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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Nonlinear proper orthogonal decomposition for convection-dominated flows

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when integrated with a time series predictive model. In this Letter, we put forth a nonlinear proper orthogonal decomposition (POD) framework, which is an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics. By eliminating the projection error due to the truncation of Galerkin models, a key enabler of the proposed nonintrusive approach is the kinematic construction of a nonlinear mapping between the full-rank expansion of the POD coefficients and the latent space where the dynamics evolve. We test our framework for model reduction of a convection-dominated system, which is generally challenging for reduced order models. Our approach not only improves the accuracy, but also significantly reduces the computational cost of training and testing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1985

A numerical study of global axisymmetric states and their stability to quasi-geostrophic disturbances

A steady, axisymmetric model of the general circulation is developed as a basis for climate stability studies. The model includes the effects of heating, rotation, and internal friction, but neglects topography. It is assumed that the axisymmetric flow may be modeled by making the Boussinesq and deep convection approximations. The hydrostatic assumption is not made, thus permitting the advective terms to be included in the vertical equation of motion. The initial set of five primitive equations is reduced to three equations in terms of the zonal velocity, meridional streamfunction, and the potential temperature perturbation. The application of the Boussinesq, deep convection, and quasi-geostrophic assumptions limits the ranges of the heating and rotation rates. For values not too far from typical atmospheric values, the model produces a stability boundary separating Hadley from Rossby flow. The boundary is characterized by a particular value of vertical wind shear, which suggests that baroclinic instability is the primary mechanism for the loss of stability. The initial growth rates are largest for longitudinal waves 4-7, also in agreement with studies of baroclinic instability.

Henderson, H. W.↗
NASA NTRS2000

Modeling of a Non-Dilute Alloy Solidification Under Terrestrial and Microgravity Conditions

A general finite element model of non-dilute alloy solidification was used to simulate growth of HgCdTe from the melt. 2-D and 3-D models with and without Oberbeck-Boussinesq (O-B) approximation were used. Verification of the 3-D model was based on experimental data. The location and the shape of the interface were determined using melting temperatures obtained from the HgCdTe liquidus curve. Double-diffusive convection in the melt is caused by radial temperature gradients and by rejection at the solid-melt interface of the heavier HgTe-rich solute. Because of these complicating factors, dimensional rather than non-dimensional modeling was performed. Models based on complete set of Navier-Stokes equations for compressible media are superior to the O-B approximation in microgravity, because they provide more accurate estimation of convection.

Bune, Andris V.↗
NASA NTRS1980

Nonlinear axially symmetric circulations in a nearly inviscid atmosphere

The structure of certain axially symmetric circulations in a stably stratified, differentially heated, rotating Boussinesq fluid on a sphere is analyzed. A simple approximate theory (similar to that introduced by Schneider (1977)) is developed for the case in which the fluid is sufficiently inviscid that the poleward flow in the Hadley cell is nearly angular momentum conserving. The theory predicts the width of the Hadley cell, the total poleward heat flux, the latitude of the upper level jet in the zonal wind, and the distribution of surface easterlies and westerlies. Fundamental differences between such nearly inviscid circulations and the more commonly studied viscous axisymmetric flows are emphasized. The theory is checked against numerical solutions to the model equations.

Held, I. M.↗
DOE OSTI2023

Mean Flow from Phase Averages in the 2D Boussinesq Equations

The atmosphere and ocean are described by highly oscillatory PDEs that challenge both our understanding of their dynamics and their numerical approximation. This paper presents a preliminary numerical study of one type of phase averaging applied to mean flows in the 2D Boussinesq equations that also has application to numerical methods. The phase averaging technique, well-known in dynamical systems theory, relies on a mapping using the exponential operator, and then an averaging over the phase. The exponential operator has connections to the Craya–Herring basis pioneered by Jack Herring to study the fluid dynamics of oscillatory, nonlinear fluid dynamics. In this paper, we perform numerical experiments to study the effect of this averaging technique on the time evolution of the solution. We explore its potential as a definition for mean flows. We also show that, as expected from theory, the phase-averaging method can reduce the magnitude of the time rate of change in the PDEs, making them potentially suitable for time stepping methods.

Wingate, Beth A.↗
NASA NTRS1992

Convection treatment for high Rayleigh number, laminar, natural convection calculation

The problem of natural convection in a square cavity of a Boussinesq incompressible fluid is computed using a consistent central-difference approximation, a consistent second-order upwind scheme, and the hybrid scheme for the energy equation. It was found that, for this problem, the second-order upwind scheme yields satisfactory solutions and that an apparently low-order combination of schemes, with the second-order upwind scheme for the momentum equations and the hybrid scheme for the energy equation, can produce satisfactory predictions for this problem.

Shyy, Wei↗
NASA NTRS1991

Numerical simulations of turbulent thermal convection with differential rotation

The solar nebula, from which the planets in our solar system formed, featured a disk of gas and dust grains in rapid, differential rotation, and at some stage was likely to have been unstable to thermal convection. This situation is suspected by many to lead to significant turbulent Reynolds stress production and angular momentum transport in such systems, and estimates of transport rates have been attempted from unsubstantiated phenomenological models. In order to determine the circumstances and physical conditions under which our own planetary system formed and to explain recent observations of young stellar systems, it is necessary to develop realistic models of heat and angular momentum transport for such flows. Developing an understanding of complicated flows featuring thermal convection, rotation, and shear is also of wide interest in stellar astrophysics and in planetary and terrestrial atmospheric studies. The ultimate objective is to develop workable models based on the numerical simulations for constructing global solar nebula models; viz., relatively simple prescriptions for heat and angular momentum fluxes from given system parameters (e.g., ratios of rotation, shear, and convective lapse rates) are characterized, quantified, and developed. Toward this end, our program has been to attempt to understand the behavior of the direct numerical simulations of Boussinesq convection, which, despite the complexity of the results, is still an overly simplified approximation to the real system and should be more amenable to analysis. These results are also intended to be tested against turbulence models, especially those designed for atmospheric boundary layers, and may provide a basis for subgrid-scale models. In order to make the numerical simulations more realistic with regard to the solar nebula problem, a fully compressible code that will allow incorporation of large density stratifications and realistic thermodynamic and radiative properties is developed. In order to explore the properties of these flows at the very high values of Re found in natural systems and the very low values of Pr found in most astrophysical contexts, we will need to employ large-eddy simulations for which we want to determine the most appropriate subgrid-scale model to incorporate.

Cabot, William H.↗
NASA NTRS1980

A simple approximate result for the maximum growth rate of baroclinic instabilities

The Charney problem for baroclinic instability involves the quasi-geostrophic instability of a zonal flow on a beta plane where the zonal flow is characterized by a constant vertical shear. The atmosphere is non-Boussinesq and continuous. The solution of this problem involves confluent hypergeometric functions, and the mathematical difficulty of the problem has precluded extracting simple results of generality. It is shown that there exists very simple, powerful approximate result for the growth rate of the most rapidly growing instability, viz., that this growth rate is linearly proportional to the surface meridional temperature gradient. The coefficient of proportionality is also easily determined. The result extends to substantially more general profiles than those in the Charney problem.

Lindzen, R. S.↗
NASA NTRS1975

Modal equations for cellular convection

We expand the fluctuating flow variables of Boussinesq convection in the planform functions of linear theory. Our proposal is to consider a drastic truncation of this expansion as a possible useful approximation scheme for studying cellular convection. With just one term included, we obtain a fairly simple set of equations which reproduces some of the qualitative properties of cellular convection and whose steady-state form has already been derived by Roberts (1966). This set of 'modal equations' is analyzed at slightly supercritical and at very high Rayleigh numbers. In the latter regime the Nusselt number varies with Rayleigh number just as in the mean-field approximation with one horizontal scale when the boundaries are rigid. However, the Nusselt number now depends also on the Prandtl number in a way that seems compatible with experiment. The chief difficulty with the approach is the absence of a deductive scheme for deciding which planforms should be retained in the truncated expansion.

Gough, D. O.↗
NASA NTRS1989

Blow-up of unsteady two-dimensional Euler and Navier-Stokes solutions having stagnation-point form

The time-dependent form of the classic, two-dimensional stagnation-point solution of the Navier-Stokes equations is considered. If the viscosity is zero, a class of solutions of the initial-value problem can be found in closed form using Lagrangian coordinates. These solutions exhibit singular behavior in finite time, because of the infinite domain and unbounded initial vorticity. Thus, the blow-up found by Stuart in three dimensions using the stagnation-point form, also occurs in two. The singularity vanishes under a discrete, finite-dimensional 'point vortex' approximation, but is recovered as the number of vortices tends to infinity. We find that a small positive viscosity does not arrest the breakdown, but does strongly alter its form. Similar results are summarized for certain Boussinesq stratified flows.

Childress, S.↗
NASA NTRS1991

GEOSIM: A numerical model for geophysical fluid flow simulation

A numerical model which simulates geophysical fluid flow in a wide range of problems is described in detail, and comparisons of some of the model's results are made with previous experimental and numerical studies. The model is based upon the Boussinesq Navier-Stokes equations in spherical coordinates, which can be reduced to a cylindrical system when latitudinal walls are used near the pole and the ratio of latitudinal length to the radius of the sphere is small. The equations are approximated by finite differences in the meridional plane and spectral decomposition in the azimuthal direction. The user can specify a variety of boundary and initial conditions, and there are five different spectral truncation options. The results of five validation cases are presented: (1) the transition between axisymmetric flow and baroclinic wave flow in the side heated annulus; (2) the steady baroclinic wave of the side heated annulus; (3) the wave amplitude vacillation of the side heated annulus; (4) transition to baroclinic wave flow in a bottom heated annulus; and (5) the Spacelab Geophysical Fluid Flow Cell (spherical) experiment.

Butler, Karen A.↗
DOE OSTI2022

Non-Boussinesq subgrid-scale model with dynamic tensorial coefficients

A major drawback of Boussinesq-type subgrid-scale stress models used in large-eddy simulations is the inherent assumption of alignment between large-scale strain rates and filtered subgrid-stresses. A priori analyses using direct numerical simulation (DNS) data have shown that this assumption is invalid locally as subgrid-scale stresses are poorly correlated with the large-scale strain rates [J. Bardina, J. Ferziger, and W. Reynolds, Improved subgrid-scale models for large-eddy simulation, in Proceedings of the 13th Fluid and Plasmadynamics Conference, AIAA (1980); C. Meneveau and K. Katz, Scale-invariance and turbulence models for large-eddy simulation, Ann. Rev. Fluid Mech. 32, 1 (2000)]. In the present work, a new, non-Boussinesq subgrid-scale model is presented where the model coefficients are computed dynamically. Some previous non-Boussinesq models have observed issues in providing adequate dissipation of turbulent kinetic energy [e.g., Bardina et al., Proceedings of the 13th Fluid and Plasmadynamics Conference (1980); R. A. Clark, J. Ferziger, and W.C. Reynolds. Evaluation of subgrid-scale models using an accurately simulated turbulent flow, J. Fluid Mech. 91, 1 (1979); S. Stolz and N. A. Adams, An approximate deconvolution procedure for large-eddy simulation, Phys. Fluids 11, 1699 (1999)]; however, the present model is shown to provide sufficient dissipation using dynamic coefficients. Modeled subgrid-scale Reynolds stresses satisfy the consistency requirements of the governing equations for large-eddy simulation (LES), vanish in laminar flow and at solid boundaries, and have the correct asymptotic behavior in the near-wall region of a turbulent boundary layer. The new model, referred to as the dynamic tensor-coefficient Smagorinsky model (DTCSM), has been tested in simulations of canonical flows: decaying and forced homogeneous isotropic turbulence, and wall-modeled turbulent channel flow at high Reynolds numbers. The results show favorable agreement with DNS data. It has been shown that DTCSM offers similar predictive capabilities as the dynamic Smagorinsky model for canonical flows. In order to assess the performance of DTCSM in more complex flows, wall-modeled simulations of high Reynolds number flow over a Gaussian bump (Boeing speed bump) exhibiting smooth-body flow separation are performed. Predictions of surface pressure and skin friction, compared against DNS and experimental data, show improved accuracy from DTCSM in comparison to existing static coefficient (Vreman) and dynamic Smagorinsky model. The computational cost of performing LES with this model is up to 15% higher than the dynamic Smagorinsky model.

42 ENGINEERING↗
NASA NTRS1994

Renormalization Group Theory of Bolgiano Scaling in Boussinesq Turbulence

Bolgiano scaling in Boussinesq turbulence is analyzed using the Yakhot-Orszag renormalization group. For this purpose, an isotropic model is introduced. Scaling exponents are calculated by forcing the temperature equation so that the temperature variance flux is constant in the inertial range. Universal amplitudes associated with the scaling laws are computed by expanding about a logarithmic theory. Connections between this formalism and the direct interaction approximation are discussed. It is suggested that the Yakhot-Orszag theory yields a lowest order approximate solution of a regularized direct interaction approximation which can be corrected by a simple iterative procedure.

Rubinstein, Robert↗
NASA NTRS1990

Model-data comparisons of moments of nonbreaking shoaling surface gravity waves

The predictions of linear and nonlinear (Boussinesq) shoaling wave models for nonbreaking unidirectional surface gravity waves are compared to field observations, with particular emphasis on quantities that may be important for cross-shore sediment transport. The extensive data sets were obtained on two natural beaches, span water depths between 1 and 10 m, and include incident wave power spectra with narrow, broad, and bimodal shapes. Significant wave heights varied between approximately 30 and 100 cm, and peak periods between approximately 8 and 18 s. The evolution of total variances of sea surface elevation, cross-shore velocity, and horizontal acceleration is modeled at least qualitatively well by both linear and nonlinear theories. Only the nonlinear theory predicts the increasingly asymmetric sea surface elevations and horizontal velocities (pitched-forward wave shapes) and the weaker variation of skewness (difference between crest and trough profiles) which are observed to occur during shoaling. The nonlinear theory also models qualitatively well the large skewed accelerations which occur during the passage of asymmetric waves.

Elgar, Steve↗
DOE OSTI2023

Statistical Analysis of the Limiting Dynamics of Two dimensional Boussinesq Turbulent Systems

In the current study, we investigate rotational and stratified turbulent systems within the framework of the Boussinesq equations. The effects of rotation and stratification give rise to a variety of dynamical regimes in atmospheric and oceanic turbulence. To develop a better understanding of the fundamental flow properties through a more straightforward mathematical framework, we commence our research with a simplified two-dimensional Boussinesq model that incorporates rotation and stratification effects. We explore two distinct limiting dynamics, considering pure rotation and pure stratification separately. We examine these intriguing dynamics through numerical investigations, applying the exact solution theory of Boussinesq equations and examining small-scale perturbations to the exact solution under rotation and stratification. We conduct an analysis of statistical quantities associated with the turbulent state variables. The results indicate that, under weak rotation at the equilibrium statistical state, the flow field exhibits vortex flow. However, strong rotation transforms the flow into vertical shear flow. We observe both downscale and upscale energy transfers with a decay rate of k −3 in the absence of external forcing and dissipation. Furthermore, we delve into the study of internal gravity wave mode interactions in the simplified two-dimensional Boussinesq system, which is a crucial aspect of geophysical turbulence due to gravity. Our findings reveal that the time series of the mode coefficients exhibit wave-like interactions between wave modes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Fully compressible simulations of waves and core convection in main-sequence stars

Context: Recent, nonlinear simulations of wave generation and propagation in full-star models have been carried out in the anelastic approximation using spectral methods. Although it makes long time steps possible, this approach excludes the physics of sound waves completely and requires rather high artificial viscosity and thermal diffusivity for numerical stability. A direct comparison with observations is thus limited. Aims: In this study, we explore the capabilities of our compressible multidimensional Seven-League Hydro (SLH) code to simulate stellar oscillations. Methods: We compare some fundamental properties of internal gravity and pressure waves in 2D SLH simulations to linear wave theory using two test cases: (1) an interval gravity wave packet in the Boussinesq limit and (2) a realistic 3 M ⊙ stellar model with a convective core and a radiative envelope. Oscillation properties of the stellar model are also discussed in the context of observations. Results: Our tests show that specialized low-Mach techniques are necessary when simulating oscillations in stellar interiors. Basic properties of internal gravity and pressure waves in our simulations are in good agreement with linear wave theory. As compared to anelastic simulations of the same stellar model, we can follow internal gravity waves of much lower frequencies. The temporal frequency spectra of velocity and temperature are flat and compatible with the observed spectra of massive stars. Conclusion: The low-Mach compressible approach to hydrodynamical simulations of stellar oscillations is promising. Our simulations are less dissipative and require less luminosity boosting than comparable spectral simulations. The fully-compressible approach allows for the coupling of gravity and pressure waves in the outer convective envelopes of evolved stars to be studied in the future.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1992

Surface tension and buoyancy-driven flow in a non-isothermal liquid bridge

The Navier-Stokes-Boussinesq equations governing the transport of momentum, mass and heat in a nonisothermal liquid bridge with a temperature-dependent surface tension are solved using a vorticity-stream-function formulation together with a nonorthogonal coordinate transformation. The equations are discretized using a pseudo-unsteady semi-implicit finite difference scheme and are solved by the ADI method. A Picard-type iteration is adopted which consists of inner and outer iterative processes. The outer iteration is used to update the shape of the free surface. Two schemes have been used for the outer iteration; both use the force balance normal to the free surface as the distinguished boundary condition. The first scheme involves successive approximation by the direct solution of the distinguished boundary condition. The second scheme uses the artificial force imbalance between the fluid pressure, viscous and capillary forces at the free surface which arises when the boundary condition for force balance normal to the surface is not satisfied. This artificial imbalance is then used to change the surface shape until the distinguished boundary condition is satisfied. These schemes have been used to examine a variety of model liquid bridge situations including purely thermocapillary-driven flow situations and mixed thermocapillary- and bouyancy-driven flow.

Zhang, Yiqiang↗