Toward a Statistical Description of Finescale Strain in the Thermocline

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  • 1 Marine Physical Laboratory of the Scripps Institution of Oceanography, University of California at San Diego, La Jolla, California
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Abstract

The statistical properties of the oceanic finescale strain field are investigated. Strain information is derived from a set of 9000 CTD profiles from the surface to 560-m depth, obtained from the Research Platform FLIP in the 1986 PATCHEX Experiment. Four hundred isopycnals, with mean vertical separation Δz = 1 m, were tracked for the 19-day duration of the experiment.

The instantaneous separation, Δz(t), between isopycnal pairs is found to be statistically independent of the mean position of the pair. The separation statistics demonstrate a number of the characteristic features of a Poisson process. If the number of isopycnals found in a given fixed-depth interval is simply tallied from profile to profile, the variability in the count, when properly rescaled, is given by a Poisson distribution. Probability density functions (pdfs) of separation are well described by the classical Gamma family.

A simple mechanistic model of the strain field is proposed as a guide for interpreting the Poisson-like observations. The model approximates the vertical profile of a passive scalar quantity as a series of constant gradient segments. The depth bounds of each segment are governed by Poisson statistics. Curiously, the strain variance is not an adjustable parameter in this model. The strain variance is 0.5 when statistics are collected in an Eulerian frame. Variance has value unity if the statistics are accumulated in an isapycnal-following frame.

The model vertical wavenumber spectrum of strain is a function of a single parameter, the Poisson scale constant κ0. For κ0 = 1.1 m−1, consistent with the observations, the spectrum has k0 form at low wavenumber. Spectral form transitions to ak−1.5 slope at vertical scales smaller than about 10 m. In contrast to spectral models based on linear dynamics, here the form of the spectrum is constrained to change with changing energy density. Also, skewness, kurtosis, and higher moments of the strain process can be inferred from observations of the second moment.

The moments of inverse separation,Δz−1, are useful in predicting fluctuations in the vertical gradients of passive scalar quantities θ(z): ∂θ/∂z ≡ (θ(ρ1) − θ(ρ2))·Δz−1. A family of probability density functions (pdfs) of vertical gradients is presented as a function of the vertical differencing interval Δz. Using the single variable κ0 = 1.1 m−1 from PATCHEX, the model pdfs of gradients compare excellently with temperature gradient data obtained by Gregg in the central Pacific in 1977.

Small but significant discrepancies appear between the observations and the idealized Poisson model. These are ascribed to the tendency of isopycnals to gather into a “sheets and layer” configuration. When a number of isopycnals gather into a thin sheet, the chances of finding successive isopycnals in the adjoining water (layer) is reduced. A weak predictive ability is implied that is inconsistent with a Poisson process.

Abstract

The statistical properties of the oceanic finescale strain field are investigated. Strain information is derived from a set of 9000 CTD profiles from the surface to 560-m depth, obtained from the Research Platform FLIP in the 1986 PATCHEX Experiment. Four hundred isopycnals, with mean vertical separation Δz = 1 m, were tracked for the 19-day duration of the experiment.

The instantaneous separation, Δz(t), between isopycnal pairs is found to be statistically independent of the mean position of the pair. The separation statistics demonstrate a number of the characteristic features of a Poisson process. If the number of isopycnals found in a given fixed-depth interval is simply tallied from profile to profile, the variability in the count, when properly rescaled, is given by a Poisson distribution. Probability density functions (pdfs) of separation are well described by the classical Gamma family.

A simple mechanistic model of the strain field is proposed as a guide for interpreting the Poisson-like observations. The model approximates the vertical profile of a passive scalar quantity as a series of constant gradient segments. The depth bounds of each segment are governed by Poisson statistics. Curiously, the strain variance is not an adjustable parameter in this model. The strain variance is 0.5 when statistics are collected in an Eulerian frame. Variance has value unity if the statistics are accumulated in an isapycnal-following frame.

The model vertical wavenumber spectrum of strain is a function of a single parameter, the Poisson scale constant κ0. For κ0 = 1.1 m−1, consistent with the observations, the spectrum has k0 form at low wavenumber. Spectral form transitions to ak−1.5 slope at vertical scales smaller than about 10 m. In contrast to spectral models based on linear dynamics, here the form of the spectrum is constrained to change with changing energy density. Also, skewness, kurtosis, and higher moments of the strain process can be inferred from observations of the second moment.

The moments of inverse separation,Δz−1, are useful in predicting fluctuations in the vertical gradients of passive scalar quantities θ(z): ∂θ/∂z ≡ (θ(ρ1) − θ(ρ2))·Δz−1. A family of probability density functions (pdfs) of vertical gradients is presented as a function of the vertical differencing interval Δz. Using the single variable κ0 = 1.1 m−1 from PATCHEX, the model pdfs of gradients compare excellently with temperature gradient data obtained by Gregg in the central Pacific in 1977.

Small but significant discrepancies appear between the observations and the idealized Poisson model. These are ascribed to the tendency of isopycnals to gather into a “sheets and layer” configuration. When a number of isopycnals gather into a thin sheet, the chances of finding successive isopycnals in the adjoining water (layer) is reduced. A weak predictive ability is implied that is inconsistent with a Poisson process.

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