arXiv subjects

George Ilhwan Park

Publications and source records attributed to George Ilhwan Park.

7 recordsLinked to original sources

arXiv2025

Spatiotemporal spectral transfers in fluid dynamics

Motivated by previous work on kinetic energy cascades in the ocean and atmosphere, we develop a spatio-temporal spectral transfer tool that can be used to study scales of variability in generalized dynamical systems. In particular, we use generalized time-frequency methods from signal analysis to broaden the applicability of frequency transfers from theoretical to practical applications such as the study of ocean or atmosphere data or simulation output. We also show that triad interactions in wavenumber used to study kinetic energy and enstrophy cascades can be generalized to study triad interactions in frequency or wavenumber-frequency. We study the effects of sweeping on the locality of frequency transfers and frequency triad interactions to better understand the locality of spatio-temporal frequency transfers. As an illustrative example, we use the spatio-temporal spectral transfer tool to study the results of a simulation of two-dimensional homogeneous isotropic turbulence. This simulated fluid is forced at a well-defined wavenumber and frequency with dissipation occurring at both large and small scales, making this one of the first studies of "modulated turbulence" in two dimensions. Our results show that the spatio-temporal transfers we develop in this paper are robust to potential practical problems such as low sampling rates or nonstationarity in time series of interest. We anticipate that this method will be a useful tool in studying scales of spatio-temporal variability in a wide range of fluids applications as higher resolution data and simulations become more widely available.

physics.flu-dyn↗

arXiv2024

Reference map technique for Lagrangian exploration of coherent structures

We explore the application of the reference map technique, originally developed for the Eulerian simulation of solid mechanics, in Lagrangian kinematics of fluid flows. Unlike traditional methods based on explicit particle tracking, the reference map facilitates the calculation of flow maps and gradients without the need for particles. This is achieved through an Eulerian update of the reference map, which records the take-off positions of fluid particles. Using the reference map, measures of Lagrangian fluid-element deformation can be computed solely from Eulerian data, such as displacement, deformation gradient, Cauchy-Green tensor, and Finite-Time Lyapunov Exponent (FTLE) fields. We first demonstrate the accuracy of FTLE calculations based on the reference map against the standard particle-based approach in a 2D Taylor-Green vortex. Then, we apply it to turbulent channel flow at $Re_τ=180$ where Lagrangian coherent structures identified as ridges of the backward-time FTLE are found to bound vortical regions of flow, consistent with Eulerian coherent structures from the Q-criterion. The reference map also proves suitable for material surface tracking despite not explicitly tracking particles. This capability can provide valuable insights into the Lagrangian landscape of turbulent momentum transport, complementing Eulerian velocity-field analysis. The evolution of initially wall-normal material surfaces in the viscous sublayer, buffer layer, and log layer sheds light on the Reynolds stress-generating events from a Lagrangian perspective. Eliminating the need for tracking numerous particles, the reference map approach offers a convenient and promising avenue for future investigations into Lagrangian kinematics and dynamics of fluid flows.

physics.flu-dyn↗

arXiv2024

Revisiting Crossflow-Based Stabilization in Channel Flows

Stabilization schemes in wall-bounded flows often invoke fluid transpiration through porous boundaries. While these have been extensively validated for external flows, their efficacy in channels, particularly from the standpoint of non-modal perturbations, is yet to be demonstrated. Here, we show that crossflow strengths previously considered ``ideal'' for optimizing stability in channels in fact admit strong non-modal energy amplification. We begin by supplementing existing modal calculations and then show via the resolvent that extremely strong and potentially unfeasible crossflows are required to suppress non-modal growth in linearly stable regimes. Investigation of unforced algebraic growth paints a similar picture. Here, a component-wise budget analysis reveals that energy redistribution through pressure-velocity correlations plays an important role in driving energy growth/decay. The superposition of a moving wall is also considered, and it is shown that while energy amplification generally worsens, it can potentially be suppressed beyond a regime shift in parameter space. However, these flows are marred by rapidly declining mass transport, rendering their ultimate utility questionable. Our results suggest that crossflow-based stabilization might not be useful in internal flows.

physics.flu-dyn↗

arXiv2024

Physics-based distinction of nonequilibrium effects in near-wall modeling of turbulent separation bubble with and without sweep

Pressure-gradient-induced separation of swept and unswept turbulent boundary layers, based on the DNS studies of Coleman et al. (J. Fluid Mech. 2018 & 2019), have been analyzed for various nonequilibrium effects. The goal is to isolate physical processes critical to near-wall flow modeling. The decomposition of skin friction into contributing physical terms, proposed by Renard and Deck (J. Fluid Mech. 2016) (short: RD decomposition), affords several key insights into the near-wall physics of these flows. In the unswept case, spatial growth term (encapsulating nonequilibrium effects) and TKE production appear to be the dominant contributing terms in the RD decomposition in the separated and pressure-gradient zones, but a closer inspection reveals that only the spatial growth term dominates in the inner layer close to the separation bubble, implying a strong need for incorporating nonequilibrium terms in the wall modeling of this case. The comparison of streamwise RD decomposition of swept and unswept cases shows that a larger accumulated Clauser-pressure-gradient parameter history in the latter energizes the outer dynamics in the APG, leading to diminished separation bubble size in the unswept case. The spanwise RD decomposition in the swept case indicates that the downstream spanwise flow largely retains the upstream ZPG characteristics. This seems to ease the near-wall modeling challenge in the separated region, especially for basic models with an inherent log-law assumption. Wall-modeled LES of the swept and unswept cases are then performed using three wall models, validating many of the modeling implications from the DNS. In particular, the extension of RD decomposition to wall models underpins the criticality of spatial growth term close to the separation bubble, and the corresponding superior predictions by the PDE wall model due to its accurate capturing of this term.

physics.flu-dyn↗

arXiv2024

Linear Stability Analysis of Oblique Couette-Poiseuille flows

We perform a detailed numerical study of modal and non-modal stability in oblique Couette-Poiseuille profiles, which are among the simplest examples of three-dimensional boundary layers. Through a comparison with the Orr-Sommerfeld operator for the aligned case, we show how an effective wall speed succinctly characterizes modal stability. Large-scale parameter sweeps reveal that the misalignment between the pressure gradient and wall motion is, in general, destabilizing. For flows that are sufficiently oblique, the instability is found to depend exclusively on the direction of wall motion and not on its speed, a conclusion supported, in part, by the perturbation energy budget and the evolution of the critical layers. Closed forms for the critical parameters in this regime are derived using a simple analysis. Finally, a modified long-wavelength approximation is developed, and the resulting asymptotic eigenvalue problem is used to show that there is no cutoff wall speed for unconditional stability whenever the angle of wall motion is non-zero, in stark contrast to the aligned case. From a non-modal perspective, pseudo-resonance is examined through the resolvent and the $ε$-pseudospectra. An analysis of the unforced initial value problem shows that the maximum energy gain is highly dependent on both the magnitude and direction of the wall velocity. However, the strongest amplification is always achieved for configurations that are only weakly skewed. Finally, the optimal perturbations appear to develop via a lift-up effect induced by an Orr-like mechanism.

physics.flu-dyn↗

arXiv2023

Implementation and performance analysis of efficient grid-free integral wall models in unstructured-grid LES solvers

Two zonal wall models based on integral form of the boundary layer differential equations, albeit with algebraic complexity, have been implemented in an unstructured-grid cell-centered finite-volume LES solver. The first model is a novel implementation of the ODE equilibrium wall model, where the velocity profile is expressed in the integral form using the constant shear-stress layer assumption and the integral is evaluated using a spectral quadrature method, resulting in a local and algebraic (grid-free) formulation. The second model, which closely follows the integral wall model of Yang et al. (Phys. Fluids 27, 025112 (2015)), is based on the vertically-integrated thin-boundary-layer PDE along with a prescribed composite velocity profile in the wall-modeled region. Several numerical challenges unique to the implementation of these integral models in unstructured mesh environments, such as the exchange of wall quantities between wall faces and LES cells, and the computation of surface gradients, are identified and possible remedies are proposed. The performance of the wall models is assessed both in a priori and a posteriori settings against the traditional finite-volume based ODE equilibrium wall model, showing a comparable computational cost for the integral wall model, and superior performance for the spectral implementation over the finite-volume based approach. Load imbalance among the processors in parallel simulations seems to severely degrade the parallel efficiency of finite-volume based ODE wall model, whereas the spectral implementation is remarkably agnostic to these effects.

math.NA↗

arXiv2022

Wall-modeled large-eddy simulation of three-dimensional turbulent boundary layer in a bent square duct

We conduct wall-modeled LES (WMLES) of a pressure-driven three-dimensional turbulent boundary layer (3DTBL) developing on the floor of a bent square duct to investigate the predictive capability of three widely used wall models, namely, a simple equilibrium stress model, an integral nonequilibrium model, and a PDE nonequilibrium model. The numerical results are compared with the experiment of Schwarz and Bradshaw (J. Fluid Mech. (1994), vol. 272, pp. 183-210). While the wall-stress magnitudes predicted by the three wall models are comparable, the PDE nonequilibrium wall model produces a substantially more accurate prediction of the wall-stress direction, followed by the integral nonequilibrium wall model. The wall-stress direction from the wall models is shown to have separable contributions from the equilibrium stress part and the integrated nonequilibrium effects, where how the latter is modeled differs among the wall models. The triangular plot of the wall-model solution reveals different capabilities of the wall models in representing variation of flow direction along the wall-normal direction. On the contrary, the outer LES solution is unaffected by the type of wall model used, resulting in nearly identical predictions of the mean and turbulent statistics in the outer region for all the wall models. This is explained by the vorticity dynamics and the inviscid skewing mechanism of generating the mean three-dimensionality. Finally, the LES solution in the outer layer is used to study the anisotropy of turbulence. In contrast to the canonical 2D wall turbulence, the Reynolds stress anisotropy exhibit strong non-monotonic behavior with increasing wall distance.

physics.flu-dyn↗