Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1996-03-17
Nonlinear Sciences
Chaotic Dynamics
20 pages, LaTeX, submitted to Phys. Rev. E
Scientific paper
10.1103/PhysRevE.54.1497
We establish exact inequalities for the structure-function scaling exponents of a passively advected scalar in both the inertial-convective and viscous-convective ranges. These inequalities involve the scaling exponents of the velocity structure functions and, in a refined form, an intermittency exponent of the convective-range scalar flux. They are valid for 3D Navier-Stokes turbulence and satisfied within errors by present experimental data. The inequalities also hold for any ``synthetic'' turbulent velocity statistics with a finite correlation in time. We show that for time-correlation exponents of the velocity smaller than the ``local turnover'' exponent, the scalar spectral exponent is strictly less than that in Kraichnan's soluble ``rapid-change'' model with velocity delta-correlated in time. Our results include as a special case an exponent-inequality derived previously by Constantin \& Procaccia [Nonlinearity {\bf 7} 1045 (1994)], but with a more direct proof. The inequalities in their simplest form follow from a Kolmogorov-type relation for the turbulent passive scalar valid in each space dimension $d.$ Our improved inequalities are based upon a rigorous version of the refined similarity hypothesis for passive scalars. These are compared with the relations implied by ``fusion rules'' hypothesized for scalar gradients.
No associations
LandOfFree
Intermittency and Anomalous Scaling of Passive Scalars in Any Space Dimension does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Intermittency and Anomalous Scaling of Passive Scalars in Any Space Dimension, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Intermittency and Anomalous Scaling of Passive Scalars in Any Space Dimension will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-604241