Bulletin of the American Physical Society
77th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 24–26, 2024; Salt Lake City, Utah
Session ZC27: Flow Instability: Theory |
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Chair: Yulia Peet, Arizona State University Room: 251 E |
Tuesday, November 26, 2024 12:50PM - 1:03PM |
ZC27.00001: Temporal Stability of Channel Flow at Low Peclet Number Patrick M McGah A phenomenon called thermal striping, consisting of quasi-periodic temperature oscillations of Ο(100 °C), is of major concern in liquid-metal-cooled small modular nuclear reactors. While it is believed to be caused by a shear-flow instability, the physical mechanism is largely unknown, and its onset is difficult to predict. We consider plane Poiseuille flow with stable density stratification in the wall-normal direction as a model for a heated, wall-bounded shear flow. The linear temporal stability eigenvalue problem is then solved. The analysis shows that, in the limit of small Peclet number, ≲ 1, the flow is stable, in the sense of negative eigenvalues, when a modified Richardson number, R = Ri·Pe, is ≳ 0.332. We further develop a semi-analytic solution of the Low-Peclet-number equations (LPNE) of Lignières [Astron. Astrophys. 348 (1999)], which contain R as the natural parameter controlling buoyancy forces in the momentum equation. A perturbation series to first-order in R is obtained for the temporal stability eigenvalue problem of the LPNE. The perturbation in the eigenvalue is found to be strictly negative for all wavenumbers/Reynolds numbers indicating the effect of stratification is purely stabilizing. |
Tuesday, November 26, 2024 1:03PM - 1:16PM |
ZC27.00002: Self-Similar Solutions of Two-, Three-, and Four-Equation RANS Models of Small Atwood Number Rayleigh–Taylor Mixing Driven by Power-Law Accelerations Oleg Schilling Analytical self-similar solutions to two-, three-, and four-equation Reynolds-averaged turbulence models describing Rayleigh–Taylor mixing driven by a temporal power-law acceleration are derived in the small Atwood number limit. The solutions generalize those previously derived for constant acceleration Rayleigh–Taylor mixing for models based on the turbulent kinetic energy and its dissipation rate, together with the scalar variance and its dissipation rate [O. Schilling, Phys. Fluids 33, 085129 (2021)]. The turbulent fields are expressed in terms of the model coefficients and power-law exponent. Mixing layer growth parameters and other physical observables are obtained as functions of the model coefficients and parameterized by the exponent of the power-law acceleration. The four-equation model is then used to numerically reconstruct the mean and turbulent fields, and turbulent equation budgets across the mixing layer for several values of the power-law exponent. |
Tuesday, November 26, 2024 1:16PM - 1:29PM |
ZC27.00003: Spatial quasilinear theory for slowly-developing free shear flows Greg P Chini, Remil Mushthaq Quasilinear (QL) theory has proven to be a useful tool for analyzing shear-driven turbulence. For such flows, the QL reduction generally involves parsing dependent field variables into streamwise-average and fluctuation components and then retaining in the reduced dynamics only those fluctuation--fluctuation nonlinearities that feed back upon the evolution of the mean fields. To date, QL theory for shear flows has been implemented primarily in the context of temporal initial-value problems. Here, a spatial QL theory is derived for free shear flows that evolve slowly in the streamwise direction, e.g., wakes, jets, and free shear layers, for which streamwise averaging is inappropriate. The derivation exploits the spatial anisotropy of the (temporal) mean flow (e.g., the slenderness of the wake). The resulting asymptotically consistent, extended QL system can be marched in the streamwise direction and consistently retains the leading fluctuation--fluctuation nonlinearities in the equations governing the evolution of the fluctuation fields. An application of this spatial QL theory to planar wakes is described, with an eye toward the efficient modeling of the multiscale fluid dynamics of wind farm wakes. |
Tuesday, November 26, 2024 1:29PM - 1:42PM |
ZC27.00004: "Provably" correct spectral calculations in hydrodynamic stability Stefan Gregory Llewellyn Smith, Saikumar Bheemarasetty, Matthew J Colbrook
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Tuesday, November 26, 2024 1:42PM - 1:55PM |
ZC27.00005: A New Methodology for Linear Asymptotic Stability Analysis of Fluid Flows in a Continuous-Time Domain Yulia T Peet In this talk, we present a new approach for analyzing linear asymptotic stability of fluid flow systems, which is not based on a conventional eigenvalue analysis. In particular, the methodology is formulated in a continuous-time domain and makes no assumption on the form of the perturbations (that is, without resorting to a normal-mode assumption on the perturbations). By analyzing all time-varying perturbations and not only the ones restricted to a specific functional form, the developed stability test provides a stronger condition with regard to the system stability. The new methodology is applied to analyze stability of linearized Navier-Stokes equations in two-dimensional and three-dimensional channel and pipe geometries. Stability results of the new continuous-time formulation are compared with a traditional eigenvalue-based analysis, demonstrating that the developed methodology indeed represents a stricter (sufficient) condition for stability. |
Tuesday, November 26, 2024 1:55PM - 2:08PM |
ZC27.00006: Stability analysis of Poiseuille flow in a fluid overlying anisotropic and highly porous domain Anjali Aleria, Premananda Bera The present study is dedicated towards the instability of non-isothermal plane Poiseuille flow in a |
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