the DNS of the fully developed turbulent boundary layer over a smooth flat plate, originally performed by Wu and Moin.