Role of pressure and viscous processes on velocity gradient dynamics

Non-local pressure and viscous processes profoundly influence velocity gradient (A_ij = ∂u_i/∂x_j) dynamics and small scale structures in turbulent flows. Development of simple closure models for the pressure and viscous processes have long been sought in literature. To facilitate model development, we propose to normalize intermittent A_ij by magnitude (A² = A_ijA_ij) leading to mathematically bounded normalized velocity gradient tensor (b_ij = A_ij/(A²)^1/2). The present study examines the role of pressure and viscous processes on b_ij-evolution described in terms of second (q) and third (r) invariants of b_ij. Direct Numerical Simulation (DNS) data is used to exhibit that q-r dynamics furnishes new physical insights and is more amenable to closure modeling. The dependence of the pressure and viscous processes on Taylor Reynolds number (Re_λ) is characterized. The nature of pressure processes are mildly sensitive to Re_λ at low Re_λ. However, the viscous processes show a strong dependence on Re_λ: the nature of viscous effects are significantly different before and after the onset of dissipation anomaly.