Tracer dispersal by mid-ocean mesoscale eddies. Part I. Ensemble statistics

doi:10.1016/0377-0265(84)90002-2

Dynamics of Atmospheres and Oceans

Volume 8, Issue 1, February 1984, Pages 1-40

https://doi.org/10.1016/0377-0265(84)90002-2 Get rights and content

Abstract

The rate at which, and the processes by which, a passive tracer is stirred and mixed in a turbulent mesoscale eddy field are examined for environmental parameters characteristic of a homogeneous mid-ocean region. The simulated, time-dependent eddy field is obtained by direct integration of the forced/damped barotropic vorticity equation; the dispersal of a spatially localized, instantaneous release of tracer (a “tracer spot”) within the evolving velocity field is subsequently computed from the advective-diffusive equation. An ensemble of 10 independent releases is used to determin the average spreading properties of the tracer spot.

On an f-plane, the ensemble-averaged dispersal is approximately isotropic, and is associated with an effective diffusion rate substantially greater than that supported in the absence of turbulent advection. Quantitatively, the effective ensemble-averaged diffusivity is shown to be 0(UL), where U and L are characteristic velocity and length scales of the turbulent flow. This estimate is consistent with the traditional mixing length hypothesis. With the addition of β, the simulated flow field has substantial zonal anisotropy. Ensemble-averaged dispersal of tracer spots is similarly anisotropic, and the overall rate of tracer dispersal is substantially reduced over its f-plane value.

Both with and without β, the initial rate at which maximum tracer concentration and total tracer variance decay are given by the approximate law exp[− αγt] where γ is the RMS rate of strain, and α is approximately constant at a value of 0.5. The heightened rate of variance loss over that associated with pure (subgridscale) diffusion is shown to be accommodated by the rapid transfer of tracer variance from the largest to the shortest scale tracer features, that is, by the rapid sharpening of tracer gradients by turbulent advection. A detailed examination of the dispersal of individual tracer realizations, and the associated question of tracer streakiness, is given in part II of this work (Keffer and Haidvogel, in preparation).

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Further studies have included simple estimates by Garrett (1983), who claimed that streaks would merge very soon after the scalar release in 3D turbulence, but that streakiness would tend to persist for a significant time for 2D stirring. This expectation was reinforced by the numerical simulations of Haidvogel and Keffer (1984) and has been borne out in tracer release experiments in the ocean (Ledwell et al., 1993). Sundermeyer and Price (1998) have conducted more sophisticated analysis of the basic fluid dynamics.
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Anisotropic horizontal viscosity for ocean models
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Lagrangian statistics in the central North Pacific
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Citation Excerpt :
Zonal dispersion is considerably faster than meridional dispersion, and is not consistent with Taylor's Theorem for a homogeneous flow in the long-time random-walk limit. This is an ubiquitous result in open-ocean drifter studies, attributed to topographic effects (Rossby et al., 1975; Freeland et al., 1975), spatial anisotropy of meanders (Colin de Verdière, 1983; Krauss and Böning, 1987), the β-effect (Haidvogel and Keffer, 1984), and meridional shear in the mean zonal flow (Krauss and Böning, 1987). The final hypothesis is consistent with the observed shear of the North Pacific Subtropical Gyre.
Lagrangian integral scales, diffusivities, dispersion and velocity spectra are calculated using surface drifter trajectories in the central North Pacific. The meridional integral time scale is relatively homogeneous throughout the region; a large increase in the zonal time and length scales south of Hawaii is attributed to meanders in the North Equatorial Current. Except in this current, the initial dispersion is consistent with Taylor's Theorem. For lags of 20–120 days, the meridional dispersion can be modeled by a constant eddy diffusivity. Shear in the mean zonal currents magnifies the zonal dispersion at long lags. In the Lagrangian spectra, the energetic eddy band is at 3–20 days west of Hawaii, 10–40 days east and north of Hawaii, and 20–60 days in the North Equatorial Current. In the wake of Hawaii, energetic lee vortices produce sharp peaks in the cyclonic and anticyclonic rotary spectra.
On the initial streakness of a dispersing tracer in two- and three-dimensional turbulence
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If a spot of tracer is released into a turbulent flow, the peak concentration at some subsequent time will initially be much greater than that implied by a solution for the ensemble average concentration at fixed points. For two-dimensional turbulence three areas may be defined: (1) an area A_d related to the ensemble average concentration field; (2) an area A_p defined in terms of the relative dispersion of particles seeded into the patch after a short initial diffusion time; and (3) the area A_t occupied by tracer. It is argued that A_d grows linearly with time, whereas A_p and A_t grow exponentially; A_p faster than A_t. Thus, the concentration field is significantly streaky, even within the particle domain, until A_t becomes comparable with A_d. The time taken for this to occur is estimated; after this time, fluctuations about the ensemble average concentration field should not be greater than those given by a simple mixing length argument. In three-dimensional turbulence the volume V_t of the tracer domain grows much more rapidly than the volume V_p of the particle domain if the merging of streaks is ignored. However, V_t cannot be greater than V_p so streaks must merge and V_p can be used to provide a rough estimate of peak concentration, or concentration variance.
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Some considerations about coastal ocean observing systems
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Research paperTracer dispersal by mid-ocean mesoscale eddies. Part I. Ensemble statistics

Abstract

Dyn. Atm. Oceans

Effects of variable and anisotropic diffusivities in a steady-state diffusion model

J. Phys. Ocean.

Low-resolution numerical simulation of decaying two-dimensional turbulence

J. Atmos. Sci.

Oceanic property transport. Lagrangian particle statistics, and their prediction

J. Mar. Res.

An observation of the horizontal and vertical diffusion of a passive tracer in the deep ocean

J. Geophys. Res.

Particle motions in large-amplitude wave fields

Geophys. Astrophys. Fluid. Dyn.

Statistical observations of the trajectories of neutrally buoyant floats in the North Atlantic

J. Mar. Res.

Phytoplankton patchiness indicates the fluctuation spectrum of mesoscale oceanic structure

Nature

Chapter XVIII, Periodic and regional models

Chapter XXI, Eddy-induced dispersionand mixing

Research paper
Tracer dispersal by mid-ocean mesoscale eddies. Part I. Ensemble statistics