3,008 research outputs found
Linear Amplification in Nonequilibrium Turbulent Boundary Layers
Resolvent analysis is applied to nonequilibrium incompressible adverse pressure gradient (APG) turbulent boundary layers (TBL) and hypersonic boundary layers with high temperature real gas effects, including chemical nonequilibrium. Resolvent analysis is an equation-based, scale-dependent decomposition of the Navier Stokes equations, linearized about a known mean flow field. The decomposition identifies the optimal response and forcing modes, ranked by their linear amplification. To treat the nonequilibrium APG TBL, a biglobal resolvent analysis approach is used to account for the streamwise and wall-normal inhomogeneities in the streamwise developing flow. For the hypersonic boundary layer in chemical nonequilibrium, the resolvent analysis is constructed using a parallel flow assumption, incorporating Nâ‚‚, Oâ‚‚, NO, N, and O as a mixture of chemically reacting gases.
Biglobal resolvent analysis is first applied to the zero pressure gradient (ZPG) TBL. Scaling relationships are determined for the spanwise wavenumber and temporal frequency that admit self-similar resolvent modes in the inner layer, mesolayer, and outer layer regions of the ZPG TBL. The APG effects on the inner scaling of the biglobal modes are shown to diminish as their self-similarity improves with increased Reynolds number. An increase in APG strength is shown to increase the linear amplification of the large-scale biglobal modes in the outer region, similar to the energization of large scale modes observed in simulation. The linear amplification of these modes grows linearly with the APG history, measured as the streamwise averaged APG strength, and relates to a novel pressure-based velocity scale.
Resolvent analysis is then used to identify the length scales most affected by the high-temperature gas effects in hypersonic TBLs. It is shown that the high-temperature gas effects primarily affect modes localized near the peak mean temperature. Due to the chemical nonequilibrium effects, the modes can be linearly amplified through changes in chemical concentration, which have non-negligible effects on the higher order modes. Correlations in the components of the small-scale resolvent modes agree qualitatively with similar correlations in simulation data.
Finally, efficient strategies for resolvent analysis are presented. These include an algorithm to autonomously sample the large amplification regions using a Bayesian Optimization-like approach and a projection-based method to approximate resolvent analysis through a reduced eigenvalue problem, derived from calculus of variations.</p
Attractors for a fluid-structure interaction problem in a time-dependent phase space
This paper is concerned with the long-time dynamics of a fluid-structure interaction problem describing a Poiseuille inflow through a 2D channel containing a rectangular obstacle. Physically, this models the interaction between the wind and the deck of a bridge in a wind tunnel experiment, as time goes to infinity. Due to this interaction, the fluid domain depends on time in an unknown fashion and the problem needs a delicate functional analytic setting. As a result, the solution operator associated to the system acts on a time- dependent phase space, and it cannot be described in terms of a semigroup nor of a process. Nonetheless, we are able to extend the notion of global attractor to this particular setting, and prove its existence and regularity. This provides a strong characterization of the asymptotic behavior of the problem. Moreover, when the inflow is sufficiently small, the attractor reduces to the unique stationary solution of the system, corresponding to a perfectly symmetric configuration
Invariance of measure under nonlinear wave and Schr\"odinger equations on the plane
We show probabilistic existence and uniqueness for the Wick-ordered cubic
nonlinear wave equation in a weighted Besov space over . To
achieve this, we show that a weak limit of measures on increasing tori
is invariant under the equation. We review and slightly simplify the periodic
theory and the construction of the weak limit measure, and then use finite
speed of propagation to reduce the infinite-volume case to the previous setup.
Our argument also gives a weak (Albeverio--Cruzeiro) invariance result on the
nonlinear Schr\"odinger equation in the same setting.Comment: 50 pages. Major reorganization of Sections 1 and 3, revision and
improvements throughou
"Le present est plein de l’avenir, et chargé du passé" : Vorträge des XI. Internationalen Leibniz-Kongresses, 31. Juli – 4. August 2023, Leibniz Universität Hannover, Deutschland. Band 2
[No abstract available]Deutschen Forschungsgemeinschaft (DFG)/Projektnr. 517991912VGH VersicherungNiedersächsisches Ministerium für Wissenschaft und Kultur (MWK
Falling Drop in an Unbounded Liquid Reservoir: Steady-state Solutions
The equations governing the motion of a three-dimensional liquid drop moving freely in an unbounded liquid reservoir under the influence of a gravitational force are investigated. Provided the (constant) densities in the two liquids are sufficiently close, existence of a steady-state solution is shown. The proof is based on a suitable linearization of the equations. A setting of function spaces is introduced in which the corresponding linear operator acts as a homeomorphism
Beam scanning by liquid-crystal biasing in a modified SIW structure
A fixed-frequency beam-scanning 1D antenna based on Liquid Crystals (LCs) is designed for application in 2D scanning with lateral alignment. The 2D array environment imposes full decoupling of adjacent 1D antennas, which often conflicts with the LC requirement of DC biasing: the proposed design accommodates both. The LC medium is placed inside a Substrate Integrated Waveguide (SIW) modified to work as a Groove Gap Waveguide, with radiating slots etched on the upper broad wall, that radiates as a Leaky-Wave Antenna (LWA). This allows effective application of the DC bias voltage needed for tuning the LCs. At the same time, the RF field remains laterally confined, enabling the possibility to lay several antennas in parallel and achieve 2D beam scanning. The design is validated by simulation employing the actual properties of a commercial LC medium
Circulation Statistics in Homogeneous and Isotropic Turbulence
This is the committee version of a Thesis presented to the PostGrad Program
in Physics of the Physics Institute of the Federal University of Rio de Janeiro
(UFRJ), as a necessary requirement for the title of Ph.D. in Science (Physics).
The development of the Vortex Gas Model (VGM) introduces a novel statistical
framework for describing the characteristics of velocity circulation. In this
model, the underlying foundations rely on the statistical attributes of two
fundamental constituents. The first is a GMC field that governs intermittent
behavior and the second constituent is a Gaussian Free field responsible for
the partial polarization of the vortices in the gas. The model is revisited in
a more sophisticated language, where volume exclusion among vortices is
addressed. These additions were subsequently validated through numerical
simulations of turbulent Navier-Stokes equations. This revised approach
harmonizes with the multifractal characteristics exhibited by circulation
statistics, offering a compelling elucidation for the phenomenon of
linearization of the statistical circulation moments, observed in recent
numerical simulation.
In the end, a field theoretical approach, known as
Martin-Siggia-Rose-Janssen-de Dominicis (MSRJD) functional method is carried
out in the context of circulation probability density function. This approach
delves into the realm of extreme circulation events, often referred to as
Instantons, through two distinct methodologies: The First investigates the
linear solutions and, by a renormalization group argument a time-rescaling
symmetry is discussed. Secondly, a numerical strategy is implemented to tackle
the nonlinear instanton equations in the axisymmetric approximation. This
approach addresses the typical topology exhibited by the velocity field
associated with extreme circulation events.Comment: Ph.D. Thesis - preliminary versio
Transition Physics and Boundary-Layer Stability: Computational Modeling in Compressible Flow
Laminar-to-turbulent transition of boundary layers remains a critical subject of study in aerodynamics. The differences in surface friction and heating between laminar and turbulent flows can be nearly an order of magnitude. Accurate prediction of the transition region between these two regimes is essential for design applications.
The objective of this work is to advance simplified approaches to representing the laminar
boundary layer and perturbation dynamics that usher flows to turbulence. A versatile boundary-layer solver called DEKAF including thermochemical effects has been created, and the in-house nonlinear parabolized stability equation technique called EPIC has been advanced, including an approach to reduce divergent growth associated with the inclusion of the mean-flow distortion. The simplified approaches are then applied to advance studies in improving aircraft energy efficiency.
Under the auspices of a NASA University Leadership Initiative, the transformative technology
of a swept, slotted, natural-laminar-flow wing is leveraged to maintain laminar flow over large
extents of the wing surface, thereby increasing energy efficiency. From an aircraft performance
perspective, sweep is beneficial as it reduces the experienced wave drag. From a boundary-layer transition perspective, though, sweep introduces several physical complications, spawned by the crossflow instability mechanism. As sweep is increased, the crossflow mechanism becomes increasingly unstable, and can lead to an early transition to turbulence. The overarching goal of the present analysis then is to address the question, how much sweep can be applied to this wing while maintaining the benefits of the slotted, natural-laminar-flow design? Linear and nonlinear stability analyses will be presented to assess various pathways to turbulence.
In addition, companion computations are presented to accompany the risk-reduction experiment run in the Klebanoff-Saric Wind Tunnel at Texas A&M University. Linear analyses assess a wide range of various configurations to inform experimentalists where relevant unstable content resides. A comparison between simulation and experimental measurements is presented, for which there is a good agreement
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