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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A Perturbative Solution for Nonlinear Stratified Upwelling over a Frictional Slope

Abstract A perturbative solution of simplified primitive equations for nonlinear weakly stratified upwelling over a frictional slope is found that resolves the vertical structure of velocity fields and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The solution uses assumptions consistent with the model proposed by Lentz and Chapman, including a steady-state, constant cross-shore density gradient, no alongshore gradients, laterally inviscid, and consideration of cross-shore advection of alongshore momentum. The solution resolves the vertical structure of velocity fields (including subsurface maxima of compensational flow, not resolved by Lentz and Chapman) and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The dynamics are similar to Lentz and Chapman; bottom stress balances alongshore wind stress in a homogeneous density ocean and is replaced by nonlinear cross-shore transport of alongshore momentum as the Burger number (S=αN/f, whereα,N, andfare the bottom slope, buoyancy frequency, Coriolis frequency, respectively) increases. When the solution uses the empirical relation between cross-shore and vertical density gradients proposed by Lentz and Chapman, vorticity conservation is not satisfied and the nonlinear momentum transport estimated by the solution linearly increases withS, asymptotically matching Lentz and Chapman forS< 1. When the solution conserves interior potential vorticity, the momentum transport is proportional toS 2 forS< 1 and is in better agreement with numerical simulations.

Oceanography↗
DOE OSTI2024

Fast explicit solutions for neutrino-electron scattering: Explicit asymptotic methods

Here, we present results of explicit asymptotic approximations applied to neutrino-electron scattering in a representative model of neutrino population evolution under conditions characteristic of core-collapse supernova explosions or binary neutron star mergers. It is shown that this approach provides stable solutions of these stiff systems of equations, with accuracy and time stepping comparable to that for standard implicit treatments such as backward Euler, fixed point iteration, and Anderson-accelerated fixed point iteration. Because each time step can be computed more rapidly with the explicit asymptotic approximation than with implicit methods, this suggests that algebraically stabilized explicit integration methods could be used to compute neutrino evolution coupled to hydrodynamics more efficiently in stellar explosions and mergers than the methods currently in use.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1990

Self-similar perturbations of a Friedmann universe

The present analysis of spherically symmetric self-similar solutions to the Einstein equations gives attention to those solutions that are asymptotically k = 0 Friedmann at large z values, and possess finite but perturbed density at the origin. Such solutions represent nonlinear density fluctuations which grow at the same rate as the universe's particle horizon. The overdense solutions span only a narrow range of parameters, and resemble static isothermal gas spheres just within the sonic point; the underdense solutions may have arbitrarily low density at the origin while exhibiting a unique relationship between amplitude and scale. Their relevance to large-scale void formation is considered.

Carr, Bernard J.↗
NASA NTRS1983

Generation of Tollmien-Schlichting waves by free-stream disturbances at low Mach numbers

The method of matched asymptotic expansions is used to study the generation of Tollmien-Schlichting waves by free stream disturbances incident on a flat plate boundary layer. Near the leading edge, the motion is governed by the unsteady boundary layer equation, while farther downstream it is governed (to lowest order) by the Orr-Sommerfeld equation with slowly varying coefficients. It is shown that there is an overlap domain where the Tollmien-Schlichting wave solutions to the Orr-Sommerfeld equation and an appropriate asymptotic solution of the unsteady boundary layer equation match, in the matched asymptotic expansion sense. The analysis leads to a set of scaling laws for the asymptotic structure of the unsteady boundary layer.

Goldstein, M. E.↗
NASA NTRS1984

Feedback in separated flows over symmetric airfoils

For a flow over an airfoil with laminar separation, a feedback cycle may exist whereby a Kelvin-Helmholtz instability wave emanating from the separation point on the airfoil surface grows along the shear layer and is diffracted as it interacts with the sharp trailing edge of the airfoil, causing acoustic radiation which, in turn, propagates upstream and regenerates the initial instability wave. The analysis is restricted to the high frequency limit. Solutions to the boundary-value problem are obtained using the slowly varying approximation and the method of matched asymptotic expansions. Resonant solutions exist for certain discrete values of the Reynolds and Strouhal numbers. The results are discussed and compared with available data.

Atassi, H. M.↗
NASA NTRS1984

Feedback in separated flows over symmetric airfoils

For a flow over an airfoil with laminar separation, a feedback cycle may exist whereby a Kelvin-Helmholtz instability wave emanating from the separation point on the airfoil surface grows along the shear layer and is diffracted as it interacts with the sharp trailing edge of the airfoil, causing acoustic radiation which , in turn, propagates upstream and regenerates the initial instability wave. The analysis is restricted to the high frequency limit. Solutions to the boundary-value problem are obtained using the slowly varying approximation and the method of matched asymptotic expansions. Resonant solutions exist for certain discrete values of the Reynolds and Strouhal numbers. The results are discussed and compared with available data.

Atassi, H. M.↗
NASA NTRS1992

Control and stabilization of nonholonomic dynamic systems

The paper establishes a theoretical framework for the control of nonholonomic dynamic systems, i.e., dynamic systems with nonintegrable constraints, with emphasis on control properties for nonholonomic systems that have no counterpart in holonomic systems. A model for nonholonomic dynamic systems is presented in terms of differential-algebraic equations defined on a phase space. A reduction procedure is carried out to obtain reduced-order state equations. Conditions for smooth asymptotic stabilization to an m-dimensional equilibrium manifold are presented. It is also demonstrated that a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback. An approach using geometric phases is developed as a basis for the control of Caplygin systems.

Bloch, Anthony M.↗
DOE OSTI2021

Electric and magnetic black holes in a new nonlinear electrodynamics model

Highlights: • We introduce a new NED model which is comparable with the BI model in the weak-field limit. • We find an electric black hole solution in the context of Einstein’s gravity minimally coupled with the new NED model. • We study the thermal stability of the electric black hole solution. • Modified Smarr’s formula consistent with the first law of black hole thermodynamics is obtained. A new nonlinear electrodynamics (NED) model is introduced in the form of a nonpolynomial Lagrangian which admits static spherical and also plane wave solutions in a flat space. Upon coupling with gravity the electric field is finite and comparable with the Born–Infeld counterpart. The electric and magnetic black hole solutions in the Einstein’s gravity coupled with this NED model are presented. The solutions give both asymptotically and in the weak field limit Reissner–Nordström (RN) black hole and unlike the other known models our electric solution is expressed in terms of elementary functions in a closed form. We study the first law and derive the modified Smarr’s formula for the electric type extension of our model. Considerable rich structure, especially thermodynamic ones, ranging from first to the second order phase transitions are added to the RN black hole of linear electrodynamics with this NED model. Having the exact solution for the metric function at our disposal we investigate the stability of the electric black hole from both the thermodynamical and causal points of view.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

A Numerical Scheme for Wave Turbulence: 3-Wave Kinetic Equations

Here, we introduce a finite volume scheme to solve a special case of isotropic 3-wave kinetic equations. We test our numerical solution against theoretical results concerning the long time behavior of the energy and observe that our solutions verify the energy cascade phenomenon. To our knowledge, this is the first numerical scheme that can capture the long time asymptotic behavior of solutions to those isotropic 3-wave kinetic equations, where the energy cascade can be observed. Our numerical energy cascade rates are in good agreement with previously obtained theoretical results. The finite volume scheme given here relies on a new identity, allowing one to reduce the number of terms needed in the collision operators.

3-wave equation↗
NASA NTRS1976

The linear quadratic optimal control problem for infinite dimensional systems over an infinite horizon - Survey and examples

Available published results are surveyed for a special class of infinite-dimensional control systems whose evolution is characterized by a semigroup of operators of class C subscript zero. Emphasis is placed on an approach that clarifies the system-theoretic relationship among controllability, stabilizability, stability, and the existence of a solution to an associated operator equation of the Riccati type. Formulation of the optimal control problem is reviewed along with the asymptotic behavior of solutions to a general system of equations and several theorems concerning L2 stability. Examples are briefly discussed which involve second-order parabolic systems, first-order hyperbolic systems, and distributed boundary control.

Bensoussan, A.↗
NASA NTRS1994

An asymptotic method for estimating the vertical ozone distribution in the Earth's atmosphere from satellite measurements of backscattered solar UV-radiation

An asymptotic approach to solution of the inverse problems of remote sensing is presented. It consists in changing integral operators characteristic of outgoing radiation into their asymptotic analogues. Such approach does not add new principal uncertainties into the problem and significantly reduces computation time that allows to develop the real (or about) time algorithms for interpretation of satellite measurements. The asymptotic approach has been realized for estimating vertical ozone distribution from satellite measurements of backscatter solar UV radiation in the Earth's atmosphere.

Ishov, Alexander G.↗
NASA NTRS1988

Primitive numerical simulation of circular Couette flow - Carrousel wind tunnel nonturbulent solutions

The azimuthal-invariant, three-dimensional cylindrical, incompressible Navier-Stokes equations are solved to steady state for a finite-length, physically realistic model. The numerical method relies on an alternating-direction implicit scheme that is formally second-order accurate in space and first-order accurate in time. The equations are linearized and uncoupled by evaluating variable coefficients at the previous time iteration. Wall grid clustering is provided by a Roberts transformation in radial and axial directions. A vorticity-velocity formulation is found to be preferable to a vorticity-streamfunction approach. Subject to no-slip, Dirichlet boundary conditions, except for the inner cylinder rotation velocity (impulsive start-up) and zero-flow initial conditions, nonturbulent solutions are obtained for sub- and supercritical Reynolds numbers of 100 to 400 for a finite geometry where R(outer)/R(inner) = 1.5, H/R(inner) = 0.73, and H/Delta-R = 1.5. An axially-stretched model solution is shown to asymptotically approach the one-dimensional analytic Couette solution at the cylinder midheight. Flowfield change from laminar to Taylor-vortex flow is discussed as a function of Reynolds number. Three-dimensional velocities, vorticity, and streamfunction are presented via two-dimensional graphs and three-dimensional surface and contour plots.

Hasiuk, Jan↗
NASA NTRS1989

Linear instability of supersonic plane wakes

In this paper we present a theoretical and numerical study of the growth of linear disturbances in the high-Reynolds-number and laminar compressible wake behind a flat plate which is aligned with a uniform stream. No ad hoc assumptions are made as to the nature of the undisturbed flow (in contrast to previous investigations) but instead the theory is developed rationally by use of proper wake-profiles which satisfy the steady equations of motion. The initial growth of near wake perturbation is governed by the compressible Rayleigh equation which is studied analytically for long- and short-waves. These solutions emphasize the asymptotic structures involved and provide a rational basis for a nonlinear development. The evolution of arbitrary wavelength perturbations is addressed numerically and spatial stability solutions are presented that account for the relative importance of the different physical mechanisms present, such as three-dimensionality, increasing Mach numbers enough (subsonic) Mach numbers, there exists a region of absolute instability very close to the trailing-edge with the majority of the wake being convectively unstable. At higher Mach numbers (but still not large-hypersonic) the absolute instability region seems to disappear and the maximum available growth-rates decrease considerably. Three-dimensional perturbations provide the highest spatial growth-rates.

Papageorgiou, D. T.↗
DOE OSTI2020

Resurgent trans-series for generalized Hastings–McLeod solutions

Here, we show that the physical Hastings–McLeod solution of the integrable Painlevé II equation generalizes in a natural way to a class of non-integrable equations, in a way that preserves many of the significant qualitative properties. The Hastings–McLeod solution of Painlevé II is an important and universal example of resurgent relations between perturbative and non-perturbative physics. We derive the trans-series structure of the generalized Hastings–McLeod solutions, demonstrating that integrability is not essential for the resurgent asymptotic properties of the solutions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1974

Small-scale yielding analysis of mixed mode plane-strain crack problems

The small-scale yielding analysis of an elastic-plastic body with a line crack under plane-strain conditions subject to combinations of Mode I and II loadings is examined. The analysis of the near-tip field follows the works of Hutchinson and Rice and Rosengren. Dominant singularity solutions governing the asymptotic behavior of the stresses and strains at the crack tip are obtained for the complete range of loadings between Mode I and II. The results of an accurate finite element technique, which imbeds the dominant singularity solutions, directly relates the near-tip behavior to the elastic stress intensity factors K(I) and K(II). Implications of this study to mixed mode fracture mechanics is also discussed, particularly with respect to the direction of crack initiation and the relation of fracture toughness under mixed modes to that in Mode I. Details of the mixed mode plastic zone sizes and shapes are also given.

Shih, C. F.↗
NASA NTRS1976

Solution of the minimum time-to-climb problem by matched asymptotic expansions

Application of singular perturbation techniques to trajectory optimization problems of flight mechanics is discussed. The method of matched asymptotic expansions is used to obtain an approximate solution to the aircraft minimum time-to-climb problem. Outer, boundary-layer, and composite solutions are obtained to zeroth and first orders. A stability criterion is derived for the zeroth-order boundary-layer solutions (the theory requires a form of boundary-layer stability). A numerical example is considered for which it is shown that the stability criterion is satisfied and a useful numerical solution is obtained. The zeroth-order solution proves to be a poor approximation, but the first-order solution gives a good approximation for both the trajectory and the minimum time-to-climb. The computational cost of the singular perturbation solution is considerably less than that of a steepest descent solution. Thus singular perturbation methods appear to be promising for the solution of optimal control problems.

Ardema, M. D.↗
NASA NTRS1983

Solution algorithms for non-linear singularly perturbed optimal control problems

The applicability and usefulness of several classical and other methods for solving the two-point boundary-value problem which arises in non-linear singularly perturbed optimal control are assessed. Specific algorithms of the Picard, Newton and averaging types are formally developed for this class of problem. The computational requirements associated with each algorithm are analysed and compared with the computational requirement of the method of matched asymptotic expansions. Approximate solutions to a linear and a non-linear problem are obtained by each method and compared.

Ardema, M. D.↗