Minimal model for double diffusion and its application to <scp>K</scp>ivu, <scp>N</scp>yos, and <scp>P</scp>owell <scp>L</scp>ake

Toffolon, Marco; Wüest, Alfred; Sommer, Tobias

doi:10.1002/2015jc010970

Cited by 9 publications

(3 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where = ∕ , = − ∕ are defined in LAKE model according to the equation of state from McCutcheon et al (1993). Stratification is stable when R > 1, but in the interval 1 < R < 10 the diffusive regime of double-diffusive convection is anticipated (Kelley et al 2003, Toffolon et al 2015. Double diffusion leads to effective vertical mixing, potent to hinder the TeM development.…”

Section: Temperature Maximum 331 Salinity-related Effectsmentioning

confidence: 99%

Mid-depth temperature maximum in an estuarine lake

Stepanenko

Репина

Artamonov

et al. 2018

Environ. Res. Lett.

View full text Add to dashboard Cite

The mid-depth temperature maximum (TeM) was measured in an estuarine Bol'shoi Vilyui Lake (Kamchatka peninsula, Russia) in summer 2015. We applied 1D k-model LAKE to the case, and found it successfully simulating the phenomenon. We argue that the main prerequisite for mid-depth TeM development is a salinity increase below the freshwater mixed layer, sharp enough in order to increase the temperature with depth not to cause convective mixing and double diffusion there. Given that this condition is satisfied, the TeM magnitude is controlled by physical factors which we identified as: radiation absorption below the mixed layer, mixed-layer temperature dynamics, vertical heat conduction and water-sediments heat exchange. In addition to these, we formulate the mechanism of temperature maximum 'pumping', resulting from the phase shift between diurnal cycles of mixed-layer depth and temperature maximum magnitude. Based on the LAKE model results we quantify the contribution of the above listed mechanisms and find their individual significance highly sensitive to water turbidity. Relying on physical mechanisms identified we define environmental conditions favouring the summertime TeM development in salinity-stratified lakes as: small-mixed layer depth (roughly, ∼< 2 m), transparent water, daytime maximum of wind and cloudless weather. We exemplify the effect of mixed-layer depth on TeM by a set of selected lakes.

show abstract

Section: Temperature Maximum 331 Salinity-related Effectsmentioning

confidence: 99%

Mid-depth temperature maximum in an estuarine lake

Stepanenko

Репина

Artamonov

et al. 2018

Environ. Res. Lett.

View full text Add to dashboard Cite

show abstract

“…However, Stern numbers have been reported as varying from O(10 −3 ) to O(10 2 ) for finger systems. Recently, Traxler et al (2011) reported Stern numbers St = 9.4 and St = 76 for DNS simulations with density ratios R ρ = 2.0 and R ρ = 1.2. These density ratios are comparable to Case 3 and Case 4, allowing us to compare our results with these DNS simulations.…”

Section: Casementioning

confidence: 99%

“…Based on a 3-D DNS model, Traxler et al (2011) found Stern numbers St = 9.4 and St = 76 for R ρ = 2.0 and R ρ = 1.2, respectively. Our simulations for R ρ = 2.04 (Case 3) and R ρ = 1.19 (Case 4) yield lower average Stern numbers of approximately 0.73 and 1.95, respectively (Fig.…”

Section: Cases 3 and 4: Salt Fingersmentioning

confidence: 99%

Author's response to Referee #1

Hilgersom¹

2016

View full text Add to dashboard Cite

The three-dimensional (3-D) modelling of water systems involving double-diffusive processes is challenging due to the large computation times required to solve the flow and transport of constituents. In 3-D systems that approach axisymmetry around a central location, computation times can be reduced by applying a 2-D axisymmetric model setup. This article applies the Reynolds-averaged Navier-Stokes equations described in cylindrical coordinates and integrates them to guarantee mass and momentum conservation. The discretized equations are presented in a way that a Cartesian finite-volume model can be easily extended to the developed framework, which is demonstrated by the implementation into a non-hydrostatic free-surface flow model. This model employs temperature-and salinity-dependent densities, molecular diffusivities, and kinematic viscosity. One quantitative case study, based on an analytical solution derived for the radial expansion of a dense water layer, and two qualitative case studies demonstrate a good behaviour of the model for seepage inflows with contrasting salinities and temperatures. Four case studies with respect to doublediffusive processes in a stratified water body demonstrate that turbulent flows are not yet correctly modelled near the interfaces and that an advanced turbulence model is required. Kunze (2003) stresses that numerical and analytical methods to model double diffusion are often only applicable on specific scales. For example in oceans, internal wave shear and strain enhance salt-finger growth, leading to higher salt and heat fluxes over stratified interfaces. Traxler et al. (2011) addresses the issue of scale by describing four modes of instability in salt-fingering systems, which play a role on different scales. Their 3-D simulations of large-scale instability in salt-fingering systems are the first known successful direct numerical simulations (DNSs). Carpenter et al. (2012) were among the first to model systems in the double-diffusive convection regime with 3-D DNS. Their detailed simulations showed that, in this regime, the salt and heat fluxes across the interface are largely governed by molecular diffusion and that these salt and heat diffusion rates control the thickness of the salt and heat interface, respectively. Kimura and Smyth (2007) used 3-D DNS to model salt sheets for a doublediffusively stratified flow interacting with inflectional shear.

show abstract

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

Sommer

Schmid

Wüest

2018

Limnology & Oceanography

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Minimal model for double diffusion and its application to Kivu, Nyos, and Powell Lake

Cited by 9 publications

References 46 publications

Mid-depth temperature maximum in an estuarine lake

Mid-depth temperature maximum in an estuarine lake

Author's response to Referee #1

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

Contact Info

Product

Resources

About