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Lyapunov Exponents for Particles Advected in Compressible Random Velocity Fields at Small and Large Kubo Numbers

Artikel i vetenskaplig tidskrift
Författare Kristian Gustafsson
Bernhard Mehlig
Publicerad i Journal of Statistical Physics
Volym 153
Nummer/häfte 5
Sidor 813-827
ISSN 0022-4715
Publiceringsår 2013
Publicerad vid Institutionen för fysik (GU)
Sidor 813-827
Språk en
Länkar dx.doi.org/10.1007/s10955-013-0848-...
Ämnesord Advection, Compressible velocity fields, Clustering, Lyapunov exponents, Kubo number, INERTIAL PARTICLES, TURBULENCE
Ämneskategorier Fysik

Sammanfattning

We calculate the Lyapunov exponents describing spatial clustering of particles advected in one- and two-dimensional random velocity fields at finite Kubo numbers (a dimensionless parameter characterising the correlation time of the velocity field). In one dimension we obtain accurate results up to by resummation of a perturbation expansion in . At large Kubo numbers we compute the Lyapunov exponent by taking into account the fact that the particles follow the minima of the potential function corresponding to the velocity field. The Lyapunov exponent is always negative. In two spatial dimensions the sign of the maximal Lyapunov exponent lambda (1) may change, depending upon the degree of compressibility of the flow and the Kubo number. For small Kubo numbers we compute the first four non-vanishing terms in the small- expansion of the Lyapunov exponents. By resumming these expansions we obtain a precise estimate of the location of the path-coalescence transition (where lambda (1) changes sign) for Kubo numbers up to approximately . For large Kubo numbers we estimate the Lyapunov exponents for a partially compressible velocity field by assuming that the particles sample those stagnation points of the velocity field that have a negative real part of the maximal eigenvalue of the matrix of flow-velocity gradients.

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