Parametrization of irreversible diapycnal diffusivity in salt-fingering turbulence using DNS

Ma, Yuchen; Peltier, W. R.

doi:10.1017/jfm.2020.1018

Cited by 10 publications

(9 citation statements)

References 43 publications

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“…2011; Traxler et al. 2011; Ma & Peltier 2021 a , b ) followed. The theory successfully predicts the upper limit of the density ratio below which the staircases are most likely to form, a result that explained the distribution of density ratio of the observed staircases in the tropical region (Radko 2013).…”

Section: Introductionmentioning

confidence: 99%

Thermohaline staircase formation in the diffusive convection regime: a theory based upon stratified turbulence asymptotics

Peltier

2021

J. Fluid Mech.

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We describe a mechanism that leads to the spontaneous formation of a thermohaline staircase in the high-latitude oceans. Our analysis of this mechanism is based upon a model in which uniform gradients of temperature and salinity are assumed and is applied to a simplified mean-field model of stratified turbulence. Detailed analysis employs a parametrization of turbulent diapycnal diffusivities (Bouffard & Boegman, Dyn. Atmos. Oceans, vol. 61, 2013, pp. 14–34). This parametrization is apparently unique in that it distinguishes between the diapycnal diffusivities for heat and salt on the basis of their Prandtl (Schmidt) numbers. Our model predicts that the temperature and salinity profiles will be susceptible to linear instability if the buoyancy Reynolds number lies in the range 0.18–91, and a nonlinear mean-field model simulation demonstrates that it evolves into a well-defined thermohaline staircase that matches the characteristics of those found in the high-latitude oceans. The criterion for initial instability is furthermore shown to be consistent with the observed regional variability of staircase occurrence in the Arctic Ocean as determined by the most recent observational datasets.

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Section: Introductionmentioning

confidence: 99%

Thermohaline staircase formation in the diffusive convection regime: a theory based upon stratified turbulence asymptotics

Peltier

2021

J. Fluid Mech.

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“…We will here proceed to extend (2.5) to a diffusive–convection system, following similar approaches that were applied in Ma & Peltier (2021) to the understanding of diapycnal diffusivities in salt-fingering turbulence. The existence of the unstably stratified scalar field of temperature in the Arctic Ocean region allows potential energy to kinetic energy conversion and thereby the creation of macroscopic motion, which was unavailable in the single-component case in which the background stratification of density was stably stratified.…”

Section: Scalar Diffusivities In a Diffusive–convection Systemmentioning

confidence: 99%

“…This was first applied to the case of salt-fingering double-diffusive turbulence, which develops under conditions in which warm salty water lies above relatively colder and fresher water. As we will demonstrate in what follows, the theoretical framework established in Ma & Peltier (2021) that is based on sorting both individual fields separately can be carried over almost without modification to the diffusive–convection system with only the roles played by temperature and salinity in the energy budget switched. In what follows, the formulae for the irreversible diapycnal diffusivities for both heat and salt will be derived that provide the basis for the new mixing analysis to be discussed herein.…”

Section: Introductionmentioning

confidence: 99%

“…It should be noticed that the distinction between reversible and irreversible processes described above had only been recognized in the study of stratified turbulence in either the single-component case or the two-component case in which both components are stably stratified scalar fields (Smyth, Nash & Moum 2005). The most recent work of Ma & Peltier (2021) extended the analysis to include the case in which one of the scalars is unstably stratified. This was first applied to the case of salt-fingering double-diffusive turbulence, which develops under conditions in which warm salty water lies above relatively colder and fresher water.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, only the density field is sorted and the separate definitions of irreversible heat fluxes and irreversible salt fluxes, which are important in our analyses to follow, cannot be defined. For this reason, we will employ the method discussed in Ma & Peltier (2021) as the basis for our turbulent analyses.…”

Section: Introductionmentioning

confidence: 99%

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Diapycnal diffusivities in Kelvin–Helmholtz engendered turbulent mixing: the diffusive–convection regime in the Arctic Ocean

Peltier

2022

J. Fluid Mech.

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Recent progress in the direct measurement of turbulent dissipation in the Arctic Ocean has highlighted the need for an improved parametrization of the turbulent diapycnal diffusivities of heat and salt that is suitable for application in the turbulent environment characteristic of this polar region. In support of this goal we describe herein a series of direct numerical simulations of the turbulence generated in the process of growth and breaking of Kelvin–Helmholtz billows. These simulations provide the data sets needed to serve as basis for a study of the stratified turbulent mixing processes that are expected to exist in the Arctic Ocean environment. The mixing properties of the turbulence are studied using a previously formulated procedure in which the temperature and salinity fields are sorted separately in order to enable the separation of irreversible Arctic mixing from reversible stirring processes and thus the definition of turbulent diffusivities for both heat and salt that depend solely upon irreversible mixing. These analyses allow us to demonstrate that the irreversible diapycnal diffusivities for heat and salt are both solely dependent on the buoyancy Reynolds number in the Arctic Ocean environment. These are found to be in close agreement with the functional forms inferred for these turbulent diffusivities in the previous work of Bouffard & Boegman (Dyn. Atmos. Oceans, vol. 61, 2013, pp. 14–34). Based on a detailed comparison of our simulation data with this previous empirical work, we propose an algorithm that can be used for inferring the diapycnal diffusivities from turbulent dissipation measurements in the Arctic Ocean.

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Interaction between double diffusion and differential diffusion in a stratified turbulent flow

Willard

Rehmann

2022

Environ Fluid Mech

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Parametrization of irreversible diapycnal diffusivity in salt-fingering turbulence using DNS

Abstract: Abstract

Cited by 10 publications

References 43 publications

Thermohaline staircase formation in the diffusive convection regime: a theory based upon stratified turbulence asymptotics

Thermohaline staircase formation in the diffusive convection regime: a theory based upon stratified turbulence asymptotics

Diapycnal diffusivities in Kelvin–Helmholtz engendered turbulent mixing: the diffusive–convection regime in the Arctic Ocean

Interaction between double diffusion and differential diffusion in a stratified turbulent flow

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