A fully consistent and conservative vertically adaptive coordinate system for SLIM 3D v0.4, a DG finite element hydrodynamic model, with an application to the thermocline oscillations of Lake Tanganyika

Abstract

Abstract. The discontinuous Galerkin (DG) finite element method is well suited to the modelling, with a relatively small number of elements, of three-dimensional flows exhibiting strong velocity or density gradients. Its performance can be highly enhanced by having recourse to r-adaptivity. Here, a vertical adaptive mesh method is developed for DG finite elements. This method, originally designed for finite difference schemes, is based on the vertical diffusion of the mesh nodes, with the diffusivity controlled by the density jumps at the mesh element interfaces. 5The mesh vertical movement is determined by means of a conservative Arbitrary Lagrangian-Eulerian (ALE) formulation.Though conservativity is naturally achieved, tracer consistency is obtained by a suitable construction of the mesh vertical velocity field, which is defined in such a way that it is fully compatible with the tracer and continuity equations at a discrete level.The vertically adaptive mesh approach is implemented in the geophysical and environmental flow model SLIM 3D (www. 10climate.be/slim). Idealised benchmarks, aimed at simulating the oscillations of a sharp thermocline, are dealt with. Then, the relevance of the vertical adaptivity technique is assessed by simulating thermocline oscillations of Lake Tanganyika. The results are compared to measured vertical profiles of temperature, showing similar stratification and outcropping events.

Simulating Lake Tanganyika's hydrodynamics under a changing climate

“…The conclusions of this paper are based on numerical simulations, for which input data and calibration are based on other models or remote sensing. A comprehensive evaluation of the model system with in-situ measurements was already performed by Delandmeter et al (2017), and our additional validation confirms that the model can be used for climate change projections.…”

“…During the dry season, southerly winds push the surface water northwards. Together with the increase in evapotransipration, this results in a decrease in the temperature gradient along the depth in the southern parts of the lake, where the thermocline is thus very shallow or even outcrops to the surface (Delandmeter et al, 2017). The wind events follow a periodic dynamics, with a period of 3 to 4 weeks, which are close to the first free mode of oscillation of the lake, resulting in a quasi-resonance of the internal wave (Gourgue et al, 2011;Naithani et al, 2002;Naithani & Deleersnijder, 2003).…”

“…Tanganyika (Delandmeter et al, 2017). In this study, SLIM 3D is applied to Lake Tanganyika in the same setup as that of Delandmeter et al (2017).…”

“…The most recent version of SLIM 3D runs with an estimated surface heat flux for which a relaxation term in the upper layer of the lake is use as defined in Delandmeter et al (2017). With this relaxation term, the simulated heat will be held in the lake for a certain period, after which it is released back into the air.…”

“…It can thus be hypothesised that the breakdown of the stratification is better simulated by SLIM than its reconstruction. Another hypothesis can be the use of the relaxation function to represent the surface heat flux (Delandmeter et al, 2017), which includes a delay compared to changes in meteorological variables. In general, it can be concluded that SLIM 3D adds value compared to FLake (1D) for simulating the lake surface water temperature, which highlights the importance of accounting for better 3D hydrodynamics Fig.…”