Speaker
Description
The dissipative anomaly, known as the zeroth law of turbulence, states that the rescaled mean kinetic energy dissipation rate ⟨ε⟩ L/Urms³ remains constant in the bulk of a turbulent flow away from surfaces when the kinematic viscosity ν approaches zero. Here, L is a characteristic outer scale of the flow and Urms is the root mean square velocity.
The framework first suggested by Duchon and Robert [1] is used to determine the anomalous dissipation term in the turbulent kinetic energy balance of a three-dimensional homogeneous isotropic incompressible Navier-Stokes flow. The incompressible anomalous dissipation term for a finite filter scale is defined by filtering the cube of the velocity increment. Anomalous contribution to the energy balance remains finite as the coarse-graining filter scale approaches zero.
In the current study, we extend this approach to compressible flow, introducing new dissipation terms that emerge from density gradients. To compute these terms in the balances, a continuous test function with compact support is chosen based on wavelet transform theory. Initially, we validate our method using an analytical solution for a single Burgers vortex [2]. The analysis is further extended using the Hatakeyama and Kambe model [3] for an ensemble of Burgers vortices. This method was proposed more than 20 years ago as a kinematic building block model for the turbulent cascade in three-dimensional homogeneous isotropic turbulence. For comparison with realistic turbulence, we calculate the anomalous dissipation for several intense vortex stretching events in a turbulent flow from a simulation. We compare the analysis of the anomalous dissipation for all three models with different levels of complexity.
To investigate dissipation terms in compressible flow, we focus on a 1D fully compressible flow, particularly to highlight dissipative effects in shock waves. The Duchon and Robert framework for compressible turbulence is applied and compared with the approach proposed by Aluie [4]. This comparison provides a better understanding on how the different methods capture the dissipation mechanisms, in particular for strong density gradients and shock-induced dissipation.
[1] Duchon and Robert, Nonlinearity 13, 249 (2000)
[2] Burgers, J. Adv. Appl. Mech. 1, 171 (1948)
[3] Hatakeyama and Kambe, Phys. Rev. Lett. 79, 1257 (1997)
[4] Aluie, Phys D: Nonl. Phen. 247, 54 (2013)
