arXiv subjects

Akhil Sadam

Publications and source records attributed to Akhil Sadam.

3 recordsLinked to original sources

arXiv2026

Modified Dynamic Mixed Subgrid-scale Models for Geophysical Flows: Forced Two-Dimensional and $\beta$-plane Turbulence

Subgrid-scale (SGS) models for large-eddy simulations (LES) of geophysical turbulence typically need to balance dissipative regularization with backscatter, the upscale transfer of energy from unresolved to resolved scales. Dynamic mixed models (DMMs) combine functional eddy viscosity and structural closures through dynamically estimated coefficients that are least-squares optimal with respect to the Germano identity error (GIE). We show that this classical DMM least-squares estimation can be dominated by the structural component, thereby limiting the functional component's dissipative regularizing role. To address this limitation, we develop a modified Gram-based framework to construct a novel parametric family of fully-coupled, sequential, and fully-decoupled DMMs with tunable structural-functional balance. We evaluate the resulting closures using an idealized forced two-dimensional and $\beta$-plane turbulence framework with the Leith model and the fourth-order nonlinear gradient model. A priori results show that structurally-dominated models achieve strong agreement with the ideal SGS forcing and accurately reproduce local SGS energy exchange, including backscatter. However, in a posteriori tests, structurally dominated models exhibit noise-like artifacts with high-wavenumber spectral deviations, indicating insufficient net dissipation. In contrast, the sequential DMM in which the functional component is determined first and then corrected by the structural component retains much of the a priori structural accuracy while improving the a posteriori vorticity fields, spectra, and domain-averaged diagnostics. Spectral SGS energy and enstrophy-transfer analyses show that this sequential DMM permits backscatter at scales larger than the forcing scale with enhanced dissipation at smaller scales, thereby improving the balance between instantaneous structural fidelity and long-term accuracy.

physics.flu-dyn↗

arXiv2025

Evaluation of Analytical Turbulence Closures for Quasi-Geostrophic Ocean Flows with Coastal Boundaries

Numerical turbulence simulations typically involve parameterizations such as Large Eddy Simulations (LES). Applications to geophysical flows, especially ocean flows, are further complicated by the presence of complex topography and interior landforms such as coastlines, islands, and capes. In this work, we extend pseudo-spectral quasi-geostrophic (QG) numerical schemes and GPU-based solvers to simulate flows with coastal boundaries using the Brinkman volume penalization approach. We incorporate sponging and a splitting scheme to handle inflow and aperiodic boundary conditions. We evaluate four analytical sub-grid-scale (SGS) closures based on the eddy viscosity hypothesis: the standard Smagorinsky and Leith closures, and their dynamic variants. We show applications to QG flows past circular islands and capes with the beta-plane approximation. We perform both a priori analysis of the SGS closure terms as well as a posteriori assessment of the SGS terms and simulated vorticity fields. Our results showcase differences between the various closures, especially their approach to phase and feature reconstruction errors in the presence of coastal boundaries.

physics.flu-dyn↗

arXiv2025

Guided Unconditional and Conditional Generative Models for Super-Resolution and Inference of Quasi-Geostrophic Turbulence

Typically, numerical simulations of Earth systems are coarse, and Earth observations are sparse and gappy. We apply four generative diffusion modeling approaches to super-resolution and inference of forced two-dimensional quasi-geostrophic turbulence on the beta-plane from coarse, sparse, and gappy observations. Two guided approaches minimally adapt a pre-trained unconditional model: SDEdit modifies the initial condition, and Diffusion Posterior Sampling (DPS) modifies the reverse diffusion process score. Two conditional approaches, a vanilla variant and classifier-free guidance, require training with paired high-resolution and observation data. We consider multiple test cases spanning: two regimes, eddy and anisotropic-jet turbulence; two Reynolds numbers, 10^3 and 10^4; and two observation types, 4x coarse-resolution fields and coarse, sparse and gappy observations. Our comprehensive skill metrics include norms of the reconstructed vorticity fields, turbulence statistical quantities, and quantifications of the super-resolved probabilistic ensembles and their errors. We also study the sensitivity to tuning parameters such as guidance strength. Results show that the generated super-resolution fields of SDEdit are unphysical, while those of DPS are reasonable but with smoothed fine-scale features; however, neither of these lower-cost models propagates observational information effectively to unobserved regions. The two conditional models require re-training, but reconstruct missing fine-scale features, are cycle-consistent with observations, and predict correct turbulence statistics, including the tails. Further, their mean errors are highly correlated with and predictable from their ensemble standard deviations. Results highlight the tradeoffs between ease of implementation, fidelity (sharpness), and cycle-consistency of the diffusion models, and offer practical guidance for deployment.

physics.flu-dyn↗