87,786 research outputs found

    Hydrodynamic stability in the presence of a stochastic forcing:a case study in convection

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    We investigate the stability of a statistically stationary conductive state for Rayleigh-B\'enard convection between stress-free plates that arises due to a bulk stochastic internal heating. This setup may be seen as a generalization to a stochastic setting of the seminal 1916 study of Lord Rayleigh. Our results indicate that stochastic forcing at small magnitude has a stabilizing effect, while strong stochastic forcing has a destabilizing effect. The methodology put forth in this article, which combines rigorous analysis with careful computation, also provides an approach to hydrodynamic stability for a variety of systems subject to a large scale stochastic forcing

    ENSO dynamics: low-dimensional-chaotic or stochastic?

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    We apply a test for low-dimensional, deterministic dynamics to the Nino 3 time series for the El Nino Southern Oscillation (ENSO). The test is negative, indicating that the dynamics is high-dimensional/stochastic. However, application of stochastic forcing to a time-delay equation for equatorial-wave dynamics can reproduce this stochastic dynamics and other important aspects of ENSO. Without such stochastic forcing this model yields low-dimensional, deterministic dynamics, hence these results emphasize the importance of the stochastic nature of the atmosphere-ocean interaction in low-dimensional models of ENSO

    Delayed-feedback chimera states: Forced multiclusters and stochastic resonance

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    A nonlinear oscillator model with negative time-delayed feedback is studied numeri- cally under external deterministic and stochastic forcing. It is found that in the unforced system complex partial synchronization patterns like chimera states as well as salt-and-pepper like soli- tary states arise on the route from regular dynamics to spatio-temporal chaos. The control of the dynamics by external periodic forcing is demonstrated by numerical simulations. It is shown that one-cluster and multi-cluster chimeras can be achieved by adjusting the external forcing frequency to appropriate resonance conditions. If a stochastic component is superimposed to the determin- istic external forcing, chimera states can be induced in a way similar to stochastic resonance, they appear, therefore, in regimes where they do not exist without noise.Comment: 6 pages of paper with references + tex style file + 5 figure

    On the evolution of mean motion resonances through stochastic forcing: Fast and slow libration modes and the origin of HD128311

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    Aims. We clarify the response of extrasolar planetary systems in a 2:1 mean motion commensurability with masses ranging from the super Jovian range to the terrestrial range to stochastic forcing that could result from protoplanetary disk turbulence. The behaviour of the different libration modes for a wide range of system parameters and stochastic forcing magnitudes is investigated. The growth of libration amplitudes is parameterized as a function of the relevant physical parameters. The results are applied to provide an explanation of the configuration of the HD128311 system. Methods. We first develop an analytic model from first principles without making the assumption that both eccentricities are small. We also perform numerical N-body simulations with additional stochastic forcing terms to represent the effects of putative disk turbulence. Results. Systems are quickly destabilized by large magnitudes of stochastic forcing but some stability is imparted should systems undergo a net orbital migration. The slow mode, which mostly corresponds to motion of the angle between the apsidal lines of the two planets, is converted to circulation more readily than the fast mode which is associated with oscillations of the semi-major axes. This mode is also vulnerable to the attainment of small eccentricities which causes oscillations between periods of libration and circulation. Conclusions. Stochastic forcing due to disk turbulence may have played a role in shaping the configurations of observed systems in mean motion resonance. It naturally provides a mechanism for accounting for the HD128311 system.Comment: 15 pages, 8 figures, added discussion in h and k coordinates, recommended for publicatio

    Linear non-normal energy amplification of harmonic and stochastic forcing in turbulent channel flow

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    The linear response to stochastic and optimal harmonic forcing of small coherent perturbations to the turbulent channel mean flow is computed for Reynolds numbers ranging from Re_tau=500 to Re_tau=20000. Even though the turbulent mean flow is linearly stable, it is nevertheless able to sustain large amplifications by the forcing. The most amplified structures consist of streamwise elongated streaks that are optimally forced by streamwise elongated vortices. For streamwise elongated structures, the mean energy amplification of the stochastic forcing is found to be, to a first approximation, inversely proportional to the forced spanwise wavenumber while it is inversely proportional to its square for optimal harmonic forcing in an intermediate spanwise wavenumber range. This scaling can be explicitly derived from the linearised equations under the assumptions of geometric similarity of the coherent perturbations and of logarithmic base flow. Deviations from this approximate power-law regime are apparent in the premultiplied energy amplification curves that reveal a strong influence of two different peaks. The dominant peak scales in outer units with the most amplified spanwise wavelength of λz3.5h\lambda_z \approx 3.5 h while the secondary peak scales in wall units with the most amplified λz+80\lambda_z^+\approx 80. The associated optimal perturbations are almost independent of the Reynolds number when respectively scaled in outer and inner units. In the intermediate wavenumber range the optimal perturbations are approximatively geometrically similar. Furthermore, the shape of the optimal perturbations issued from the initial value, the harmonic forcing and the stochastic forcing analyses are almost indistinguishable. The optimal streaks corresponding to the large-scale peak strongly penetrate into the inner layer, where their amplitude is proportional to the mean-flow profile. At the wavenumbers corresponding to the large-scale peak, the optimal amplifications of harmonic forcing are at least two orders of magnitude larger than the amplifications of the variance of stochastic forcing and both increase with the Reynolds number. This confirms the potential of the artificial forcing of optimal large-scale streaks for the flow control of wall-bounded turbulent flows

    Uniqueness of the Invariant Measure for a Stochastic PDE Driven by Degenerate Noise

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    We consider the stochastic Ginzburg-Landau equation in a bounded domain. We assume the stochastic forcing acts only on high spatial frequencies. The low-lying frequencies are then only connected to this forcing through the non-linear (cubic) term of the Ginzburg-Landau equation. Under these assumptions, we show that the stochastic PDE has a unique invariant measure. The techniques of proof combine a controllability argument for the low-lying frequencies with an infinite dimensional version of the Malliavin calculus to show positivity and regularity of the invariant measure. This then implies the uniqueness of that measure.Comment: 45 pages, 0 figures, needs 3 latex run

    Scalar conservation laws with stochastic forcing

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    We show that the Cauchy Problem for a randomly forced, periodic multi-dimensional scalar first-order conservation law with additive or multiplicative noise is well-posed: it admits a unique solution, characterized by a kinetic formulation of the problem, which is the limit of the solution of the stochastic parabolic approximation
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