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NASA NTRS1987

Nonlinear magnetohydrodynamic waves in a steady zonal circulation for a shallow fluid shell on the surface of a rotating sphere

This paper considers two-dimensional nonlinear MHD waves of large horizontal spatial scales for a thin magnetofluid layer on the surface of a rotating sphere. The 'shallow fluid' hydrodynamic equations are generalized to include the effects of magnetic fields, and it is shown that the resulting MHD equations can be reduced to a single scalar equation for a stream function involving several free functions. For special choices of these free functions, two kinds of finite-amplitude MHD waves are obtained, propagating in the azimuthal direction relative to the uniformly rotating background atmosphere in the presence of a background zonal magnetic field and a steady differential zonal flow. These two kinds of MHD waves are fundamentally due to the joint effects of the uniform rotation of the background atmosphere and background magnetic field; the first is an inertial wave of the Rossby (1939) and Haurwitz (1940) type, modified by the presence of the background zonal magnetic field, while the second is a magnetic Alfven-like wave which is modified by the uniform rotation of the background atmosphere.

Lou, Y. Q.↗

NASA NTRS2005

Unified Models of Turbulence and Nonlinear Wave Evolution in the Extended Solar Corona and Solar Wind

The paper discusses the following: 1. No-cost Extension. The no-cost extension is required to complete the work on the unified model codes (both hydrodynamic and kinetic Monte Carlo) as described in the initial proposal and previous annual reports. 2. Scientific Accomplishments during the Report Period. We completed a comprehensive model of Alfvtn wave reflection that spans the full distance from the photosphere to the distant heliosphere. 3. Comparison of Accomplishments with Proposed Goals. The proposal contained two specific objectives for Year 3: (1) to complete the unified model code, and (2) to apply it to various kinds of coronal holes (and polar plumes within coronal holes). Although the anticipated route toward these two final goals has changed (see accomplishments 2a and 2b above), they remain the major milestones for the extended period of performance. Accomplishments la and IC were necessary prerequisites for the derivation of "physically relevant transport and mode-coupling terms" for the unified model codes (as stated in the proposal Year 3 goals). We have fulfilled the proposed "core work" to study 4 general types of physical processes; in previous years we studied turbulence, mode coupling (Le., non-WKB reflection), and kinetic wave damping, and accomplishment lb provides the fourth topic: nonlinear steepening.

Wagner, William↗

NASA NTRS1988

Analysis of the Space Shuttle Orbiter skin panels under simulated hydrodynamic loads

The Space Shuttle orbiter skin panels were analyzed under pressure loads simulating hydrodynamic loads to determine their capability to sustain a potential ditching and to determine pressures that typically would produce failures. Two Dynamic Crash Analysis of Structures (DYCAST) finite element models were used. One model was used to represent skin panels (bays) in the center body, while a second model was used to analyze a fuselage bay in the wing region of the orbiter. From an assessment of the DYCAST nonlinear computer results, it is concluded that the probability is extremely high that most, if not all, of the lower skin panels would rupture under ditching conditions. Extremely high pressure loads which are produced under hydrodynamic planning conditions far exceed the very low predicted failure pressures for the skin panels. Consequently, a ditching of the orbiter is not considered to have a high probability of success and should not be considered a means of emergency landing unless no other option exists.

Carden, Huey D.↗

DOE OSTI2026

Multibody for Everybody (M4E) - A Linearization Approach to Enable Frequency Domain Analysis, Time Integration and Control Co-Design

1.1 Background/Objectives: Marine energy represents a promising yet underexploited source of power. To increase the harvested power, significant efforts have been made to improve wave energy converter (WEC) modeling capabilities and optimize power take-off (PTO) performance; however, these efforts have often treated WEC dynamics, PTO design, and controller development sequentially. In contrast, control co-design (CCD) is emerging as a promising strategy to address these issues directly, creating a growing need for fast analysis tools suitable for repeated simulation and parametric studies [1]. To support this need, this work presents the Multibody for Everybody (M4E) [2] linearization module, which employs a symbolic toolbox to provide deeper insight of WEC design parameters. The objective is to demonstrate that a minimal-coordinate linearization of articulated WEC dynamics can provide accurate wave response predictions and substantial computational savings relative to nonlinear time-domain simulation, while preserving compatibility with broader wave-energy analysis workflows, enabling CCD. 1.2 Approach/Activities: The proposed approach linearizes the equations of motion, generated by M4E, in minimal coordinates about a selected operating point and combines the resulting system with frequencydomain hydrodynamic terms to incorporate the reduced mass, damping, stiffness, and forcing operators. The linearized model is used for both impedance-based response amplitude operator (RAO) prediction and rapid regular-wave time integration. The methodology is demonstrated on a single-flap device and a FOSWEC configuration, with linearized M4E responses compared against the corresponding nonlinear M4E simulations and WEC-Sim results. Regular-wave time histories, RAO trends, and runtime differences are assessed. The framework is also compatible with broader wave-energy workflows, including coupling to WecOptTool, although that capability is not the focus of this work [3]. 1.3 Results/Lessons: The linearized M4E model reproduces key regularwave response characteristics such as integration and Response Amplitude over multiple frequencies. This module matches nonlinear M4E and WEC-Sim results while substantially reducing integration cost. Thus, the proposed framework can serve as a rapid analysis layer for articulated WEC design, parameter studies, and controls-oriented workflows. The analysis is most appropriate in the near-equilibrium regime, about the linearization point.

16 TIDAL AND WAVE POWER↗

DOE OSTI2024

Synergistic Integration of Multiple Wave Energy Converters with Adaptive Resonance and Offshore Floating Wind Turbines through Bayesian Optimization

We developed a synergistic ocean renewable system where an array of Wave Energy Converters (WEC) with adaptive resonance was collocated with a Floating Offshore Wind Turbine (FOWT) such that the WECs, capturing wave energy through the resonance adapting to varying irregular waves, consequently reduced FOWFT loads and turbine motions. Combining Surface-Riding WECs (SR-WEC) individually designed to feasibly relocate their natural frequency at the peak of the wave excitation spectrum for each sea state, and to obtain the highest capture width ratio at one of the frequent sea states for annual average power in a tens of kilowatts scale with a 15 MW FOWT based on a semi-submersible, Bayesian Optimization is implemented to determine the arrangement of WECs that minimize the annual representation of FOWT’s wave excitation spectra. The time-domain simulation of the system in the optimized arrangement is performed, including two sets of interactions: one set is the wind turbine dynamics, mooring lines, and floating body dynamics for FOWT, and the other set is the nonlinear power-take-off dynamics, linear mooring, and individual WECs’ floating body dynamics. Those two sets of interactions are further coupled through the hydrodynamics of diffraction and radiation. For sea states comprising Annual Energy Production, we investigate the capture width ratio of WECs, wave excitation on FOWT, and nacelle acceleration of the turbine compared to their single unit operations. We find that the optimally arranged SR-WECs reduce the wave excitation spectral area of FOWT by up to 60% and lower the turbine’s peak nacelle acceleration by nearly 44% in highly occurring sea states, while multiple WECs often produce more than the single operation, achieving adaptive resonance with a larger wave excitation spectra for those sea states. The synergistic system improves the total Annual Energy Production (AEP) by 1440 MWh, and we address which costs of Levelized Cost Of Energy (LCOE) can be reduced by the collocation.

Engineering↗

DOE OSTI2021

How Snow Aggregate Ellipsoid Shape and Orientation Variability Affects Fall Speed and Self-Aggregation Rates

Snow aggregate shapes and orientations have long been known to exhibit substantial variability. Despite this observed variability, most weather and climate prediction models use fixed power-law functions that deterministically map particle size to mass and fall speed. As such, integrated quantities like precipitation and self-aggregation rates currently ignore nonlinear effects resulting from variation in shape and orientation for aggregates of the same size. This study therefore develops an analytic framework that couples an empirically based bivariate distribution of ellipsoid shapes to classical hydrodynamic theory so as to capture an appropriate dispersion of masses, projected areas, and fall speeds for an assumed size distribution. For a fixed aggregate size, shape variations produce approximately ±0.13 m s -1 standard deviation of fall speed which increases the mass flux fall speed dispersion by more than 100% over traditional microphysics models. This increased fall speed dispersion results predominantly from shape-induced mass dispersion whereas orientation and drag dispersion play a lesser role. Shape variations can increase mass- and reflectivity-weighted fall speeds by up to 60% of traditional models whereas self-aggregation rates can increase by a factor of 100 for very small slope parameters. This implies that aggregate shape variations effectively forestall the theorized onset of fall speed distribution narrowing and subsequent quenching of the aggregation process. As a result, it is likely that secondary ice formation is necessary to prevent an ever decreasing slope parameter. The mathematical theory presented in this study is used to develop simple correction factors for snow forecast and climate models.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1989

Coherent structures in transitional and turbulent free shear flows

The development of a quantitative understanding of large-scale coherent structures in shear flows has led to the recognition of their evolutionary features and 'rules' of nonlinear interaction among each other. These determinations, in conjunction with the study of fine-grained turbulence and mean motion, constitute a general view of hydrodynamical instabilities that has resulted in useful concepts for the achievement of shear-flow control. The dynamical role of longitudinal structures in free shear flows is presently exemplified by the axisymmetric and helical modes in a round jet, which resemble the two-dimensional and spanwise-periodic three-dimensional modes in a two-dimensional mean flow.

Liu, J. T. C.↗

DOE OSTI2025

Collision-Energy Dependence in Heavy-Ion Collisions from Nonlinear QCD Evolution

We explore the effects of including the energy dependence determined from evolution equations within the color glass condensate framework on observables in ultrarelativistic heavy-ion collisions. This amounts to integrating the JIMWLK evolution equations into the impact parameter-dependent glasma model, which is then coupled to viscous relativistic hydrodynamics. This methodology allows for a systematic representation of nuclei at specific Bjorken-x values, which are probed at different center-of-mass energies of the collision and rapidities of final state particles. Comparing the methodology to the conventional impact parameter-dependent glasma model, we find significant effects on multiplicity distributions and particle spectra, especially in smaller collision systems at the highest center-of-mass energies. Our results highlight the importance of incorporating nonlinear QCD evolution in the description of heavy-ion collisions at varying center-of-mass energies, as the precise extraction of transport coefficients will be affected. This Letter establishes a robust framework for understanding the quark gluon plasma and nuclear structure at high energy, integrating small-x physics into the initial conditions of heavy-ion collisions.

Mäntysaari, Heikki↗

DOE OSTI2026

thornado+FLASH-X: A Hybrid Discontinuous Galerkin–Implicit-explicit and Finite-volume Framework for Neutrino-radiation Hydrodynamics in Core-collapse Supernovae

We present neutrino-transport algorithms implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado) and their coupling to self-gravitating hydrodynamics within the adaptive mesh refinement–based multiphysics simulation framework FLASH-X. thornado, developed primarily for simulations of core-collapse supernovae (CCSNe), employs a spectral, six-species two-moment formulation with algebraic closure and special-relativistic observer corrections accurate to $\mathcal{O}(v/c)$, and uses discontinuous Galerkin (DG) methods for phase-space discretization combined with implicit-explicit time stepping. A key development is a nonlinear neutrino–matter coupling algorithm based on nested fixed-point iteration with Anderson acceleration, enabling fully implicit treatment of collisional processes, including energy-coupling interactions such as neutrino–electron scattering and pair production. Coupling to finite-volume (FV) hydrodynamics is achieved through a hybrid DG-FV representation of the fluid variables and operator-split evolution within FLASH-X. The implementation is verified using basic transport tests with idealized opacities and relaxation and deleptonization problems with tabulated microphysics. Spherically symmetric CCSN simulations demonstrate accuracy and robustness of the coupled scheme, including close agreement with the CCSN simulation code Chimera. An axisymmetric CCSN simulation further demonstrates the viability of DG-based neutrino transport for multidimensional supernova modeling within FLASH-X. thornado’s neutrino-transport solver is GPU-enabled using OpenMP offloading or OpenACC, and all CCSN applications included in this work use the GPU implementation. Together, these results establish a foundation for future enhancements in physics fidelity, numerical algorithms, and computational performance, for increasingly realistic large-scale CCSN simulations.

Endeve, Eirik [Oak Ridge National Laboratory (ORNL↗

DOE OSTI2025

Precision measurements of EFT parameters and BAO peak shifts for the Lyman- α forest

We present precision measurements of the bias parameters of the one-loop power spectrum model of the Lyman- α (Ly- α ) forest, derived within the effective field theory (EFT) of large-scale structure. We fit our model to the three-dimensional flux power spectrum measured from the ACCEL 2 hydrodynamic simulations. The EFT model fits the data with an accuracy of below 2% up to k = 2 h Mpc − 1 . Further, we analytically derive how nonlinearities in the three-dimensional clustering of the Ly- α forest introduce biases in measurements of the baryon acoustic oscillations (BAOs) scaling parameters in radial and transverse directions. From our EFT parameter measurements, we obtain a theoretical error budget of Δ α ∥ = − 0.2 % ( Δ α ⊥ = − 0.3 % ) for the radial (transverse) parameters at redshift z = 2.0 . This corresponds to a shift of − 0.3 % (0.1%) for the isotropic (anisotropic) distance measurements. We provide an estimate for the shift of the BAO peak for Ly- α -quasar cross-correlation measurements assuming analytical and simulation-based scaling relations for the nonlinear quasar bias parameters resulting in a shift of − 0.2 % ( − 0.1 % ) for the radial (transverse) dilation parameters, respectively. This analysis emphasizes the robustness of Ly- α forest BAO measurements to the theory modeling. We provide informative priors and an error budget for measuring the BAO feature—a key science driver of the currently observing Dark Energy Spectroscopic Instrument (DESI). Our work paves the way for full-shape cosmological analyses of Ly- α forest data from DESI and upcoming surveys such as the Prime Focus Spectrograph, WEAVE-QSO, and 4MOST. Published by the American Physical Society 2025

de Belsunce, Roger (ORCID:0000000336604028)↗

DOE OSTI2021

The MBARI-WEC: a power source for ocean sensing

Abstract Interest in wave energy converters to provide autonomous power to various ocean-bound systems, such as autonomous underwater vehicles, sensor systems, and even aquaculture farms, has grown in recent years. The Monterey Bay Aquarium Research Institute has developed and deployed a small two-body point absorber wave energy device suitable to such needs. This paper provides a description of the system to support future open-source access to the device and further the general development of similar wave energy systems. Additionally, to support future control design and system modification efforts, a set of hydrodynamic models are presented and cross-compared. To test the viability of using a linear frequency-domain admittance model for controller tuning, the linear model is compared against four WEC-Sim models of increasing complexity. The linear frequency-domain model is found to be generally adequate for capturing system dynamics, as the model agreement is good and the degree of nonlinearity introduced in the WEC-Sim models is generally less than 2.5%.

16 TIDAL AND WAVE POWER↗

NASA NTRS1990

Reynolds stress closure in jet flows using wave models

A collection of papers is presented. The outline of this report is as follows. Chapter three contains a description of a weakly nonlinear turbulence model that was developed. An essential part of the application of such a closure scheme to general geometry jets is the solution of the local hydrodynamic stability equation for a given jet cross-section. Chapter four describes the conformal mapping schemes used to map such geometries onto a simple computational domain. Chapter five describes a solution of a stability problem for circular, elliptic, and rectangular geometries. In chapter six linear models for the shock shell structure in non-circular jets is given. The appendices contain reprints of papers also published during this study including the following topics: (1) instability of elliptic jets; (2) a technique for predicting the shock cell structure in non-circular jets using a vortex sheet model; and (3) the resonant interaction between twin supersonic jets.

Morris, Philip J.↗

NASA NTRS2002

Static and Dynamic Effects of Lateral Carrier Diffusion in Semiconductor Lasers

Electron and hole diffusions in the plane of semiconductor quantum wells play an important part in the static and dynamic operations of semiconductor lasers. It is well known that the value of diffusion coefficients affects the threshold pumping current of a semiconductor laser. At the same time, the strength of carrier diffusion process is expected to affect the modulation bandwidth of an AC-modulated laser. It is important not only to investigate the combined DC and AC effects due to carrier diffusion, but also to separate the AC effects from that of the combined effects in order to provide design insights for high speed modulation. In this presentation, we apply a hydrodynamic model developed by the present authors recently from the semiconductor Bloch equations. The model allows microscopic calculation of the lateral carrier diffusion coefficient, which is a nonlinear function of the carrier density and plasma temperature. We first studied combined AC and DC effects of lateral carrier diffusion by studying the bandwidth dependence on diffusion coefficient at a given DC current under small signal modulation. The results show an increase of modulation bandwidth with decrease in the diffusion coefficient. We simultaneously studied the effects of nonlinearity in the diffusion coefficient. To clearly identify how much of the bandwidth increase is a result of decrease in the threshold pumping current for smaller diffusion coefficient, thus an effective increase of DC pumping, we study the bandwidth dependence on diffusion coefficient at a given relative pumping. A detailed comparison of the two cases will be presented.

Li, Jian-Zhong↗

DOE OSTI2022

Nonlinear Model Predictive Control Based on Real-Time Iteration Scheme for Wave Energy Converters Using WEC-Sim

One of several challenges that wave energy technologies face is their inability to generate electricity cost-competitively with other grid-scale energy generation sources. Several studies have identified two approaches to lower the levelised cost of electricity: reduce the cost over the device's lifetime or increase its overall electrical energy production. Several advanced control strategies have been developed to address the latter. However, only a few take into account the overall efficiency of the power take-off (PTO) system, and none of them solve the optimisation problem that arises at each sampling time on real-time. In this paper, a detailed Nonlinear model predictive control (NMPC) approach based on the real-time iteration (RTI) scheme is presented, and the controller performance is evaluated using a time-domain hydrodynamics model (WEC-Sim). The proposed control law incorporates the PTO system's efficiency in a control law to maximise the energy extracted. The study also revealed that RTI-NMPC clearly outperforms a simple resistive controller.

model predictive control↗

NASA NTRS1985

A granular flow model for dense planetary rings

In the present study of the viscosity of a differentially rotating particle disk, in the limiting case where the particles are densely packed and their collective behavior resembles that of a liquid, the pressure tensor is derived from both the equations of hydrodynamics and a simple kinetic model of collisions due to Haff (1983). Density waves and narrow circular rings are unstable if the liquid approximation applies, and the consequent nonlinear perturbations may generate 'splashing' of the ring material in the vertical direction. These results are pertinent to the origin of the ellipticities of ringlets, the nonaxisymmetric features near the outer edge of the Saturn B ring, and unexplained residuals in kinematic models of the Saturn and Uranus rings.

Borderies, N.↗

DOE OSTI2022

Nonlinear Model Predictive Control Based on Real-Time Iteration Scheme for Wave Energy Converters Using WEC-Sim: Preprint

model predictive control↗

NASA NTRS2011

A Fully Nonlinear, Dynamically Consistent Numerical Model for Solid-Body Ship Motion. I. Ship Motion with Fixed Heading

In this paper, we describe the details of our numerical model for simulating ship solidbody motion in a given environment. In this model, the fully nonlinear dynamical equations governing the time-varying solid-body ship motion under the forces arising from ship wave interactions are solved with given initial conditions. The net force and moment (torque) on the ship body are directly calculated via integration of the hydrodynamic pressure over the wetted surface and the buoyancy effect from the underwater volume of the actual ship hull with a hybrid finite-difference/finite-element method. Neither empirical nor free parametrization is introduced in this model, i.e. no a priori experimental data are needed for modelling. This model is benchmarked with many experiments of various ship hulls for heave, roll and pitch motion. In addition to the benchmark cases, numerical experiments are also carried out for strongly nonlinear ship motion with a fixed heading. These new cases demonstrate clearly the importance of nonlinearities in ship motion modelling.

Lin, Ray-Quing↗

NASA NTRS1995

Galactic cosmic-ray mediation of a spherical solar wind flow. 1: The steady state cold gas hydrodynamical approximation

Realistic models of the outer heliosphere should consider that the interstellar cosmic-ray pressure becomes comparable to pressures in the solar wind at distances more than 100 AU from the Sun. The cosmic-ray pressure dynamically affects solar wind flow through deceleration. This effect, which occurs over a scale length of the order of the effective diffusion length at large radial distances, has important implications for cosmic-ray modulation and acceleration. As a first step toward solution of this nonlinear problem, a steady state numerical model was developed for a relatively cold spherical solar wind flow which encounters the confining isotropic pressure of the surrounding Galactic medium. This pressure is assumed to be dominated by energetic particles (Galactic cosmic rays). The system of equations, which are solved self-consistently, includes the relevant hydrodynamical equations for the solar wind flow and the spherical cosmic-ray transport equation. To avoid the closure parameter problem of the two-fluid model, the latter equation is solved for the energy-dependent cosmic-ray distribution function.

Le Roux, J. A.↗