New Method for Estimating Double-Diffusive Dissipation Rates

<p>Understanding the transport of heat in the Arctic ocean will be vital for predicting the fate of sea-ice in the decades to come. Small-scale turbulence is an important driver of heat transport and one of the major forms of this turbulence is known as `double-diffusive convection'. Double diffusion refers to a variety of turbulent processes in which potential energy is released into kinetic energy, made possible in the ocean by the difference in molecular diffusivities between salinity and temperature. &#160;The most direct measurements of ocean mixing require sampling velocity or temperature gradients on scales <1mm, so-called microstructure measurements. Here we present a new method for estimating the energy dissipated by double-diffusive convection using temperature and salinity measurements on larger scales (100s to 1000s of metres). The method estimates the up-gradient diapycnal buoyancy flux, which is hypothesised to balance the dissipation rate. To calculate the temperature and salinity gradients on small scales we apply a canonical scaling for compensated thermohaline variance (or `spice') and project the gradients down to small scales. We apply the method to a high-resolution survey of temperature and salinity through a subsurface Arctic eddy (Fine et al. 2018) and compare the results with simultaneous microstructure measurements. The new technique can reproduce up to 70% of the observed dissipation rates to within a factor of 3. This suggests the method could be used to estimate the dissipation and heat fluxes associated with double-diffusive convection in regions without microstructure measurements. Finally, we show the method maintains predictive skill when applied to a sub-sampling of the CTD data at lower resolutions.</p>

Download Full-text

Does Rotation Influence Double-Diffusive Fluxes in Polar Oceans?

Journal of Physical Oceanography ◽

10.1175/jpo-d-13-098.1 ◽

2014 ◽

Vol 44 (1) ◽

pp. 289-296 ◽

Cited By ~ 12

Author(s):

J. R. Carpenter ◽

M.-L. Timmermans

Keyword(s):

Arctic Ocean ◽

Heat Fluxes ◽

Small Scale ◽

Previous Theory ◽

Thermal Interface ◽

Diffusive Convection ◽

Polar Oceans ◽

Diffusive Fluxes ◽

Mixed Layers ◽

Double Diffusive

Abstract The diffusive (or semiconvection) regime of double-diffusive convection (DDC) is widespread in the polar oceans, generating “staircases” consisting of high-gradient interfaces of temperature and salinity separated by convectively mixed layers. Using two-dimensional direct numerical simulations, support is provided for a previous theory that rotation can influence DDC heat fluxes when the thickness of the thermal interface sufficiently exceeds that of the Ekman layer. This study finds, therefore, that the earth’s rotation places constraints on small-scale vertical heat fluxes through double-diffusive layers. This leads to departures from laboratory-based parameterizations that can significantly change estimates of Arctic Ocean heat fluxes in certain regions, although most of the upper Arctic Ocean thermocline is not expected to be dominated by rotation.

Download Full-text

Double diffusion, shear instabilities, and heat impacts of a Pacific Summer Water intrusion in the Beaufort Sea

Journal of Physical Oceanography ◽

10.1175/jpo-d-21-0074.1 ◽

2021 ◽

Author(s):

Jennifer A. MacKinnon ◽

Matthew H. Alford ◽

Leo Middleton ◽

John Taylor ◽

John B. Mickett ◽

...

Keyword(s):

Density Ratio ◽

Arctic Basin ◽

Heat Fluxes ◽

Double Diffusive Convection ◽

Thermohaline Structure ◽

Water Intrusion ◽

Diffusive Convection ◽

Vertical Heat ◽

Pacific Summer Water ◽

Double Diffusive

Abstract Pacific Summer Water eddies and intrusions transport heat and salt from boundary regions into the western Arctic basin. Here we examine concurrent effects of lateral stirring and vertical mixing using microstructure data collected within a Pacific Summer Water intrusion with a length scale of ∼20 km. This intrusion was characterized by complex thermohaline structure in which warm Pacific Summer Water interleaved in alternating layers of O(1 m) thickness with cooler water, due to lateral stirring and intrusive processes. Along interfaces between warm/salty and cold/fresh water masses, the density ratio was favorable to double-diffusive processes. The rate of dissipation of turbulent kinetic energy (ε) was elevated along the interleaving surfaces, with values up to 3×10−8 W kg−1 compared to background ε of less than 10−9 W kg−1. Based on the distribution of ε as a function of density ratio Rρ , we conclude that double-diffusive convection is largely responsible for the elevated ε observed over the survey. The lateral processes that created the layered thermohaline structure resulted in vertical thermohaline gradients susceptible to double-diffusive convection, resulting in upward vertical heat fluxes. Bulk vertical heat fluxes above the intrusion are estimated in the range of 0.2-1 W m−2, with the localized flux above the uppermost warm layer elevated to 2- 10 W m−2. Lateral fluxes are much larger, estimated between 1000-5000 W m−2, and set an overall decay rate for the intrusion of 1-5 years.

Download Full-text

Applicability and failure of the flux-gradient laws in double-diffusive convection

Journal of Fluid Mechanics ◽

10.1017/jfm.2014.244 ◽

2014 ◽

Vol 750 ◽

pp. 33-72 ◽

Cited By ~ 8

Author(s):

Timour Radko

Keyword(s):

Large Scale ◽

Numerical Models ◽

Vertical Transport ◽

Double Diffusive Convection ◽

Flux Gradient ◽

Salinity Gradients ◽

Diffusive Convection ◽

Small Scales ◽

New Formulation ◽

Double Diffusive

AbstractDouble-diffusive flux-gradient laws are commonly used to describe the development of large-scale structures driven by salt fingers – thermohaline staircases, collective instability waves and intrusions. The flux-gradient model assumes that the vertical transport is uniquely determined by the local background temperature and salinity gradients. While flux-gradient laws adequately capture mixing characteristics on scales that greatly exceed those of primary double-diffusive instabilities, their accuracy rapidly deteriorates when the scale separation between primary and secondary instabilities is reduced. This study examines conditions for the breakdown of the flux-gradient laws using a combination of analytical arguments and direct numerical simulations. The applicability (failure) of the flux-gradient laws at large (small) scales is illustrated through the example of layering instability, which results in the spontaneous formation of thermohaline staircases from uniform temperature and salinity gradients. Our inquiry is focused on the properties of the ‘point-of-failure’ scale ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}H_{pof}$) at which the vertical transport becomes significantly affected by the non-uniformity of the background stratification. It is hypothesized that$H_{pof} $can control some key characteristics of secondary double-diffusive phenomena, such as the thickness of high-gradient interfaces in thermohaline staircases. A more general parametrization of the vertical transport – the flux-gradient-aberrancy law – is proposed, which includes the selective damping of relatively short wavelengths that are inadequately represented by the flux-gradient models. The new formulation is free from the unphysical behaviour of the flux-gradient laws at small scales (e.g. the ultraviolet catastrophe) and can be readily implemented in theoretical and large-scale numerical models of double-diffusive convection.

Download Full-text

Numerical Simulations of Melt-Driven Double-Diffusive Fluxes in a Turbulent Boundary Layer beneath an Ice Shelf

Journal of Physical Oceanography ◽

10.1175/jpo-d-20-0114.1 ◽

2020 ◽

Author(s):

Leo Middleton ◽

Catherine A. Vreugdenhil ◽

Paul R. Holland ◽

John R. Taylor

Keyword(s):

Boundary Layer ◽

Numerical Simulations ◽

Isotropic Turbulence ◽

Small Scale ◽

Relevant Parameter ◽

Double Diffusive Convection ◽

Ice Shelf ◽

Diffusive Convection ◽

Forced Turbulence ◽

Double Diffusive

AbstractThe transport of heat and salt through turbulent ice shelf-ocean boundary layers is a large source of uncertainty within ocean models of ice shelf cavities. This study uses small-scale, high resolution, 3D numerical simulations to model an idealised boundary layer beneath a melting ice shelf to investigate the influence of ambient turbulence on double-diffusive convection (i.e. convection driven by the difference in diffusivities between salinity and temperature). Isotropic turbulence is forced throughout the simulations and the temperature and salinity are initialised with homogeneous values similar to observations. The initial temperature and the strength of forced turbulence are varied as controlling parameters within an oceanographically relevant parameter space. Two contrasting regimes are identified. In one regime double-diffusive convection dominates, and in the other convection is inhibited by the forced turbulence. The convective regime occurs for high temperatures and low turbulence levels, where it is long-lived and affects the flow, melt rate and melt pattern. A criterion for identifying convection in terms of the temperature and salinity profiles, and the turbulent dissipation rate, is proposed. This criterion may be applied to observations and theoretical models to quantify the effect of double-diffusive convection on ice shelf melt rates.

Download Full-text

Initiation of diffusive layering by time-dependent shear

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.790 ◽

2018 ◽

Vol 858 ◽

pp. 588-608 ◽

Cited By ~ 4

Author(s):

Justin M. Brown ◽

Timour Radko

Keyword(s):

Internal Gravity Waves ◽

Shear Instability ◽

The Arctic ◽

Small Scale ◽

Buoyancy Frequency ◽

Diffusive Convection ◽

Plausible Mechanism ◽

The Impact ◽

Double Diffusive ◽

Static Shear

The Arctic halocline is generally stable to the development of double-diffusive and dynamic instabilities – the two major sources of small-scale mixing in the mid-latitude oceans. Despite this, observations show the abundance of double-diffusive staircases in the Arctic Ocean, which suggests the presence of some destabilizing process facilitating the transition from smooth-gradient to layered stratification. Recent studies have shown that an instability can develop in such circumstances if weak static shear is present even when the flow is dynamically and diffusively stable. However, the impact of oscillating shear, associated with the presence of internal gravity waves, has not yet been addressed for the diffusive case. Through two-dimensional simulations of diffusive convection, we have investigated the impact of the magnitude and frequency of externally forced oscillatory shear on the thermohaline-shear instability. Simulations with stochastic shear – characterized by a continuous spectrum of frequencies from inertial to buoyancy – indicate that thermohaline layering does occur due to the presence of destabilizing modes (oscillations of near the buoyancy frequency). These simulations show that such layers appear as well-defined steps in the temperature and salinity profiles. Thus, the thermohaline-shear instability is a plausible mechanism for staircase formation in the Arctic and merits substantial future study.

Download Full-text