Document Type



Doctor of Philosophy


Mechanical Engineering

First Adviser

Arindam Banerjee


The evolution of buoyancy-driven homogeneous variable-density turbulence (HVDT) at Atwood numbers (A) up to 0.75 and large Reynolds numbers (Re) is studied by using high-resolution Direct Numerical Simulations. Domain sizes up to 2048^3 covering a broad range of density ratios from 1.105:1 (close to the traditional Boussinesq case) to 7:1 (corresponding to Atwood number value of 0.75) are used.

In HVDT, initially, a triply periodic domain contains large regions of two incompressible, miscible fluids with different densities. The two fluids start to move in opposite directions under the presence of an acceleration field and the buoyancy-driven motions produce turbulence. However, at some point, kinetic energy dissipation starts to overcome turbulence production as the buoyancy forces weaken due to molecular mixing, leading to a subsequent turbulence decay. HVDT flow aims to mimic the acceleration-driven Rayleigh-Taylor (RTI) and shock-driven Richtmyer-Meshkov instabilities (RMI) and to reveal new physics that arise from variable-density effects on the turbulent mixing such as in variable-density mixing layers and jets. The late time decay stage of buoyancy-driven HVDT, where the VD effects are minimal, also has some similarities with buoyancy-driven Rayleigh-Benard convection, and atmospheric and oceanic flows.

To help understand the highly non-equilibrium nature of buoyancy-driven HVDT, the flow evolution is divided into four different regimes based on the behavior of turbulent kinetic energy (E_TKE). Each regime has its own characteristics concerning velocity behavior, molecular mixing and dependency on A and Re numbers. The major characteristics of the four regimes can be defined as:

I- Explosive Growth: E_TKE undergoes rapid growth with dE_TKE/dt>0 and d^2E_TKE/dt^2>0. It has strong similarities with the core region of an RTI mixing layer, where pure fluids are stirred under buoyancy forces. During this regime, the entrainment associated with the buoyancy generated motions is not high enough to stir large structures, and mixing is localized at the interface between the pure fluids; the mole fraction behaves similarly for both low and high A number cases. However, the velocity field starts to behave differently just after the acceleration is turned on.

II - Saturated Growth: E_TKE behavior is similar to RTI under decaying acceleration, where turbulence growth rate undergoes a gradual decay with dE_TKE/dt>0 and d^2E_TKE/dt^2 < 0. During this regime, stirring is no longer localized. Density gradients increase as turbulence is amplified, which in turn enhances the mixing. The velocity field continues to be different for different A numbers. However, due to the high rate of mixing observed during this regime, the buoyancy forces start to decrease within the flow.

III - Fast Decay: This stage is initiated when dissipation starts to overcome E_TKE generation. The rapid E_TKE decay with dE_TKE/dt<0 and d^2E_TKE/dt^2<0 has some similarities with RMI and RTI under reversed acceleration. There are still some pure fluid regions within the flow; for the high A number cases, the density distribution is asymmetric. Meanwhile, the distribution of the velocity field within the domain becomes similar for all A numbers.

IV - Gradual Decay: During this stage, HVDT experiences a retarded E_TKE decay with dE_TKE/dt<0 and d^2E_TKE/dt^2>0 as it is a decay of buoyancy-assisted turbulence. Buoyancy forces continue to weaken, and there are no traces of pure fluids within the flow. This regime has similarities with late time evolution of the mixing core of the RMI and RTI under reversed acceleration. The flow is also similar with atmospheric and oceanic flows where the turbulence decays under weak buoyancy forces.

The results show that each regime has a unique type of dependency on both Atwood and Reynolds numbers. The energy conversion rates from potential energy to total and turbulent kinetic energies are strongly dependent on Atwood number and peak at different Atwood numbers during the growth regimes. In addition, it is found that the local statistics of the flow based on the flow composition are more sensitive to Atwood and Reynolds numbers compared to those based on the entire flow. These sensitivities and asymmetric flow features at high-density ratios are also studied by extending the PDF methods to variable-density turbulence. It is also observed that at higher Atwood numbers, different flow features reach their asymptotic Reynolds number behavior at different times which is also related to the concept of mixing transition.

The energy spectrum defined based on the Favre fluctuations momentum is shown to be the relevant spectrum for variable density flows. The evolution of the energy spectrum highlights distinct dynamical features of the four flow regimes. Thus, the slope of the energy spectrum at intermediate to large scales evolves from -7/3 to -1, as a function of the production to dissipation ratio. The classical Kolmogorov spectrum emerges at intermediate to high scales at the highest Reynolds numbers examined, after the turbulence starts to decay.

The effects of asymmetric initial density distributions on the evolution of buoyancy-driven HVDT at low-density ratio 1.105:1 and high-density ratio 7:1 are also studied. The initial amounts of pure light and pure heavy flows are altered to mimic the VD turbulence at the different locations of the mixing layers of RTI and RMI where the amounts of the mixing fluids are not equal. It is found that for the low-density ratio cases the asymmetric initial density distribution has limited effects on both global and local flow evolution for HVDT. Meanwhile, at high-density ratio, both global flow evolution and the local flow structures are strongly affected by the initial composition ratio. The flow composed of more light fluid reaches higher turbulent levels and local statistics reach their self-similar behavior earlier. During gradual decay, where most of the flow is fully-mixed, all parameters become independent of the initial density distribution for both low and high-density ratios. Finally, the similarities and differences between buoyancy-driven HVDT and the more conventional stationary turbulence are discussed and new strategies and tools for analysis are proposed. The findings of this research are summarized and the paths how this research can be expanded are discussed.

Available for download on Thursday, August 26, 2021