Open ocean regimes of relative dispersion

Abstract

As two fluid particles separate in time, the entire spectrum of eddy motions is being sampled from the smallest to the largest scales. In large-scale geophysical systems for which the Earth rotation is important, it has been conjectured that the relative diffusivity should vary respectively as D 2 and D 4/3 for distances respectively smaller and larger than a well-defined forcing scale of the order of the internal Rossby radius (with D the r.m.s. separation distance). Particle paths data from a mid-latitude float experiment in the central part of the North Atlantic appear to support these statements partly: two particles initially separated by a few km within two distinct clusters west and east of the mid-Atlantic ridge, statistically dispersed following a Richardson regime (D 2 ∼ t 3 asymptotically) for r.m.s. separation distances between 40 and 300 km, in agreement with a D 4/3 law. At early times, and for smaller separation distances, an exponential growth, in agreement with a D 2 law, was briefly observed but only for the eastern cluster (with an e-folding time around 6 days). After a few months or separation distances greater than 300 km, the relative dispersion slowed down naturally to the Taylor absolute dispersion regime. IntroductionObservations of the separation of pairs of particles is one of the few experimental methods available to examine the spatial structure of geophysical turbulent flows. Richardson (1926) proposed that the relative diffusivity of an ensemble of pairs should scale as the 4/3 power of the (r.m.s.) separation distance. In his review of the subject, Corrsin (1962) emphasized the concept that turbulent eddies much smaller or much larger than the separation scale are relatively inefficient in further separation at the difference of eddies near the separation scale: the small eddies cause independent random walks of each member of the pair while the larger ones move the pair coherently as a single unit. As a result the relative velocity of the pair changes with the separation and is a non-stationary random variable. This accelerating property of relative diffusion has been used to infer properties of the energy wavenumber spectrum in the inertial range. The key quantity in the inertial range of three-dimensional turbulence is the energy dissipation rate. When the relative diffusivity is assumed to depend only on this energy dissipation rate and on separation, Richardson's law is recovered (Obukhov 1941;Batchelor 1952). The study of particle dispersion is important because of the interest in transport and mixing of chemicals in large-scale geophysical systems. While Taylor's (1921) single-particle dispersion theory relates to tracer dispersal from a fixed geographical origin and for very large times, two-particle dispersion relates to the spreading of a cloud of tracer from its centre of gravity (Batchelor 1952) and will

Evaluation and Tuning of Model Trajectories and Spreading Rates in the Baltic Sea Using Surface Drifter Observations

“…As the filter did little change to the relative dispersion for the SVP drifters, it should not markedly influence the results from the GPS/GSM drifters either. Differently from a number of similar studies (Ollitrault et al 2005;Döös and Engqvist 2007;Lumpkin and Elipot 2010) the experiments performed in the western and central part of the Gulf of Finland in August-October 2010 were concentrated on relatively small initial separations of the drifters (∼100 m). The deployments resulted in 7 pairs of drifter trajectories.…”

“…Thus, for an ideal 2D turbulence with a single energy input scale λ, Lin's law is expected to be valid for scales below λ whereas Richardson's law is related to large-scale circulation (Salazar and Collins 2009). Both these flow regimes have been observed using observed and simulated drifters in the open ocean (Ollitrault et al 2005) and in the Baltic Sea for different scales (Döös and Engqvist 2007).…”

Turbulent dispersion properties from a model simulation of the western Mediterranean Sea

“…Due to homogeneity, the mean-square relative velocity becomes just four times the eddy kinetic energy (Ollitrault et al, 2005;LaCasce and Bower, 2000):…”

“…> x is the spatial average of the relative velocity over the entire domain) (Babiano et al, 1990;Ollitrault et al, 2005).…”

“…At longer times, the time dependence was a power law with an exponent lying between 2 and 3. Ollitrault et al (2005) analyzed subsurface float pairs in the western and eastern North Atlantic from the TOPOGULF experiment. They found an exponential regime for scales smaller than the Rossby radius of deformation (D < 25 km) and for times t < 6 days, followed by a Richardson's law from scales 40 to 300 km, and a linear regime was then observed.…”