TY - JOUR
T1 - Inverse versus direct cascades in turbulent advection
AU - Chertkov, M.
AU - Kolokolov, I.
AU - Vergassola, M.
PY - 1998
Y1 - 1998
N2 - A model of scalar turbulent advection in compressible flow is analytically investigated. It is shown that, depending onthe dimensionality d of space and the degree of compressibility of the smooth advecting velocity field, the cascade of the scalar is direct or inverse. If d > 4 the cascade is always direct. For a small enough degree of compressibility, the cascade is direct again. Otherwise it is inverse; i.e., very large scales are excited. The dynamical hint for the direction of the cascade is the sign of the Lyapunov exponent for particles separation. Positive Lyapunov exponents are associated to direct cascade and Gaussianity at small scales. Negative Lyapunov exponents lead to inverse cascade, Gaussianity at large scales, and strong intermittency at small scales.
AB - A model of scalar turbulent advection in compressible flow is analytically investigated. It is shown that, depending onthe dimensionality d of space and the degree of compressibility of the smooth advecting velocity field, the cascade of the scalar is direct or inverse. If d > 4 the cascade is always direct. For a small enough degree of compressibility, the cascade is direct again. Otherwise it is inverse; i.e., very large scales are excited. The dynamical hint for the direction of the cascade is the sign of the Lyapunov exponent for particles separation. Positive Lyapunov exponents are associated to direct cascade and Gaussianity at small scales. Negative Lyapunov exponents lead to inverse cascade, Gaussianity at large scales, and strong intermittency at small scales.
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U2 - 10.1103/PhysRevLett.80.512
DO - 10.1103/PhysRevLett.80.512
M3 - Article
AN - SCOPUS:4243864415
SN - 0031-9007
VL - 80
SP - 512
EP - 515
JO - Physical review letters
JF - Physical review letters
IS - 3
ER -