A novel forcing technique to simulate turbulent mixing in a decaying scalar field

To realize the full potential of Direct Numerical Simulation in turbulent mixing studies, it is necessary to develop numerical schemes capable of sustaining the flow physics of turbulent scalar quantities. In this work, a new scalar field forcing technique, termed “linear scalar forcing,” is presented and evaluated for passive scalars. It is compared to both the well-known mean scalar gradient forcing technique and a low waveshell spectral forcing technique. The proposed forcing is designed to capture the physics of one-time scalar variance injection and the subsequent self-similar turbulent scalar field decay, whereas the mean scalar gradient forcing and low waveshell forcing techniques are representative of continuous scalar variance injection. The linear scalar forcing technique is examined over a range of Schmidt numbers, and the behavior of the proposed scalar forcing is analyzed using single and two-point statistics. The proposed scalar forcing technique is found to be perfectly isotropic, preserving accepted scalar field statistics (fluxes) and distributions (scalar quantity, dissipation rate). Additionally, it is found that the spectra resulting from the three scalar forcing techniques are comparable for unity Schmidt number conditions, but differences manifest at high Schmidt numbers. These disparities are reminiscent of those reported between scaling arguments suggested by theoretical predictions and experimental results for the viscous-convective subrange

A proposed modification to Lundgren's physical space velocity forcing method for isotropic turbulence

As an alternative to spectral space velocity field forcing techniques commonly used in simulation studies of isotropic turbulence,Lundgren [Linearly forced isotropic turbulence,” in Annual Research Briefs (Center for Turbulence Research, Stanford, 2003), pp. 461–473] proposed and Rosales and Meneveau [“Linear forcing in numerical simulations of isotropic turbulence: Physical space implementations and convergence properties,” Phys. Fluids17, 095106 (2005)] validated a physical space forcing method termed “linear forcing.” Linear forcing has the advantages of being less memory intensive, less computationally expensive, and more easily extended to variable density simulations. However, this forcing method generates turbulent statistics that are highly oscillatory, requiring extended simulation run times to attain time-invariant properties. A slight modification of the forcing term is proposed, and it is shown to reduce this oscillatory nature without altering the turbulent physics

The effect of velocity field forcing techniques on the Karman–Howarth equation

Many velocity field forcing methods exist to simulate isotropic turbulence, but no in-depth analysis of the effects that these methods have on the generated turbulence has been performed. This work contains such a detailed study. It focuses on Lundgren’s linear and Alvelius’ spectral velocity forcing methods. Based on the constraints imposed on their associated forcing terms, these two are representative of the numerous forcing methods available in the literature. This study is conducted in the context of the Karman–Howarth equation, which, as a consequence of velocity forcing, has a source term appended to it. The expressions for the forcing method-specific Karman–Howarth source terms are derived, and their effect on key turbulent metrics, e.g. structure functions and spectra, is investigated. The behaviour of these source terms determines the state to which all turbulent metrics evolve, allowing for the differences noted between linearly and spectrally forced turbulent fields to be explained

A new framework for simulating forced homogeneous buoyant turbulent flows

This work proposes a new simulation methodology to study variable density turbulent buoyant flows. The mathematical framework, referred to as homogeneous buoyant turbulence, relies on a triply periodic domain and incorporates numerical forcing methods commonly used in simulation studies of homogeneous, isotropic flows. In order to separate the effects due to buoyancy from those due to large-scale gradients, the linear scalar forcing technique is used to maintain the scalar variance at a constant value. Two sources of kinetic energy production are considered in the momentum equation, namely shear via an isotropic forcing term and buoyancy via the gravity term. The simulation framework is designed such that the four dimensionless parameters of importance in buoyant mixing, namely the Reynolds, Richardson, Atwood, and Schmidt numbers, can be independently varied and controlled. The framework is used to interrogate fully non-buoyant, fully buoyant, and partially buoyant turbulent flows. The results show that the statistics of the scalar fields (mixture fraction and density) are not influenced by the energy production mechanism (shear vs. buoyancy). On the other hand, the velocity field exhibits anisotropy, namely a larger variance in the direction of gravity which is associated with a statistical dependence of the velocity component on the local fluid density