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Modeling BiOS?

Modeling BiOS?. Why not.. Renzo Mosetti OGS. Main question : Is the pseudo-periodic reversal of the circulation in the Ionian sustainable only through internal dynamics?. A feedback mechanism is the core of BiOS . Let’s try to do something in this direction…. First :.

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Modeling BiOS?

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  1. Modeling BiOS? Why not.. Renzo Mosetti OGS

  2. Main question: Is the pseudo-periodic reversal of the circulation in the Ionian sustainable only through internal dynamics? A feedback mechanism is the core of BiOS. Let’s try to do something in this direction….

  3. First : Squeezing the theory to extract the simplest physical mechanism The feedback state variables: Ionian Sea Level Anomaly vs. ADW Salinity Anomaly

  4. FACTS

  5. The feedback: ANTICICLONIC CICLONIC Enter AMW Lower ADW sal.an. NO AMW Increase ADW sal.an

  6. Setting the Model Accumulation of salinity anomaly Feedback from SL anomaly Non linear damping/discharge (Eq. 1) Feedback from Salinity anomaly S ADW salinity anomaly IONIAN sea level anomaly Recharge oscillator: Fei-Fei Jin 1997, J. Atm. Sc. 54,811

  7. Some math (*)… A-dimensional equation by scaling: Where: T= 2.592 X 10^6 H=200m *

  8. By differentiating and substituting: Rearranging : (Eq.2) This stuff has a familiar aspect….

  9. and the winner is: (Eq. 3) We can rewrite Eq (2) in the standard form (3) by the following positions: The van der Pol equation has a unique, stable limit cycle for each The van der Pol equation has a unique, stable limit cycle for each > 0. > 0.

  10. How to choose the parameters? Crude estimate: A residence time of Adriatic deep water: 26 Months (Vilibic,sic!) C estimate from data: 1.13 x 10^(-9) B estimate from data : 1.58 x 10 ^(-10) D: estimate from data: 2.75 x 10^(-6) We do need better estimate from a deep statistical analysis of all available data Nevertheless…

  11. Salinity anomaly MONTHS SL anomaly (scaled to H) Period T = 16 yrs !

  12. Salinity anomaly MONTHS SL anomaly

  13. Phase plane s - Limit cycle

  14. Some comments and future developments • This is a conceptual model: • May be it is the simplest physical model based on the BiOS hypothesis; • Over a wide range of coupling coefficients, the model can be self-excited with a robust decadal period; • The role of an external seasonal /inter-annual forcing (Salinity flux; wind stress) should be investigated: what happens to the oscillations? • What will be the effect of a stochastic forcing?

  15. The forced, or driven, Van der Pol oscillator takes the 'original' function and adds a driving function: There exist two frequencies in this system, namely, the frequency of self-oscillation determined by ϵ and the frequency of the periodic forcing. The response of the system is shown in Figure (upper) for Tin=10 and F=1.2 . It is observed that the mean period Tout of x often locks to mTin/n , where m and n are integers. It is also known thatchaoscan be found in the system when the nonlinearity of the system is sufficiently strong. Figure (lower) shows the largest Lyapunov exponent, and it is observed that chaos takes place in the narrow ranges of ϵ .

  16. A QUESTION for you: Who is “right” Van der Pol ? a) Anneliese Van der Pol b) Balthasar Van der Pol

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