TY - JOUR

T1 - Hard turbulence in a finite dimensional dynamical system?

AU - Bartuccelli, Michele

AU - Constantin, Peter

AU - Doering, Charles R.

AU - Gibbon, John D.

AU - Gisselfält, Magnus

PY - 1989/12/18

Y1 - 1989/12/18

N2 - We present new time-averaged and time-asymptotic bounds on various norms of solutions to the 2-d complex Ginzburg-Landau (CGL) equation, ∂A ∂t = RA + (1 + iv)ΔA - (1 + iμ)|A|2A. These bounds establish the existence of a finite dimensional global attractor and inertial manifolds, so that the dynamics on the attractor are those of a finite dimensional dynamical system. The CGL equation is known to have chaotic solutions characterized by relatively long length-scale, low-modal dynamics, also known as soft turbulence. Our new estimates suggest that near the nonlinear Schrödinger (NLS) limit (|v|, |μ| →∞, if and only it vμ<0), solutions of the CGL equation are dominated by the remnants of the blow-up solutions of the NLS equation, resulting in asymptotic dynamics marked by large intermittent spikes in space and time, i.e., hard turbulence.

AB - We present new time-averaged and time-asymptotic bounds on various norms of solutions to the 2-d complex Ginzburg-Landau (CGL) equation, ∂A ∂t = RA + (1 + iv)ΔA - (1 + iμ)|A|2A. These bounds establish the existence of a finite dimensional global attractor and inertial manifolds, so that the dynamics on the attractor are those of a finite dimensional dynamical system. The CGL equation is known to have chaotic solutions characterized by relatively long length-scale, low-modal dynamics, also known as soft turbulence. Our new estimates suggest that near the nonlinear Schrödinger (NLS) limit (|v|, |μ| →∞, if and only it vμ<0), solutions of the CGL equation are dominated by the remnants of the blow-up solutions of the NLS equation, resulting in asymptotic dynamics marked by large intermittent spikes in space and time, i.e., hard turbulence.

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U2 - 10.1016/0375-9601(89)90380-0

DO - 10.1016/0375-9601(89)90380-0

M3 - Article

AN - SCOPUS:5544322654

VL - 142

SP - 349

EP - 356

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 6-7

ER -