The Primary Nonlinear Dynamics of Modal and Nonmodal Perturbations of Monochromatic Inertia–Gravity Waves

2007 ◽  
Vol 64 (1) ◽  
pp. 74-95 ◽  
Author(s):  
Ulrich Achatz
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Instability ◽  
Normal Modes ◽  
Large Degree ◽  
Small Scale ◽  
Turbulent Dissipation ◽  
Static And Dynamic Instability ◽  
Boussinesq Fluid ◽  
Secondary Instabilities ◽  
Elliptically Polarized

Abstract The breaking of an inertia–gravity wave (IGW), initiated by its leading normal modes (NMs) or singular vectors (SVs), and the resulting small-scale eddies are investigated by means of direct numerical simulations of a Boussinesq fluid characterizing the upper mesosphere. The focus is on the primary nonlinear dynamics, neglecting the effect of secondary instabilities. It is found that the structures with the strongest impact on the IGW and also the largest turbulence amplitudes are the NM (for a statically unstable IGW) or short-term SV (statically and dynamically stable IGW) propagating horizontally transversely with respect to the IGW, possibly in agreement with observations of airglow ripples in conjunction with statically unstable IGWs. In both cases these leading structures reduce the IGW amplitude well below the static and dynamic instability thresholds. The resulting turbulent dissipation rates are within the range of available estimates from rocket soundings, even for IGWs at amplitudes low enough precluding NM instabilities. Thus SVs can help explain turbulence occurring under conditions not amenable for the classic interpretation via static and dynamic instability. Because of the important role of the statically enhanced roll mechanism in the energy exchange between IGW and eddies, the turbulent velocity fields are often conspicuously anisotropic. The spatial turbulence distribution is determined to a large degree by the elliptically polarized horizontal velocity field of the IGW.

scholarly journals Modal and Nonmodal Perturbations of Monochromatic High-Frequency Gravity Waves: Primary Nonlinear Dynamics

2007 ◽  
Vol 64 (6) ◽  
pp. 1977-1994 ◽  
Author(s):  
Ulrich Achatz
Keyword(s):  
Nonlinear Dynamics ◽  
Gravity Waves ◽  
High Frequency ◽  
Normal Modes ◽  
Wave Interactions ◽  
Resonant Wave ◽  
Spatial Dimensions ◽  
Phase Direction ◽  
Parallel Mode ◽  
Boussinesq Fluid

The primary nonlinear dynamics of high-frequency gravity waves (HGWs) perturbed by their most prominent normal modes (NMs) or singular vectors (SVs) in a rotating Boussinesq fluid have been studied by direct numerical simulations (DNSs), with wave scales and values of viscosity and diffusivity characteristic for the upper mesosphere. The DNS is 2.5D in that it has only two spatial dimensions, defined by the direction of propagation of the HGW and the direction of propagation of the perturbation in the plane orthogonal to the HGW phase direction, but describes a fully 3D velocity field. Many results of the more comprehensive fully 3D simulations in the literature are reproduced. So it is found that statically unstable HGWs are subject to wave breaking ending in a wave amplitude with respect to the overturning threshold near 0.3. It is shown that this is a result of a perturbation of the HGW by its leading transverse NM. For statically stable HGWs, a parallel NM has the strongest effect, quite in line with previous results on the predominantly 2D instability of such HGWs. This parallel mode is, however, not the leading NM but a larger-scale pattern, seemingly driven by resonant wave–wave interactions, leading eventually to energy transfer from the HGW into another gravity wave with steeper phase propagation. SVs turn out to be less effective in triggering HGW decay but they can produce turbulence of a strength that is (as that from the NMs) within the range of measured values, however with a more pronounced spatial confinement.

Pull-In Dynamics of an Elastic Beam Actuated by Distributed Electrostatic Force

2003 ◽  
Author(s):  
Slava Krylov ◽  
Ronen Maimon
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Instability ◽  
Electrostatic Force ◽  
Normal Modes ◽  
Elastic Beam ◽  
Nonlinear Damping ◽  
Rotational Inertia ◽  
Electrostatic Forces ◽  
Spatial Region ◽  
Electrically Actuated

A detailed study of the transient nonlinear dynamics of an electrically actuated micron scale beam is presented. A model developed using the Galerkin procedure with normal modes as a basis accounts for the distributed nonlinear electrostatic forces, nonlinear distributed squeezed film damping forces, and rotational inertia of a mass carried by the beam. Special attention is paid to the dynamics of the beam near instability points. Results generated by the model and confirmed experimentally show that nonlinear damping leads to shrinkage of the spatial region where stable motion is realizable. The voltage that causes dynamic instability, in turn, approaches the static pull-in value.

Pull-in Dynamics of an Elastic Beam Actuated by Continuously Distributed Electrostatic Force

2004 ◽  
Vol 126 (3) ◽  
pp. 332-342 ◽  
Author(s):  
Slava Krylov ◽  
Ronen Maimon
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Instability ◽  
Electrostatic Force ◽  
Normal Modes ◽  
Elastic Beam ◽  
Nonlinear Damping ◽  
Rotational Inertia ◽  
Electrostatic Forces ◽  
Spatial Region ◽  
Electrically Actuated

A detailed study of the transient nonlinear dynamics of an electrically actuated micron scale beam is presented. A model developed using the Galerkin procedure with normal modes as a basis accounts for the distributed nonlinear electrostatic forces, nonlinear squeezed film damping, and rotational inertia of a mass carried by the beam. Special attention is paid to the dynamics of the beam near instability points. Results generated by the model and confirmed experimentally show that nonlinear damping leads to shrinkage of the spatial region where stable motion is realizable. The voltage that causes dynamic instability, in turn, approaches the static pull-in value.

Nonlinear evolution of the elliptical instability: an example of inertial wave breakdown

1999 ◽  
Vol 396 ◽  
pp. 73-108 ◽  
Author(s):  
D. M. MASON ◽  
R. R. KERSWELL
Keyword(s):  
Finite Amplitude ◽  
Complex Conjugate ◽  
Small Scale ◽  
Conjugate Pair ◽  
Weakly Nonlinear ◽  
Elliptical Instability ◽  
Elliptical Flow ◽  
Complex Conjugate Pair ◽  
Generic Instability ◽  
Secondary Instabilities

A direct numerical simulation is presented of an elliptical instability observed in the laboratory within an elliptically distorted, rapidly rotating, fluid-filled cylinder (Malkus 1989). Generically, the instability manifests itself as the pairwise resonance of two different inertial modes with the underlying elliptical flow. We study in detail the simplest ‘subharmonic’ form of the instability where the waves are a complex conjugate pair and which at weakly supercritical elliptical distortion should ultimately saturate at some finite amplitude (Waleffe 1989; Kerswell 1992). Such states have yet to be experimentally identified since the flow invariably breaks down to small-scale disorder. Evidence is presented here to support the argument that such weakly nonlinear states are never seen because they are either unstable to secondary instabilities at observable amplitudes or neighbouring competitor elliptical instabilities grow to ultimately disrupt them. The former scenario confirms earlier work (Kerswell 1999) which highlights the generic instability of inertial waves even at very small amplitudes. The latter represents a first numerical demonstration of two competing elliptical instabilities co-existing in a bounded system.

scholarly journals AxiSEM: broadband 3-D seismic wavefields in axisymmetric media

Solid Earth ◽  
2014 ◽  
Vol 5 (1) ◽  
pp. 425-445 ◽  
Author(s):  
T. Nissen-Meyer ◽  
M. van Driel ◽  
S. C. Stähler ◽  
K. Hosseini ◽  
S. Hempel ◽  
...  
Keyword(s):  
Normal Modes ◽  
Spectral Element ◽  
Multipole Expansion ◽  
Small Scale ◽  
Computational Domain ◽  
Diverse Range ◽  
Earthquake Sources ◽  
Third Dimension ◽  
Computational Resources ◽  
Background Models

Abstract. We present a methodology to compute 3-D global seismic wavefields for realistic earthquake sources in visco-elastic anisotropic media, covering applications across the observable seismic frequency band with moderate computational resources. This is accommodated by mandating axisymmetric background models that allow for a multipole expansion such that only a 2-D computational domain is needed, whereas the azimuthal third dimension is computed analytically on the fly. This dimensional collapse opens doors for storing space–time wavefields on disk that can be used to compute Fréchet sensitivity kernels for waveform tomography. We use the corresponding publicly available AxiSEM (www.axisem.info) open-source spectral-element code, demonstrate its excellent scalability on supercomputers, a diverse range of applications ranging from normal modes to small-scale lowermost mantle structures, tomographic models, and comparison with observed data, and discuss further avenues to pursue with this methodology.

scholarly journals Non-Extensive Statistical Analysis of Energetic Particle Flux Enhancements Caused by the Interplanetary Coronal Mass Ejection-Heliospheric Current Sheet Interaction

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 648 ◽  
Author(s):  
Pavlos ◽  
Malandraki ◽  
Khabarova ◽  
Karakatsanis ◽  
Pavlos ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Equilibrium Phase ◽  
Surrogate Data ◽  
Heliospheric Current Sheet ◽  
Diagnostic Tools ◽  
Small Scale ◽  
Magnetic Islands ◽  
Theoretical Concepts ◽  
Long Range Correlations ◽  
Interplanetary Coronal Mass Ejection

In this study we use theoretical concepts and computational-diagnostic tools of Tsallis non-extensive statistical theory (Tsallis q-triplet: qsen, qrel, qstat), complemented by other known tools of nonlinear dynamics such as Correlation Dimension and surrogate data, Hurst exponent, Flatness coefficient, and p-modeling of multifractality, in order to describe and understand Small-scale Magnetic Islands (SMIs) structures observed in Solar Wind (SW) with a typical size of ~0.01–0.001 AU at 1 AU. Specifically, we analyze ~0.5 MeV energetic ion time-intensity and magnetic field profiles observed by the STEREO A spacecraft during a rare, widely discussed event. Our analysis clearly reveals the non-extensive character of SW space plasmas during the periods of SMIs events, as well as significant physical complex phenomena in accordance with nonlinear dynamics and complexity theory. As our analysis also shows, a non-equilibrium phase transition parallel with self-organization processes, including the reduction of dimensionality and development of long-range correlations in connection with anomalous diffusion and fractional acceleration processes can be observed during SMIs events.

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