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## Understanding hydrodynamic turbulence and possible analogy with volatility bubbles

The Onsager model of hydrodynamic turbulence has three basic parameters of interest, L the diameter, V, the velocity, and v the viscosity and the dimensionless Re=LV/v is the Reynold’s number. Turbulence occurs when Re>>1.  New vortices form when there is negative (absolute) temperature.

We would like to consider price bubble and persistent volatility as an analogy for these turbulence vortices.  We don’t necessarily expect the Onsager model to be an exact match but we can attempt a mapping and then try to understand the parameters from the Onsager model viewpoint.

So we create an imaginary geography where each stock or financial asset is placed on the map and nearness will be determined by correlations.  We can call this a correlation geography of the market.  We can begin with randomly placing totally uncorrelated stocks, say and randomly place them in a 2D region.  Then we add more stocks based on correlations to the uncorrelated stocks in rings with growing radius. We will come back to the problem of the best spatial arrangement that is useful.

The initial thought experiment is to be a good theorist and try to look at the situation with some new tools whether useless or not.  The purpose of this exercise is to check if L, V and v could actually make sense in some arrangement in 2D so that an exact version of Onsager model could hold.  We don’t expect so but it’s worth a shot.

So we want V to be like volatility and L to be something not known yet and viscosity is controlling laminar from nonlaminar flow so some sort of control.  Usually we want to calibrate even intuitively to some sort of known steady flow.  Well maybe blue chips would be ok except the bailout of AIG tells us that’s not a good idea.  So maybe Standard & Poors 500 or 100.  After calibration, we consider L fixed and so viscosity is relative to some reference laminar or steady object in the market and so L(V/v) is basically just a ratio of volatilities.  I am not yet sure this is the best definition but it’s a start.

So does it make sense that there is movement in this imaginary 2D space?