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Register a new userModeling of anisotropic turbulent flows with either magnetic fields or imposed rotation
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We present two models for turbulent flows with periodic boundary conditions and with either rotation, or a magnetic field in the magnetohydrodynamics (MHD) limit. One model, based on Lagrangian averaging, can be viewed as an invariant-preserving filter, whereas the other model, based on spectral closures, generalizes the concepts of eddy viscosity and eddy noise. These models, when used separately or in conjunction, may lead to substantial savings for modeling high Reynolds number flows when checked against high resolution direct numerical simulations (DNS), the examples given here being run on grids of up to 1536^3 points.
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We present data driven kinematic models for the motion of bubbles in high-Re turbulent fluid flows based on recurrent neural networks with long-short term memory enhancements. The models extend empirical relations, such as Maxey-Riley (MR) and its variants, whose applicability is limited when either the bubble size is large or the flow is very complex. The recurrent neural networks are trained on the trajectories of bubbles obtained by Direct Numerical Simulations (DNS) of the Navier Stokes equations for a two-component incompressible flow model. Long short term memory components exploit the time history of the flow field that the bubbles have encountered along their trajectories and the networks are further augmented by imposing rotational invariance to their structure. We first train and validate the formulated model using DNS data for a turbulent Taylor-Green vortex. Then we examine the model predictive capabilities and its generalization to Reynolds numbers that are different from those of the training data on benchmark problems, including a steady (Hills spherical vortex) and an unsteady (Gaussian vortex ring) flow field. We find that the predictions of the developed model are significantly improved compared with those obtained by the MR equation. Our results indicate that data-driven models with history terms are well suited in capturing the trajectories of bubbles in turbulent flows.
The nonlinear and nonlocal coupling of vorticity and strain-rate constitutes a major hindrance in understanding the self-amplification of velocity gradients in turbulent fluid flows. Utilizing highly-resolved direct numerical simulations of isotropic turbulence in periodic domains of up to $12288^3$ grid points, and Taylor-scale Reynolds number $R_lambda$ in the range $140-1300$, we investigate this non-locality by decomposing the strain-rate tensor into local and non-local contributions obtained through Biot-Savart integration of vorticity in a sphere of radius $R$. We find that vorticity is predominantly amplified by the non-local strain coming beyond a characteristic scale size, which varies as a simple power-law of vorticity magnitude. The underlying dynamics preferentially align vorticity with the most extensive eigenvector of non-local strain. The remaining local strain aligns vorticity with the intermediate eigenvector and does not contribute significantly to amplification; instead it surprisingly attenuates intense vorticity, leading to breakdown of the observed power-law and ultimately also the scale-invariance of vorticity amplification, with important implications for prevailing intermittency theories.
We investigate the capability of neural network-based model order reduction, i.e., autoencoder (AE), for fluid flows. As an example model, an AE which comprises of a convolutional neural network and multi-layer perceptrons is considered in this study. The AE model is assessed with four canonical fluid flows, namely: (1) two-dimensional cylinder wake, (2) its transient process, (3) NOAA sea surface temperature, and (4) $y-z$ sectional field of turbulent channel flow, in terms of a number of latent modes, a choice of nonlinear activation functions, and a number of weights contained in the AE model. We find that the AE models are sensitive against the choice of the aforementioned parameters depending on the target flows. Finally, we foresee the extensional applications and perspectives of machine learning based order reduction for numerical and experimental studies in fluid dynamics community.
We explore the role of gravitational settling on inertial particle concentrations in a wall-bounded turbulent flow. While it may be thought that settling can be ignored when the settling parameter $Svequiv v_s/u_tau$ is small ($v_s$ - Stokes settling velocity, $u_tau$ - fluid friction velocity), we show that even in this regime the settling may make a leading order contribution to the concentration profiles. This is because the importance of settling is determined, not by the size of $v_s$ compared with $u_tau$ or any other fluid velocity scale, but by the size of $v_s$ relative to the other mechanisms that control the vertical particle velocity and concentration profile. We explain this in the context of the particle mean-momentum equation, and show that in general, there always exists a region in the boundary layer where settling cannot be neglected, no matter how small $Sv$ is (provided it is finite). Direct numerical simulations confirm the arguments, and show that the near-wall concentration is highly dependent on $Sv$ even when $Svll 1$, and can reduce by an order of magnitude when $Sv$ is increased from $O(10^{-4})$ and $O(10^{-2})$. The results also show that the preferential sampling of ejection events in the boundary layer by inertial particles when $Sv=0$ is profoundly altered as $Sv$ is increased, and is replaced by a preferential sampling of sweep events due to the onset of the preferential sweeping mechanism.
Periodically forced, oscillatory fluid flows have been the focus of intense research for decades due to their richness as a nonlinear dynamical system and their relevance to applications in transportation, aeronautics, and energy conversion. Recently, it has been observed that turbulent bluff-body wakes exhibit a subharmonic resonant response when excited with specific spatial symmetries at twice the natural vortex shedding frequency, which is hypothesized to be caused by triadic interactions. The focus of this paper is to provide new physical insight into the dynamics of turbulent oscillator flows, based on improved mechanistic models informed by a comprehensive experimental study of the turbulent wake behind a D-shaped body under periodic forcing. We confirm for the first time the role of resonant triadic interactions in the forced flow by studying the dominant components in the power spectra across multiple excitation frequencies and amplitudes. We then develop an extended Stuart-Landau model for the forced global wake mode, incorporating parametric and non-harmonic forcing. This model captures the system dynamics and reveals the boundaries of multiple synchronization regions. Further, it is possible to identify model coefficients from sparse measurement data, making it applicable to a wide range of turbulent oscillator flows. We believe these generalized synchronization models will be valuable for prediction, control, and understanding of the underlying physics in this ubiquitous class of flows.
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