Tipping points induced by parameter drift in an excitable low-order model of the wind-driven ocean circulation

2021 ◽  
Author(s):  
Stefano Pierini ◽  
Michael Ghil
Keyword(s):  
Wind Stress ◽  
Ocean Circulation ◽  
Nonlinear Resonance ◽  
High Amplitude ◽  
Time Dependent ◽  
Tipping Points ◽  
Order Model ◽  
Periodic Perturbations ◽  
Small Periodic ◽  
Low Order

<p>A quasi-geostrophic, low-order model of the wind-driven ocean circulation is used to illustrate tipping points induced by time-dependent forcing in excitable chaotic systems. When the wind stress amplitude G is constant in time, our model has a bifurcation from low-amplitude oscillations to high-amplitude relaxation oscillations (ROs) at a wind intensity value G<sub>c</sub>. In the presence of time-dependent wind stress, the corresponding tipping point time t<sub>tp</sub> is defined as the time at which ROs arise. Numerical experiments are carried out using ensemble simulations in the presence of different drift rates of monotonically increasing forcing. Additional experiments include small periodic perturbations of such forcing. The results indicate substantial sensitivity of t<sub>tp</sub> and G(t<sub>tp</sub>) Rate-induced tipping, coexisting pullback attractors and total independence from initial states are found for subsets of parameter space. Besides, nonlinear resonance occurs in the presence of periodic perturbations for periods comparable to the RO time scale. The small periodic perturbation can be thought of as the seasonal-to-interannual variability in the wind stress, while the monotonically increasing component stands for the effect of amplification in the midlatitude winds due to anthropogenic warming.</p>

scholarly journals Interaction between surface wind and ocean circulation in the Carolina Capes in a coupled low-order model

1997 ◽  
Vol 17 (12) ◽  
pp. 1483-1511
Author(s):  
Lian Xie ◽  
Leonard J. Pietrafesa ◽  
Sethu Raman
Keyword(s):  
Ocean Circulation ◽  
Surface Wind ◽  
Order Model ◽  
Low Order

Hybrid Reduced Model of Rotor

2013 ◽  
Vol 60 (3) ◽  
pp. 319-333
Author(s):  
Rafał Hein ◽  
Cezary Orlikowski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hybrid Model ◽  
Rotor System ◽  
Reduced Model ◽  
Order Model ◽  
Gyroscopic Effect ◽  
Reduced Models ◽  
Rigid Finite Element Method ◽  
Low Order

Abstract In the paper, the authors describe the method of reduction of a model of rotor system. The proposed approach makes it possible to obtain a low order model including e.g. non-proportional damping or the gyroscopic effect. This method is illustrated using an example of a rotor system. First, a model of the system is built without gyroscopic and damping effects by using the rigid finite element method. Next, this model is reduced. Finally, two identical, low order, reduced models in two perpendicular planes are coupled together by means of gyroscopic and damping interaction to form one model of the system. Thus a hybrid model is obtained. The advantage of the presented method is that the number of gyroscopic and damping interactions does not affect the model range

On-line thermal regulation of a capillary pumped loop via state feedback control using a low order model

2016 ◽  
Vol 108 ◽  
pp. 614-627 ◽  
Author(s):  
Etienne Videcoq ◽  
Manuel Girault ◽  
Vincent Ayel ◽  
Cyril Romestant ◽  
Yves Bertin
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
State Feedback Control ◽  
Thermal Regulation ◽  
Order Model ◽  
Capillary Pumped Loop ◽  
On Line ◽  
Low Order

Investigation of the stability of boundary layers by a finite-difference model of the Navier—Stokes equations

1976 ◽  
Vol 78 (2) ◽  
pp. 355-383 ◽  
Author(s):  
H. Fasel
Keyword(s):  
Finite Difference ◽  
Stability Theory ◽  
Stokes Equations ◽  
Time Dependent ◽  
Linear Stability Theory ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
The Stability ◽  
Small Periodic

The stability of incompressible boundary-layer flows on a semi-infinite flat plate and the growth of disturbances in such flows are investigated by numerical integration of the complete Navier–;Stokes equations for laminar two-dimensional flows. Forced time-dependent disturbances are introduced into the flow field and the reaction of the flow to such disturbances is studied by directly solving the Navier–Stokes equations using a finite-difference method. An implicit finitedifference scheme was developed for the calculation of the extremely unsteady flow fields which arose from the forced time-dependent disturbances. The problem of the numerical stability of the method called for special attention in order to avoid possible distortions of the results caused by the interaction of unstable numerical oscillations with physically meaningful perturbations. A demonstration of the suitability of the numerical method for the investigation of stability and the initial growth of disturbances is presented for small periodic perturbations. For this particular case the numerical results can be compared with linear stability theory and experimental measurements. In this paper a number of numerical calculations for small periodic disturbances are discussed in detail. The results are generally in fairly close agreement with linear stability theory or experimental measurements.

Gradient-Free Optimization in Thermoacoustics: Application to A Low-Order Model

2021 ◽  
Author(s):  
Johann Moritz Reumschüssel ◽  
Jakob G. R. von Saldern ◽  
Yiqing Li ◽  
Christian Oliver Paschereit ◽  
Alessandro Orchini
Keyword(s):  
Optimization Algorithms ◽  
Optimization Methods ◽  
Theoretical Studies ◽  
Order Model ◽  
Output Data ◽  
Fuel Injectors ◽  
Solution Strategies ◽  
The Past ◽  
Downhill Simplex ◽  
Low Order

Abstract Machine learning and automatized routines for parameter optimization have experienced a surge in development in the past years, mostly caused by the increasing availability of computing capacity. Gradient-free optimization can avoid cumbersome theoretical studies as input parameters are purely adapted based on output data. As no knowledge about the objective function is provided to the algorithms, this approach might reveal unconventional solutions to complex problems that were out of scope of classical solution strategies. In this study, the potential of these optimization methods on thermoacoustic problems is examined. The optimization algorithms are applied to a generic low-order thermoacoustic can-combustor model with several fuel injectors at different locations. We use three optimization algorithms — the well established Downhill Simplex Method, the recently proposed Explorative Gradient Method, and an evolutionary algorithm — to find optimal fuel distributions across the fuel lines while maintaining the amount of consumed fuel constant. The objective is to have minimal pulsation amplitudes. We compare the results and efficiency of the gradient-free algorithms. Additionally, we employ model-based linear stability analysis to calculate the growth rates of the dominant thermoacoustic modes. This allows us to highlight general and thermoacoustic-specific features of the optimization methods and results. The findings of this study show the potential of gradient-free optimization methods on combustor design for tackling thermoacoustic problems, and motivate further research in this direction.

Sign in / Sign up

Export Citation Format

Share Document