Energy and Variance Budgets of a Diffusive Staircase with Implications for Heat Flux Scaling

Hieronymus, Magnus; Carpenter, Jeffrey R.

doi:10.1175/jpo-d-15-0155.1

Cited by 14 publications

(18 citation statements)

References 48 publications

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“…This energy input of C. okenii is converted into an increase of the system's potential energy, dE p /dt, or it is dissipated into heat by friction. Two more contributions to the energy balance (dE k /dt and D V , supporting information Text S4 [Hieronymus and Carpenter, 2016;Winters et al, 1995]) were found negligible. At t = 10 h, when the mixed layer thickness in the simulation reached 0.3 m, as measured in Lake Cadagno, the mean dissipation rate ε within the C. okenii layer was (1.0 ± 1.5) × 10 À10 W kg À1 , or 42% of the bacterial energy input rate R = 2.4 × 10 À10 W kg À1 .…”

Section: 1002/2017gl074868mentioning

confidence: 90%

Bacteria‐induced mixing in natural waters

Sommer

Danza

Berg

et al. 2017

Geophysical Research Letters

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Swimming organisms can enhance mixing in their natural environments by creating eddies in their wake and by dragging water along. However, these mixing mechanisms are inefficient for microorganisms, because swimming‐induced variations in velocity, temperature, and dissolved substances are evened out before they can be advected. In bioconvection, however, microorganisms induce water movement not by propulsion directly but by locally changing the fluid density, which drives convection. Observations of bioconvection have so far mainly been limited to laboratory settings. We report the first observation and quantification of bioconvection within a stratified natural water body. Using in situ measurements, laboratory experiments, and numerical simulations, we demonstrate that the bacterium Chromatium okenii is capable of mixing 0.3 to 1.2 m thick water layers at around 12 m water depth in the Alpine Lake Cadagno (Switzerland). As many species are capable of driving bioconvection, this phenomenon potentially plays a role in species distributions and influences large‐scale phenomena like algal blooms.

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Section: 1002/2017gl074868mentioning

confidence: 90%

Bacteria‐induced mixing in natural waters

Sommer

Danza

Berg

et al. 2017

Geophysical Research Letters

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“…Estimates of heat and salt fluxes can be made by considering the steady state energy balance for a layer (e.g., Hieronymus & Carpenter, ):

ϵ = g α F_{θ} - g β F_{S},

which relates the dissipation of turbulent kinetic energy ϵ within a layer and the net buoyancy flux for large Rayleigh numbers (Rayleigh numbers are

≳ 1 0^{8}

for the Canada Basin layers; Shibley et al, ). Note that assumes that there is no large‐scale background shear which is a reasonable assumption given that the lateral density gradient in the Canada Basin at these depths is effectively 0.…”

Section: Theoretical Formulationmentioning

confidence: 99%

Double‐Diffusive Layering in the Canada Basin: An Explanation of Along‐Layer Temperature and Salinity Gradients

Bebieva

Timmermans

2019

JGR Oceans

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Double-diffusive mixing gives rise to layered structures in the Arctic Ocean: layers within a double-diffusive staircase overlying deeper layers associated with thermohaline intrusions. These layers exhibit well-defined lateral temperature and salinity gradients. Gradients in salinity along individual layers change sign with depth, while along-layer gradients in temperature remain the same sign with depth. A theoretical formalism is put forward to explain these features in terms of vertical divergences of double-diffusive fluxes; temperature and salinity gradients along layers are set by the depth-dependent ratio of double-diffusive heat to salt fluxes. Examination of fine structure in temperature and salinity profiles reveals how the net flux ratio depends upon whether the layer is part of an evolving thermohaline intrusion or a staircase. The physical framework in context with observations of varying along-layer gradients in temperature and salinity provides evidence for thermohaline intrusions evolving to a staircase and describes the parameters that dictate this process. Results bring new understanding to heat and salt transport in the Arctic Ocean as well as the physics of double-diffusive layering in the world's oceans.Plain Language Summary A type of ocean mixing process, double-diffusive convection, gives rise to layers in the Arctic Ocean that may be characterized by their differing temperature and salinity properties. The properties and physics of these layers are key to understanding how heat is transported vertically and laterally in the Arctic Ocean. A theoretical formalism is put forward to explain distinct features of the layers that are characterized in the observations. The physical framework in context with observations brings new understanding to how the layers evolve and how they relate to heat and salt transport in the Arctic Ocean.

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“…The second method for estimating vertical diffusive heat fluxes F H ε is based on measured ε and assumes mechanical energy conservation (i.e., potential plus kinetic energy) within the double‐diffusive layers (Hieronymus and Carpenter ). The buoyancy flux J int through a double‐diffusive interface is equal to the dissipation rate ε within the mixed layer plus a diffusive buoyancy flux J d within the mixed layer (for derivation see Hieronymus and Carpenter []):

J_{int} = ε + J_{d}

…”

Section: Methodsmentioning

confidence: 99%

“…The ratio γ H ≡ J d / J int of the two buoyancy flux terms is ~ 0.20 for a mixed‐layer‐based Rayleigh number of ~ 10 8 typical for Lake Kivu (Sommer et al ; Hieronymus and Carpenter ). Using this definition for γ H leads to a relation to the measured dissipation ε by

J_{int} = \frac{ε}{1 - γ_{H}}

…”

Section: Methodsmentioning

confidence: 99%

The role of double diffusion for the heat and salt balance in Lake Kivu

Sommer

Schmid

Wüest

2018

Limnology & Oceanography

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Double diffusion in lakes and oceans can transform vertical gradients into staircases of convectively mixed layers separated by thin stable interfaces. Lake Kivu is an outstanding double‐diffusive natural laboratory with > 300 such steps over the permanently stratified deep basin. Here, we use 315 microstructure profiles (225 measured in Rwanda and 90 in the DRC) to shed light on the heat and salt balances of Lake Kivu. Comparing profiles from 2011 and 2015 reveals warming of 8.6 mK yr−1 below 80 m depth and negligible changes in salinity. The double‐diffusive layering is coherent over horizontal distances of 20–30 km and remained unchanged between 2011 and 2015, indicating little variability. The mean estimated dissipation within mixed layers is 1.5 × 10−10 W kg−1. If unshaped Batchelor microstructure spectra are interpreted as nonturbulent, the rescaled dissipation of 0.44 × 10−10 W kg−1 corresponds to a vertical heat flux of 0.10 W m−2, which agrees with the molecular heat flux through the adjacent stable interfaces. Using estimates of upwelling, temporal changes of temperature and salt, and vertical double‐diffusive fluxes, we established heat and salt balances, which require lateral heat and salt inputs. For salt, lateral input of freshwater at the main gradients balances upwelling. For temperature, however, the divergence of the vertical double‐diffusive fluxes can only be balanced by horizontal inputs supplying cool water above and warm water below the main gradients. This suggests that lateral inputs of water at various depths are the main drivers for this unique double‐diffusive phenomenon in Lake Kivu.

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Energy and Variance Budgets of a Diffusive Staircase with Implications for Heat Flux Scaling

Cited by 14 publications

References 48 publications

Bacteria‐induced mixing in natural waters

Bacteria‐induced mixing in natural waters

Double‐Diffusive Layering in the Canada Basin: An Explanation of Along‐Layer Temperature and Salinity Gradients

The role of double diffusion for the heat and salt balance in Lake Kivu

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