scholarly journals Strongly Nonlinear Transverse Perturbations in Phononic Crystals

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
S. Nikitenkova ◽  
E. Pelinovsky
Keyword(s):  
Finite Amplitude ◽  
Phononic Crystals ◽  
Strongly Nonlinear ◽  
Riemann Wave ◽  
Wave Deformation ◽  
Highly Nonlinear ◽  
Low Dimensional ◽  
Time Existence

The dynamics of the surface heterogeneities formation in low-dimensional phononic crystals is studied. It is shown that phononic transverse perturbations in this medium are highly nonlinear. They can be described with the help of the Riemann wave and may form stable wave structures of the finite amplitude. The Riemann wave deformation is described analytically. The Riemann wave time existence up to the beginning of the gradient catastrophe is calculated.

Low-Dimensional Components of Flows With Large Free/Moving-Surface Motion

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Yi Zhang ◽  
Solomon C. Yim
Keyword(s):  
Flow Field ◽  
Level Set ◽  
Wave Impact ◽  
Moving Surface ◽  
Surface Motion ◽  
Level Set Function ◽  
Highly Nonlinear ◽  
Flow Systems ◽  
Low Dimensional ◽  
Set Function

Flow systems with highly nonlinear free/moving surface motion are common in engineering applications, such as wave impact and fluid-structure interaction (FSI) problems. In order to reveal the dynamics of such flows, as well as provide a reduced-order modeling (ROM) for large-scale applications, we propose a proper orthogonal decomposition (POD) technique that couples the velocity flow field and the level-set function field, as well as a proper normalization for the snapshots data so that the low-dimensional components of the flow can be retrieved with a priori knowledge of equal distribution of the total variance between velocity and level-set function data. Through numerical examples of a sloshing problem and a water entry problem, we show that the low-dimensional components obtained provide an efficient and accurate approximation of the flow field. Moreover, we show that the velocity contour and orbits projected on the space of the reduced basis greatly facilitate understanding of the intrinsic dynamics of the flow systems.

Finite-amplitude acoustic-gravity waves: exact solutions

2015 ◽  
Vol 767 ◽  
pp. 52-64 ◽  
Author(s):  
Oleg A. Godin
Keyword(s):  
Gravity Waves ◽  
Wave Motion ◽  
Analytic Solutions ◽  
Finite Amplitude ◽  
Compressible Fluids ◽  
Acoustic Gravity Waves ◽  
Strongly Nonlinear ◽  
Exact Analytic Solutions ◽  
Nonlinear Hydrodynamics ◽  
Hydrodynamics Equations

AbstractWe consider strongly nonlinear waves in fluids in a uniform gravity field, and demonstrate that an incompressible wave motion, in which pressure remains constant in each fluid parcel, is supported by compressible fluids with free and rigid boundaries. We present exact analytic solutions of nonlinear hydrodynamics equations which describe the incompressible wave motion. The solutions provide an extension of the Gerstner wave in an incompressible fluid with a free boundary to waves in compressible three-dimensionally inhomogeneous moving fluids such as oceans and planetary atmospheres.

scholarly journals Slug genesis in cylindrical pipe flow

2010 ◽  
Vol 663 ◽  
pp. 180-208 ◽  
Author(s):  
Y. DUGUET ◽  
A. P. WILLIS ◽  
R. R. KERSWELL
Keyword(s):  
Phase Space ◽  
Vortex Shedding ◽  
Coherent Structures ◽  
Pipe Flow ◽  
Edge State ◽  
Shear Layers ◽  
Finite Amplitude ◽  
Spatial Expansion ◽  
Cylindrical Pipe ◽  
Low Dimensional

Transition to uniform turbulence in cylindrical pipe flow occurs experimentally via the spatial expansion of isolated coherent structures called ‘slugs’, triggered by localized finite-amplitude disturbances. We study this process numerically by examining the preferred route in phase space through which a critical disturbance initiates a ‘slug’. This entails first identifying the relative attractor – ‘edge state’ – on the laminar–turbulent boundary in a long pipe and then studying the dynamics along its low-dimensional unstable manifold, leading to the turbulent state. Even though the fully turbulent state delocalizes at Re ≈ 2300, the edge state is found to be localized over the range Re = 2000–6000, and progressively reduces in both energy and spatial extent as Re is increased. A key process in the genesis of a slug is found to be vortex shedding via a Kelvin–Helmholtz mechanism from wall-attached shear layers quickly formed at the edge state's upstream boundary. Whether these shedded vortices travel on average faster or slower downstream than the developing turbulence determines whether a puff or a slug (respectively) is formed. This observation suggests that slugs are out-of-equilibrium puffs which therefore do not co-exist with stable puffs.

Empirical Modeling of Unsteady Flows

2003 ◽  
Author(s):  
Sue Ellen Haupt
Keyword(s):  
Empirical Model ◽  
Large Scale ◽  
Flow System ◽  
Unsteady Flows ◽  
Nonlinear Problems ◽  
Empirical Models ◽  
Empirical Modeling ◽  
Atmospheric Flow ◽  
Highly Nonlinear ◽  
Low Dimensional

In this work we demonstrate the utility of stochastic empirical models. Linear stochastic models have been successful at reproducing responses to forcing of large-scale atmospheric flow. However, the linear forms of the models reach their limit on highly nonlinear problems. It is shown here that for simple low dimensional problems, a quadratically nonlinear empirical model is successful at reproducing a chaotic attractor. In addition, empirical models can be used to diagnose the important dynamics of a flow system and identify the essential terms to include in a forward dynamical model. Once the empirical model has been built, it can then be used to diagnose the underlying dynamics.

Sigma-Point Kalman Filter Data Assimilation Methods for Strongly Nonlinear Systems

2009 ◽  
Vol 66 (2) ◽  
pp. 261-285 ◽  
Author(s):  
Jaison Thomas Ambadan ◽  
Youmin Tang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Kalman Filters ◽  
Joint Estimation ◽  
Sigma Point ◽  
Strongly Nonlinear ◽  
Data Assimilation Scheme ◽  
Higher Dimensional ◽  
Highly Nonlinear ◽  
Assimilation Scheme

Abstract Performance of an advanced, derivativeless, sigma-point Kalman filter (SPKF) data assimilation scheme in a strongly nonlinear dynamical model is investigated. The SPKF data assimilation scheme is compared against standard Kalman filters such as the extended Kalman filter (EKF) and ensemble Kalman filter (EnKF) schemes. Three particular cases—namely, the state, parameter, and joint estimation of states and parameters from a set of discontinuous noisy observations—are studied. The problems associated with the use of tangent linear model (TLM) or Jacobian when using standard Kalman filters are eliminated when using SPKF data assimilation algorithms. Further, the constraints and issues of SPKF data assimilation in real ocean or atmospheric models are emphasized. A reduced sigma-point subspace model is proposed and investigated for higher-dimensional systems. A low-dimensional Lorenz 1963 model and a higher-dimensional Lorenz 1995 model are used as the test beds for data assimilation experiments. The results of SPKF data assimilation schemes are compared with those of standard EKF and EnKF, in which a highly nonlinear chaotic case is studied. It is shown that the SPKF is capable of estimating the model state and parameters with better accuracy than EKF and EnKF. Numerical experiments showed that in all cases the SPKF can give consistent results with better assimilation skills than EnKF and EKF and can overcome the drawbacks associated with the use of EKF and EnKF.

Mechanisms for the Development of Locally Low-Dimensional Atmospheric Dynamics

2005 ◽  
Vol 62 (4) ◽  
pp. 1135-1156 ◽  
Author(s):  
Michael Oczkowski ◽  
Istvan Szunyogh ◽  
D. J. Patil
Keyword(s):  
Phase Space ◽  
Numerical Experiments ◽  
Practical Implication ◽  
Finite Amplitude ◽  
Diagnostic Tools ◽  
Atmospheric Flow ◽  
Initial Transient ◽  
Wide Range ◽  
Environmental Prediction ◽  
Low Dimensional

Abstract The complexity of atmospheric instabilities is investigated by a combination of numerical experiments and diagnostic tools that do not require the assumption of linear error dynamics. These tools include the well-established analysis of the local energetics of the atmospheric flow and the recently introduced ensemble dimension (E dimension). The E dimension is a local measure that varies in both space and time and quantifies the distribution of the variance between phase space directions for an ensemble of nonlinear model solutions over a geographically localized region. The E dimension is maximal, that is, equal to the number of ensemble members (k), when the variance is equally distributed between k phase space directions. The more unevenly distributed the variance, the lower the E dimension. Numerical experiments with the state-of-the-art operational Global Forecast System (GFS) of the National Centers for Environmental Prediction (NCEP) at a reduced resolution are carried out to investigate the spatiotemporal evolution of the E dimension. This evolution is characterized by an initial transient phase in which coherent regions of low dimensionality develop through a rapid local decay of the E dimension. The typical duration of the transient is between 12 and 48 h depending on the flow; after the initial transient, the E dimension gradually increases with time. The main goal of this study is to identify processes that contribute to transient local low-dimensional behavior. Case studies are presented to show that local baroclinic and barotropic instabilities, downstream development of upper-tropospheric wave packets, phase shifts of finite amplitude waves, anticyclonic wave breaking, and some combinations of these processes can all play crucial roles in lowering the E dimension. The practical implication of the results is that a wide range of synoptic-scale weather events may exist whose prediction can be significantly improved in the short and early medium range by enhancing the prediction of only a few local phase space directions. This potential is demonstrated by a reexamination of the targeted weather observations missions from the 2000 Winter Storm Reconnaissance (WSR00) program.

Suppression of nonlinear aeroelastic vibrations by learned neural network controller

2019 ◽  
Vol 91 (3) ◽  
pp. 420-427
Author(s):  
Franciszek Dul
Keyword(s):  
Neural Network ◽  
Control Method ◽  
Robust Methods ◽  
Content Type ◽  
Strongly Nonlinear ◽  
Neural Network Controller ◽  
Network Controller ◽  
Hysteresis Nonlinearity ◽  
Highly Nonlinear ◽  
Aeroelastic Vibrations

PurposeThe purpose of the paper is to analyze the active suppression of the aeroelastic vibrations of ailerons with strongly nonlinear characteristics by neural network/reinforcement learning (NN/RL) control method and comparing it with the classic robust methods of suppression.Design/methodology/approachThe flexible wing and aileron with hysteresis nonlinearity is treated as a plant-controller system and NN/RL and robust controller are used to suppress the nonlinear aeroelastic vibrations of aileron. The simulation approach is used for analyzing the efficiency of both types of methods in suppressing of such vibrations.FindingsThe analysis shows that the NN/RL controller is able to suppress the nonlinear vibrations of aileron much better than linear robust method, although its efficiency depends essentially on the NN topology as well as on the RL strategy.Research limitations/implicationsOnly numerical analysis was carried out; thus, the proposed solution is of theoretical value, and its application to the real suppression of aeroelastic vibrations requires further research.Practical implicationsThe work shows the NN/RL method has a great potential in improving suppression of highly nonlinear aeroelastic vibrations, opposed to the classical robust methods that probably reach their limits in this area.Originality/valueThe work raises the questions of controllability of the highly nonlinear aeroelastic systems by means of classical robust and NN/RL methods of control.

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