Tobias Sommer

Interface structure and flux laws in a natural double‐diffusive layering

The diffusive regime of double-diffusive convection generates staircases consisting of thin high-gradient interfaces sandwiched between convectively mixed layers. Simultaneous microstructure measurements of both temperature and conductivity from the staircases in Lake Kivu are used to test flux laws and theoretical models for double diffusion. Density ratios in Lake Kivu are between one and ten and mixed layer thicknesses on average 0.7 m. The larger interface thickness of temperature (average 9 cm) compared to dissolved substances (6 cm) confirms the boundary-layer structure of the interface. Our observations suggest that the boundary-layer break-off cannot be characterized by a single critical boundary-layer Rayleigh number, but occurs within a range of O(10(2)) to O(10(4)). Heat flux parameterizations which assume that the Nusselt number follows a power law increase with the Rayleigh number Ra are tested for their exponent . In contrast to the standard estimate =1/3, we found =0.200.03 for density ratios between two and six. Therefore, we suggest a correction of heat flux estimates which are based on =1/3. The magnitude of the correction depends on Ra in the system of interest. For Lake Kivu (average heat flux 0.10 W m(-2)) with Ra=O(10(8)), corrections are marginal. In the Arctic Ocean with Ra=O(10(8)) to O(10(12)), however, heat fluxes can be overestimated by a factor of four.

Stability of a Double-Diffusive Interface in the Diffusive Convection Regime

AbstractIn this paper, the authors explore the conditions under which a double-diffusive interface may become unstable. Focus is placed on the case of a cold, freshwater layer above a warm, salty layer [i.e., the diffusive convection (DC) regime]. The “diffusive interface” between these layers will develop gravitationally unstable boundary layers due to the more rapid diffusion of heat (the destabilizing component) relative to salt. Previous studies have assumed that a purely convective-type instability of these boundary layers is what drives convection in this system and that this may be parameterized by a boundary layer Rayleigh number. The authors test this theory by conducting both a linear stability analysis and direct numerical simulations of a diffusive interface. Their linear stability analysis reveals that the transition to instability always occurs as an oscillating diffusive convection mode and at boundary layer Rayleigh numbers much smaller than previously thought. However, these findings are ...

Revisiting Microstructure Sensor Responses with Implications for Double-Diffusive Fluxes

Thinhigh-gradientinterfacesthatoccurnaturallywithindouble-diffusivestaircasesareusedtoestimatethe response characteristics of temperature and conductivity microstructure sensors. The knowledge of these responses is essentialfor resolvingsmall-scaleturbulencein natural waterbodies and for determining doublediffusive fluxes of heat and salt. Here, the authors derive microstructure sensor responses from observed differences in the statistical distributions of interface thicknesses at various profiling speeds in Lake Kivu (central Africa). In contrast to the standard approach for determining sensor responses, this method is independent of any knowledge of the true in situ temperature and salinity structure. Assuming double-pole frequency response functions, the time constants for the Sea-Bird Electronics SBE-7 conductivity sensor and the Rockland Scientific International FP07 thermistor are estimated to be 2.2 and 10ms, respectively. In contrast to previous assumptions, the frequency response for the SBE-7 is found to be substantial and dominates the wavenumber response for profiling speeds larger than 0.19ms 21 .

Double Diffusion in Saline Powell Lake, British Columbia

Powell Lake contains a deep layer of relic seawater separated from the ocean since the last ice age. Permanently stratified and geothermally heated from below, this deep layer is an isolated geophysical domain suitable for studying double-diffusive convection. High-resolution CTD and microstructure measurements showseveraldouble-diffusivestaircases(Rr 51.6to6)inthedeepwater,separatedverticallybysmoothhighgradientregionswithmuchlargerdensityratios.Theloweststaircasecontainsstepsthatarelaterallycoherent on the basin scale and have a well-defined vertical structure. On average, temperature steps in this staircase are 4mK, salinity steps are 2mgkg 21 , and mixed layer heights are 70cm. The CTD is capable of measuring bulk characteristics of the staircase in both temperature and salinity. Microstructure measurements are limited to temperature alone, but resolve the maximum temperature gradients in the center of selected laminar interfaces. Two different algorithms for characterizing the staircase are compared. Consistent estimates of the steady-state heat flux (27mWm 22 ) are obtained from measurements above and below the staircase,as well as from microstructure measurements in the center of smooth interfaces. Estimates obtained from bulk interface gradients underestimate the steady-state flux by nearly a factor of 2. The mean flux calculated using a standard 4/3 flux law parameterization agrees well with the independent estimates, but inconsistencies between the parameterization and the observations remain. These inconsistencies are examined by comparing the underlying scaling relationship to the measurements.

Bacteria-induced mixing in natural waters

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 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.

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

Double diffusion originates from the markedly different molecular diffusion rates of heat and salt in water, producing staircase structures under favorable conditions. The phenomenon essentially consists of two processes: molecular diffusion across sharp interfaces and convective transport in the gravitationally unstable layers. In this paper, we propose a model that is based on the one-dimensional description of these two processes only, and—by self-organization—is able to reproduce both the large-scale dynamics and the structure of individual layers, while accounting for different boundary conditions. Two parameters characterize the model, describing the time scale for the formation of unstable water parcels and the optimal spatial resolution. Theoretical relationships allow for the identification of the influence of these parameters on the layer structure and on the mass and heat fluxes. The performances of the model are tested for three different lakes (Powell, Kivu, and Nyos), showing a remarkable agreement with actual microstructure measurements.