Development of overturning circulation in sloping waterbodies due to surface cooling

Damien Bouffard, Tomy Doda, Cintia Luz Ramon Casanas, Hugo Nicolás Ulloa Sánchez, Alfred Johny Wüest
CAMBRIDGE UNIV PRESS, 2021
Article

Résumé

Cooling the surface of freshwater bodies, whose temperatures are above the temperature of maximum density, can generate differential cooling between shallow and deep regions. When surface cooling occurs over a long enough period, the thermally induced cross-shore pressure gradient may drive an overturning circulation, a phenomenon called 'thermal siphon'. However, the conditions under which this process begins are not yet fully characterised. Here, we examine the development of thermal siphons driven by a uniform loss of heat at the air-water interface in sloping, stratified basins. For a two-dimensional framework, we derive theoretical time and velocity scales associated with the transition from Rayleigh-Benard type convection to a horizontal overturning circulation across the shallower sloping basin. This transition is characterised by a three-way horizontal momentum balance, in which the cross-shore pressure gradient balances the inertial terms before reaching a quasi-steady regime. We performed numerical and field experiments to test and show the robustness of the analytical scaling, describe the convective regimes and quantify the cross-shore transport induced by thermal siphons. Our results are relevant for understanding the nearshore fluid dynamics induced by nighttime or seasonal surface cooling in lakes and reservoirs.

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https://infoscience.epfl.ch/record/290537?ln=fr

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Damien Bouffard, Tomy Doda, Cintia Luz Ramon Casanas, Hugo Nicolás Ulloa Sánchez, Alfred Johny Wüest
CAMBRIDGE UNIV PRESS, 2021
Article

Résumé

Official source

https://infoscience.epfl.ch/record/290537?ln=fr

À propos de ce résultat

Concepts associés (14)

Concepts associés

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Publications associées (4)

Publications associées

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High velocity aerated flow on stepped chutes with macro-roughness elements

Stéphanie Joëlle André

Uncontrolled overtopping during flood events can endanger embankment dams. Erosion of the downstream slope and scouring of its base caused by the high velocity and energy of the overflow can indeed lead to breach formation until complete failure. In this context and faced with the important number of overtopped embankment dams to be rehabilitated, since the early eighties, researchers have investigated surface protection solutions for downstream slope. Overlays against erosion such as seeded goetextile or cable-tied cellular concrete blocks, are not sufficient. In fact, they can resist only short events with low discharge and velocity. Solution to overcome more severe overflow lies in overlays which dissipate flow energy along the downstream embankment slope. Conventional steps resulting from Roller Compacted Concrete (RCC) techniques fulfill efficiently this challenge. However, flows over steep stepped chutes are quite complex, characterizing by great aeration, high turbulence and confused wavy free surface. Then, most of hydraulic studies of such flows are performed on physical model. Yet, understanding and definition of flow behaviour and accurate approach to estimate energy dissipation are still lacking. General guidelines of hydraulics of aerated flows over stepped macro-roughness chutes and for optimal design of protection overlay remain confusing. To contribute to reduce these uncertainties, experimental study of flow over stepped chutes equipped with macro-roughness elements is performed in a laboratory gated flume for mild (~ 1:7H : 1V ) and weak (~ 3H : 1V ) chutes. Thus, they are representative of the range of embankment dams and spillways slopes. Three types of stepped macro-roughness overlays are assessed, namely rectangular conventional steps, steps equipped with endsills fixed on their nose over all the flume width and steps equipped with rectangular spaced blocks. Endsills overlays were characterized with different longitudinal distributions whereas blocks overlays consisted in different transverse patterns. Tests were conducted for the three nappe, transition and skimming flow regimes. Results can be extrapolated to 1/5 to 1/15 scaled prototypes using the Froude similarity with negligible scale effects. Flow depth, local air concentration and longitudinal velocities are measured with a double fiber-optical probe. Pressures at macro-roughness faces are taken with piezo-resistive sensors. Sequent depths of the hydraulic jump forced in the stilling basin at the flume base are measured with ultrasound sensors. Thus, this experimental phase of the thesis has allowed: to define flow parameters (regimes, depths, velocity and air concentration distributions, hydrodynamic forces) for tested overlays, to highlight that air-water flow depth is divided into: a rough boundary layer influenced by shear stress and by drag form (macro-turbulence) caused by macro-roughness, a homogeneous aerated layer which represents the main portion of flow involved in energy dissipation mechanism, a free surface layer which must be considered in the side walls design, to stress that energy dissipation is mainly a question of drag losses, to validate indirect method of hydraulic jump for energy dissipation estimation, to estimate relative energy loss for several stepped macro-roughness overlays. Tests finally show that an optimal alternative to dissipate the overflow energy during an overtopping event consists in spaced blocks, with transverse space larger than the width of block and fixed alternately on conventional steps. However, experimental results remain related and limited to their tested domains. Then, in order to provide more general governing equations of aerated flows over macro-roughness stepped chutes, a numerical modeling of two phase flows over conventional stepped flume was performed in collaboration with the Laboratory of Applied Hydrodynamics and Hydraulic Constructions at University of Liège. A quasi-2D numerical model based on the finite volume method was developed. It consists in applying the classical depth-averaged simplified Navier-Stokes equations (viscosity and Coriolis terms neglected) to a 1D incompressible air-water mixture flow over mild and steep slopes with a stepped topography. Self-aeration process is modeled by a transport equation of depth-averaged air concentration whereas turbulent structures are indirectly implemented through the Boussinesq coefficient. This first 1D-approach of semi-theoretical description of aerated flow over steps is tested for a 30o gated stepped flume and a 52° crested spillway laboratory model. This numerical model leads to realistic results regarding mixture depth, mean flow velocity, air concentration and wave amplitudes of the flow free surface. Finally, on the basis of existing protections of embankment dams and previous studies, the present experimental and numerical results contribute to extend the knowledge of high velocity aerated flows over macro-roughness and to provide elements of guidelines to optimize stepped macro-roughness overlays for embankment dams safety.

EPFL2004

Chargement

Soil moisture is crucial to water-cycle as it affects infiltration, runoff and land-atmosphere interactions. In dry soils the role of water vapor fluxes becomes essential and causes a tight coupling between soil moisture dynamics and heat transfer, which makes measurements and modeling extremely difficult. Since advances in both theory and experimental techniques are required, we have focused on both aspects: we have performed theoretical-numerical investigations of soil moisture and energy dynamics at the land surface; tested novel measurements techniques, in laboratory and at field scale, to provide new insights into soil moisture dynamics and contribute to a comprehensive theory of coupled energy and moisture transport. As the dynamics of physical systems are dictated by conservation equations, it is common practice to estimate quantities that cannot be directly measured (e.g. vapor fluxes) from the residuals of balance equations. In laboratory as well as in field experiments, residuals are calculated from measurements that are sparse in space and discrete in time. We have theoretically and numerically shown how the use of discrete data may lead to large residuals even without measurements or model errors. We have demonstrated that residuals are very sensitive to the distance between the measurements and that they increase in presence of nonlinear processes, such as moisture transport. A careful error analysis is required to assess the reliability of residuals computed from discrete data and avoid misinterpretations of the underlying physical processes. Another crucial element dictating soil moisture dynamics and evaporation into the atmosphere is soil water-retention. Popular parametric models of the retention curve present a matric potential that becomes infinite at residual saturation, which is the water content below which liquid flow stops. Few extensions of the water-retention curves have been proposed, which remain rarely used in practice. We have studied the effects of different models on liquid and vapor transport. We have shown that parameterizations that allow vapor flux below residual saturation yield larger vapor fluxes that result in a drier soil surface, whereas deep soil remains relatively wet. When diurnal forcing is considered, potential evaporation is reduced in the energy-limited regime and enhanced in the moisture-limited regime. We have established that in this case extended water-retention models predict larger heat fluxes that might critically impact models at whole scales (possibly including global circulation models). Discrimination between different theoretical descriptions and parametric models requires experiments that monitor moisture and energy dynamics. This demands the use of accurate sensors and measurement techniques that are able to simultaneously monitor several quantities (e.g. soil moisture, temperature, soil thermal properties, solute concentration in soil water). As in general different probes are used, problems arise due to different footprints and sampled soil volumes. Multi functional heat pulse probes (MFHPPs) have been conceived to overcome these issues by allowing simultaneous measurements of all required variables. We have assessed MFHPPs ability to measure ground heat flux, which has to be accurately known to avoid significant imbalances in the surface energy budget. We have employed an experimental setup able to generate a non-uniform heat-flux field and we have demonstrated that MFHPPs can reliably capture the magnitudes and directions of the fluxes. This allows more complete information on ground heat flux than that obtained by the classic probes (e.g. ground heat flux plates). To monitor soil state in large-scale field applications we have investigated the possibility to infer distributed thermal conductivity and soil moisture profiles with an optical fiber. Information is obtained by monitoring soil response to an active heat pulse generated from the metal shield armoring the optic cable, and analyzing the temperature differences of the cooling phase, monitored each meter by a distributed temperature sensing system (DTS). We have shown that soil moisture measurements inferred from soil thermal response (recorded by the DTS) are in good agreement with independent measurements in wet and intermediately wet soils; however in dry soils moisture content is underestimated and further investigations are required to improve this technique for dry conditions. In this study we have significantly improved the knowledge of coupled energy and moisture transport on both theoretical-numerical and experimental sides. We have proven that reliable measurements can be obtained at different spatiotemporal scales, and provided both prognostic and diagnostic methods to optimize their use. Finally, we have suggested crucial improvements to numerical models which might have implications beyond field-soils dynamics.

EPFL2013

Chargement

Differential cooling and near-shore dynamics in a large lake (Lake Geneva)

Ulrich Lemmin, Rafael Sebastian Reiss

Density currents generated by differential cooling in lakes with shallow shore regions or side basins are associated with increased vertical mixing, deep water renewal and cross-shore transport of nutrients and other substances. Previous field experiments in Lake Geneva, the largest lake in Western Europe, showed that such cold-water density currents are a common phenomenon during winter, frequently reaching the thermocline at O(100 m) depth. As part of a project investigating large-scale interbasin exchange in Lake Geneva, we examined near-shore wintertime density currents in order to better understand cold-water formation. The study is based on field observations taken on the northern shore of Lake Geneva near Buchillon, 20 km west of Lausanne, in the winters of 2016-2018. Bottom temperatures are inferred from a fiber-optic Distributed Temperature Sensing (DTS) system, laid down on the lateral slope starting at the shore, with a spatial and temporal resolution of O(1 m) and O(0.1°C), respectively. Temperature and current velocities in the water column were recorded by ADCP and thermistor chain moorings. The time-series data are complemented by several CTD profiles taken along transects normal to the shoreline near the moorings. Data from a nearby meteorological mast were used to select calm days favoring convective cooling. Earlier studies focused on the steady-state dynamics along one transect. Our goal is to investigate the generation of density currents and the effect of different shore geometries. During periods of surface heat loss, i.e., positive surface buoyancy flux B0, DTS bottom temperatures show cold fronts progressing downslope with the coldest temperatures in the near-shore part, illustrating differential cooling. However, our observations indicate that even during periods with low wind and strong cooling, currents on the shallow shelf have a dominant alongshore component. This suggests that local wind stress and possibly the large-scale circulation might have to be taken into account when investigating nearshore cold-water formation and cooling dynamics in Lake Geneva. The wide and narrow parts of the shelf show significantly different responses to surface cooling. Starting with similar temperatures the wide shelf cooled down by 0.5°C whereas only minor temperature fluctuations were observed at the narrow shelf. At the wide shelf a cold bottom layer of up to 10-m thickness was visible in the CTD transect until the thermocline at 100-m depth. To further elucidate the effect of the shallow shelf width on the generation of cold-water density currents as well as the contribution of both surface heat loss and wind stress a numerical modeling study is planned.

2018

Chargement

High velocity aerated flow on stepped chutes with macro-roughness elements

Stéphanie Joëlle André

EPFL2004

Differential cooling and near-shore dynamics in a large lake (Lake Geneva)

Ulrich Lemmin, Rafael Sebastian Reiss

2018

EPFL2013