Probability Distribution of Turbulent Kinetic Energy Dissipation Rate in Ocean: Observations and Approximations

Lozovatsky, Iossif; Fernando, Harindra J. S.; Planella-Morato, Jesús; Liu, Zhiyu; Lee, Jae Hak; Jinadasa, S.U.P.

doi:10.1002/2017jc013076

Cited by 19 publications

(13 citation statements)

References 69 publications

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“…For all analyzed CASPER‐west stations, the CDF ( ε ) could be well fitted by the Burr probability distribution (Burr, ) in concurrence with the finding of Lozovatsky, Fernando, et al (). The Burr (type XII) cumulative distribution function CDF ( ε ) is specified as

{CDF}_{B} ((), ε) = 1 - {(1 + {((), ε / ε_{0})}^{c})}^{- k},

where both c > 0 and k > 0 are shape parameters and ε 0 ≡ α B is a scale parameter; ε > 0 by definition.…”

Section: Probability Distributions Of the Dissipation Ratesupporting

confidence: 87%

“…An important questions in the applications of Burr model to dissipation distribution in ocean pycnocline is the possible variability of the model parameters, which could be associated with background hydrodynamic conditions. Lozovatsky, Fernando, et al () discovered that shape parameters c ≡ c B and k ≡ k B of the Burr model for CDFs ( ε ) are correlated over almost two decades of c B and k B values in different regions (Figure a). The newly obtained values of c B and k B vary in a narrower range, but the SCB samples analyzed here closely overlap with the multiregional data set shown in Figure a.…”

Section: Variation Of the Cdf(ε) Parametersmentioning

confidence: 99%

“…Dependence between parameters of the Burr model k B , c B , and α B for CDFs ( ε ) obtained in the pycnoclines of the East China Sea (ECS), Bay of Bengal (BoB), West Monsoon Current south of Sri Lanka (WMC), and Gulf Stream (GS)—all are from Lozovatsky, Fernando, et al ()—supplemented by the newer Southern California Bight (SCB) data.…”

Section: Variation Of the Cdf(ε) Parametersmentioning

confidence: 99%

“…The probability distributions of dissipation field in a specific region can be influenced by larger‐scale dynamical processes that depend on energy sources and ambient stratification. Although non‐lognormality of

{\overset{true¯}{ε}}_{δ}

in the stratified ocean has been demonstrated years ago (e.g., Baker & Gibson, ; Lozovatsky et al, ; Moum & Rippeth, ; Yamazaki & Lueck, ), no alternative statistical model has been proposed until Lozovatsky, Fernando, et al () reported the success of Burr XII distribution (e.g., Burr, ) to model the probability distribution of

{\overset{true¯}{ε}}_{δ}

in the upper ocean pycnocline. This notion was supported by its application to various regions, including the East China Sea, Northern Indian Ocean, and Gulf Stream.…”

Section: Introductionmentioning

confidence: 99%

“…This notion was supported by its application to various regions, including the East China Sea, Northern Indian Ocean, and Gulf Stream. Justification for the applicability of Burr model for

{\overset{true¯}{ε}}_{δ}

distribution in the ocean pycnocline was given by Lozovatsky, Fernando, et al () based on the concept that in stably stratified flow energetic turbulence events are generated rarely and randomly (mostly due to internal wave activity) forming confined regions of high values of

{\overset{true¯}{ε}}_{δ}

(turbulent patches) embedded in background turbulence at various stages of evolution. Random patches of intense turbulence produce tails of the dissipation rate distribution heavier than the exponential bounds, which is a typical pattern for such models as Burr XII and generalized extreme value distribution (GEVD; e.g., Martins & Stedinger, ).…”

Section: Introductionmentioning

confidence: 99%

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Probability Distribution of Turbulent Kinetic Energy Dissipation Rate in Stratified Turbulence: Microstructure Measurements in the Southern California Bight

et al. 2019

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A month of microstructure measurements in the Southern California Bight allowed to confirm the hypothesis that in ocean pycnocline, below the surface mixed layer, the probability distribution of turbulent kinetic energy dissipation rate ε averaged over equal time segments (2 s with 512‐Hz sampling rate, corresponding to about 1.4‐m vertical averaging) follows the Burr distribution suggested by Lozovatsky, Fernando, et al. (2017, https://doi.org/10.1002/2017JC013076). The bin‐median estimates of ε was well correlated with the medians of the Burr model. The parameters of the Burr distribution varied in time, but no relationship was found between these variations and the changes in wind patterns and phases of barotropic tide. In the range 10−9~ < ε < 10−8 W/kg, the dissipation rate could be related to internal wave activity in the region.

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{CDF}_{B} ((), ε) = 1 - {(1 + {((), ε / ε_{0})}^{c})}^{- k},

where both c > 0 and k > 0 are shape parameters and ε 0 ≡ α B is a scale parameter; ε > 0 by definition.…”

Section: Probability Distributions Of the Dissipation Ratesupporting

confidence: 87%

Section: Variation Of the Cdf(ε) Parametersmentioning

confidence: 99%

Section: Variation Of the Cdf(ε) Parametersmentioning

confidence: 99%

{\overset{true¯}{ε}}_{δ}

{\overset{true¯}{ε}}_{δ}

in the upper ocean pycnocline. This notion was supported by its application to various regions, including the East China Sea, Northern Indian Ocean, and Gulf Stream.…”

Section: Introductionmentioning

confidence: 99%

“…This notion was supported by its application to various regions, including the East China Sea, Northern Indian Ocean, and Gulf Stream. Justification for the applicability of Burr model for

{\overset{true¯}{ε}}_{δ}

{\overset{true¯}{ε}}_{δ}

Section: Introductionmentioning

confidence: 99%

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Probability Distribution of Turbulent Kinetic Energy Dissipation Rate in Stratified Turbulence: Microstructure Measurements in the Southern California Bight

et al. 2019

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A snapshot of turbulence in the Northeastern Magellan Strait

Lozovatsky,

Escauriaza,

Suarez

et al. 2024

Ocean Dynamics

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First-ever measurements of the turbulent kinetic energy (TKE) dissipation rate in the northeastern Strait of Magellan (Segunda Angostura region) taken in March 2019 are reported here. At the time of microstructure measurements, the magnitude of the reversing tidal current ranged between 0.8 and 1.2 ms−1. The probability distribution of the TKE dissipation rate in the water interior above the bottom boundary layer was lognormal with a high median value $${\varepsilon }_{med}^{MS}=1.2\times {10}^{-6}$$ ε med MS = 1.2 × 10 - 6 Wkg−1. Strong vertical shear, $$\left(1-2\right)\times {10}^{-2}$$ 1 - 2 × 10 - 2 s−1, in the weakly stratified water interior ensued a sub-critical gradient Richardson number $$Ri<{10}^{-1}-{10}^{-2}$$ R i < 10 - 1 - 10 - 2 . In the bottom boundary layer (BBL), the vertical shear and the TKE dissipation rate both decreased exponentially with the distance from the seafloor $$\xi$$ ξ , leading to a turbulent regime with an eddy viscosity $${K}_{M}\sim {10}^{-3}$$ K M ∼ 10 - 3 m2/s, which varied with time and location, while being independent of the vertical coordinate in the upper part of BBL (for $$\xi >\sim 2$$ ξ > ∼ 2 meters above the bottom).

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Ocean Turbulence and Mixing Near the Shelf Break South-East of Nova Scotia

Lozovatsky

Wainwright

Creegan

et al. 2020

Boundary-Layer Meteorol

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Formation of coastal fog was observed near the southern tip of Nova Scotia when warm, humid air was advected towards the shore over an area of colder water. The sea-surface temperature in the colder and higher salinity patch near the coast was below 14°C compared to that of the surrounding sea of ≈ 17-18°C. Measurements of stratification, currents, and the dissipation rate of turbulence kinetic energy (ε) on the Nova Scotia shelf, shelf break, and continental slope revealed the frequent occurrence of shear instability in the pycnocline. The probability of the gradient Richardson number (Ri) being less than a critical value of Ri cr 0.25 in the depth range 30-90 m exceeded 50% on the shelf and over the slope, and it was above 75% along the shelf break, while in the open ocean pycnocline the probability of Ri < 0.25 is below 5%. The cumulative distribution functions of the dissipation rate in the pycnocline south-east of Nova Scotia followed the Burr probability model with median values from 7.9 × 10 −9 W kg −1 on the slope to 1.9 × 10 −8 W kg −1 at the shelf break. The eddy diffusivity (K N ) estimates follow a generalized extreme value distribution with a high median value of K N 5.8 × 10 −5 m 2 s −1 at the shelf break. The diffusivity K N depended on Ri in general agreement with the parametrization previously suggested by Lozovatsky and Fernando (Philos Trans R Soc A 371:20120213, 2013) but with a higher level of mixing at Ri > 1. This could be relevant to the nature of turbulence generation near the shelf break by random wave instabilities in the pycnocline at high Richardson and high Reynolds numbers.

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Probability Distribution of Turbulent Kinetic Energy Dissipation Rate in Ocean: Observations and Approximations

Cited by 19 publications

References 69 publications

Probability Distribution of Turbulent Kinetic Energy Dissipation Rate in Stratified Turbulence: Microstructure Measurements in the Southern California Bight

Probability Distribution of Turbulent Kinetic Energy Dissipation Rate in Stratified Turbulence: Microstructure Measurements in the Southern California Bight

A snapshot of turbulence in the Northeastern Magellan Strait

Ocean Turbulence and Mixing Near the Shelf Break South-East of Nova Scotia

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