Trajectory encounter number as a diagnostic of mixing potential in fluid flows
Irina I. Rypina and Larry J. Pratt
Woods Hole Oceanographic Institution, Physical Oceanography department, 266 Woods Hole rd., Woods Hole MA, 02543
Received: 28 Nov 2016 – Accepted for review: 05 Dec 2016 – Discussion started: 07 Dec 2016
Abstract. Fluid parcels can exchange water properties when coming in contact with each other, leading to mixing. The trajectory encounter number, which quantifies the number of fluid parcel trajectories that pass close to a reference trajectory over a finite time interval, is introduced as a measure of the mixing potential of a flow. Regions characterized by low encounter numbers, such as cores of coherent eddies, have low mixing potential, whereas turbulent or chaotic regions characterized by large encounter numbers have high mixing potential. The encounter number diagnostic was used to characterize mixing potential in 3 flows of increasing complexity: the Duffing Oscillator, the Bickley Jet, and the altimetry-based velocity in the Gulf Stream Extension region. An additional example was presented where the encounter number was combined with the u-star-approach of Pratt et al., 2016 to characterize the mixing potential for a specific tracer distribution in the Bickley Jet flow. Analytical relationships were derived connecting encounter number to diffusivity for purely-diffusive flows, and to shear and strain rates for linear shear and linear strain flows, respectively. It is shown that in a diffusive regime the encounter number grows as a square-root of time, whereas in a linear shear and strain flows the encounter number is proportional to time.
Rypina, I. I. and Pratt, L. J.: Trajectory encounter number as a diagnostic of mixing potential in fluid flows, Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2016-72, in review, 2016.