Session I — Fluid Mechanics

Monday, October 26 · 9:00–10:30 a.m.
Ballroom A

Chair: Harishankar Manikantan

High-resolution probabilistic estimation of three-dimensional regional ocean dynamics from sparse surface observations

Niloofar Asefi · UC Santa Cruz

The ocean interior regulates Earth’s climate but remains sparsely observed due to limited in situ measurements, while satellite observations are restricted to the surface. We present a depth-aware generative framework for reconstructing high-resolution three-dimensional ocean states from extremely sparse surface data. Our approach employs a conditional denoising diffusion probabilistic model (DDPM) trained on sea surface height and temperature observations with up to 99.9% sparsity, without reliance on a background dynamical model. By incorporating continuous depth embeddings, the model learns a unified vertical representation of the ocean states and generalizes to previously unseen depths. Applied to the Gulf of Mexico, the framework accurately reconstructs subsurface fields across multiple depths. These results establish generative diffusion models as a scalable approach for probabilistic ocean reconstruction in data-limited regimes.

Local, matrix-free Poisson solve and its projection scheme for a high-order finite volume MHD method

Dongwook Lee · UC Santa Cruz

We present a fifth-order accurate multidimensional finite volume MHD scheme using a divergence-cleaning projection method to preserve the magnetic field's solenoidal constraint. The projection step employs a new hyperbolic-variant successive over-relaxation (SORh) iteration to solve the Poisson equation. Unlike conventional global FFT approaches, SORh is a local method with performance comparable to a highly optimized FFT solver. Integrated into the MHD framework via a fifth-order Gaussian-process (GP) approximation, SORh features a matrix-free, single-stencil-pass-per-sweep structure. This allows straightforward extensions to mixed/non-periodic boundary conditions, variable-coefficient elliptic operators, and adaptive meshes. Benchmark tests, including smooth circularly polarized Alfvén waves and shock-dominated problems, validate that the new method matches highly optimized spectral FFT projection in accuracy, stability, and efficiency.

A Differentiable, Entropy-Stable Multilayer Ocean Model

Henry Waterhouse · UC Santa Cruz

We present a new multilayer hydrostatic ocean model. It uses a high-order entropy-stable formulation based on that of Ersing et al., pairing high-order accuracy with provable nonlinear stability. We take advantage of this robustness and extend the scheme with an entropy-stable viscous term, making viscosity a free physical parameter rather than a numerical consideration. We replace the overly dissipative scalar Rusanov interface dissipation with a matrix dissipation acting on the entropy variables, applied layer by layer. Our Julia code is fully differentiable, supplying Jacobians for implicit time stepping and opening the door to data assimilation and online training of neural closures. The model is implemented within Raven.jl, our general multi-GPU framework, allowing large high-order simulations. Ongoing work targets a layer-aware matrix dissipation that can be calculated efficiently and shallow-water-targeted kernel optimization informed by our prior work on the Euler equations.

Examining How Molecular Motors Affect Flagellar Beat

Kelli Gutierrez · CSU Monterey Bay

Many microswimmers propel themselves using flagella, which are thin, threadlike filaments that beat in a periodic wavelike motion. The flagellar beat emerges from the coupled interactions between the surrounding fluid and the active and passive responses of the flagellum. It is thought that this spatiotemporal coordination among motors is due to mechanical feedback on dynein motors. However, the mechanisms of mechanochemical feedback are not well understood, since the motor forces cannot be measured directly. We develop a computational model for the microorganism Chlamydomonas reinhardtii that couples a molecular motor model with a nonlinear swimming simulation to examine how motor forces respond to external loading. Although these motor models have been shown to qualitatively reproduce the Chlamydomonas reinhardtii waveform, we find that they do not reproduce the beat frequency or beat asymmetry observed in our dataset.

Finite Time Blow-Up in a Damped Klein-Gordon Equation

Cristian Ramirez · California State University, East Bay

We consider a nonlinear Klein-Gordon equation with the introduction of a spatial damping term \(a(x) \in L^\infty\) where \(a(x)\) shares the same sign of \(u_{tt}\). We prove, using nonconservative energy methods and H. A. Levine's established concavity condition (Levine 1973), that under sufficient initial conditions we get finite-time blow-up of solutions.