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1. Data-Driven Model Reduction for Stochastic Burgers Equations

   https://doi.org/10.3390/e22121360  

   Lu, Fei (December 2020, Entropy)

   null (Ed.)

   We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variable’s trajectory. The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares. The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations. Taking advantage of the simplicity of the NAR models, we investigate maximal space-time reduction. Reduction in space dimension is unlimited, and NAR models with two Fourier modes can perform well. The NAR model’s stability limits time reduction, with a maximal time step smaller than that of the K-mode Galerkin system. We report a potential criterion for optimal space-time reduction: the NAR models achieve minimal relative error in the energy spectrum at the time step, where the K-mode Galerkin system’s mean Courant–Friedrichs–Lewy (CFL) number agrees with that of the full model. 

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2. State Space Modeling of Viscous Unsteady Aerodynamic Loads

   https://doi.org/10.2514/6.2021-1830  

   Taha, Haitham E.; Rezaei, Amir S. (January 2021, AIAA SciTech)

   null (Ed.)

   In this paper, we started by summarizing our recently developed viscous unsteady theory based on coupling potential flow with the triple deck boundary layer theory. This approach provides a viscous extension of potential flow unsteady aerodynamics. As such, a Reynolds- number-dependence could be determined. We then developed a finite-state approximation of such a theory, presenting it in a state space model. This novel nonlinear state space model of the viscous unsteady aerodynamic loads is expected to serve aerodynamicists better than the classical Theodorsen’s model, as it captures viscous effects (i.e., Reynolds number dependence) as well as nonlinearity and additional lag in the lift dynamics; and allows simulation of arbitrary time-varying airfoil motions (not necessarily harmonic). Moreover, being in a state space form makes it quite convenient for simulation and coupling with structural dynamics to perform aeroelasticity, flight dynamics analysis, and control design. We then proceeded to develop a linearization of such a model, which enables analytical results. So, we derived an analytical representation of the viscous lift frequency response function, which is an explicit function of, not only frequency, but also Reynolds number. We also developed a state space model of the linearized response. We finally simulated the nonlinear and linear models to a non- harmonic, small-amplitude pitching maneuver at 100 , 000 Reynolds number and compared the resulting lift and pitching moment with potential flow, in reference to relatively higher fidelity computations of the Unsteady Reynolds-Averaged Navier-Stokes equations. 

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3. Contraction for large perturbations of traveling waves in a hyperbolic–parabolic system arising from a chemotaxis model

   https://doi.org/10.1142/S0218202520500104  

   Choi, Kyudong; Kang, Moon-Jin; Kwon, Young-Sam; Vasseur, Alexis F. (February 2020, Mathematical Models and Methods in Applied Sciences)

   null (Ed.)

   We consider a hyperbolic–parabolic system arising from a chemotaxis model in tumor angiogenesis, which is described by a Keller–Segel equation with singular sensitivity. It is known to allow viscous shocks (so-called traveling waves). We introduce a relative entropy of the system, which can capture how close a solution at a given time is to a given shock wave in almost [Formula: see text]-sense. When the shock strength is small enough, we show the functional is non-increasing in time for any large initial perturbation. The contraction property holds independently of the strength of the diffusion. 

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4. Radiation and heat transport in divergent shock–bubble interactions

   https://doi.org/10.1063/5.0185056  

   Kurzer-Ogul, K.; Haines, B_M; Montgomery, D_S; Pandolfi, S.; Sauppe, J_P; Leong, A_F_T; Hodge, D.; Kozlowski, P_M; Marchesini, S.; Cunningham, E.; et al (March 2024, Physics of Plasmas)

   Shock–bubble interactions (SBIs) are important across a wide range of physical systems. In inertial confinement fusion, interactions between laser-driven shocks and micro-voids in both ablators and foam targets generate instabilities that are a major obstacle in achieving ignition. Experiments imaging the collapse of such voids at high energy densities (HED) are constrained by spatial and temporal resolution, making simulations a vital tool in understanding these systems. In this study, we benchmark several radiation and thermal transport models in the xRAGE hydrodynamic code against experimental images of a collapsing mesoscale void during the passage of a 300 GPa shock. We also quantitatively examine the role of transport physics in the evolution of the SBI. This allows us to understand the dynamics of the interaction at timescales shorter than experimental imaging framerates. We find that all radiation models examined reproduce empirical shock velocities within experimental error. Radiation transport is found to reduce shock pressures by providing an additional energy pathway in the ablation region, but this effect is small (∼1% of total shock pressure). Employing a flux-limited Spitzer model for heat conduction, we find that flux limiters between 0.03 and 0.10 produce agreement with experimental velocities, suggesting that the system is well-within the Spitzer regime. Higher heat conduction is found to lower temperatures in the ablated plasma and to prevent secondary shocks at the ablation front, resulting in weaker primary shocks. Finally, we confirm that the SBI-driven instabilities observed in the HED regime are baroclinically driven, as in the low energy case. 

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5. A Scale‐Dependent Analysis of the Barotropic Vorticity Budget in a Global Ocean Simulation

   https://doi.org/10.1029/2023MS003813  

   Khatri, Hemant; Griffies, Stephen_M; Storer, Benjamin_A; Buzzicotti, Michele; Aluie, Hussein; Sonnewald, Maike; Dussin, Raphael; Shao, Andrew (June 2024, Journal of Advances in Modeling Earth Systems)

   Abstract The climatological mean barotropic vorticity budget is analyzed to investigate the relative importance of surface wind stress, topography, planetary vorticity advection, and nonlinear advection in dynamical balances in a global ocean simulation. In addition to a pronounced regional variability in vorticity balances, the relative magnitudes of vorticity budget terms strongly depend on the length‐scale of interest. To carry out a length‐scale dependent vorticity analysis in different ocean basins, vorticity budget terms are spatially coarse‐grained. At length‐scales greater than 1,000 km, the dynamics closely follow the Topographic‐Sverdrup balance in which bottom pressure torque, surface wind stress curl and planetary vorticity advection terms are in balance. In contrast, when including all length‐scales resolved by the model, bottom pressure torque and nonlinear advection terms dominate the vorticity budget (Topographic‐Nonlinear balance), which suggests a prominent role of oceanic eddies, which are of km in size, and the associated bottom pressure anomalies in local vorticity balances at length‐scales smaller than 1,000 km. Overall, there is a transition from the Topographic‐Nonlinear regime at scales smaller than 1,000 km to the Topographic‐Sverdrup regime at length‐scales greater than 1,000 km. These dynamical balances hold across all ocean basins; however, interpretations of the dominant vorticity balances depend on the level of spatial filtering or the effective model resolution. On the other hand, the contribution of bottom and lateral friction terms in the barotropic vorticity budget remains small and is significant only near sea‐land boundaries, where bottom stress and horizontal viscous friction generally peak. 

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