Simulations of the flow in the Mahakam river–lake–delta system,Indonesia

Large rivers often present a river–lake–delta system, with a wide range of temporal and spatial scales of the flow due to the combined effects of human activities and various natural factors, e.g., river discharge, tides, climatic variability, droughts, floods. Numerical models that allow for simulating the flow in these river–lake–delta systems are essential to study them and predict their evolution under the impact of various forcings. This is because they provide information that cannot be easily measured with sufficient temporal and spatial detail. In this study, we combine one-dimensional sectional-averaged (1D) and two-dimensional depth-averaged (2D) models, in the framework of the finite element model SLIM, to simulate the flow in the Mahakam river–lake–delta system (Indonesia). The 1D model representing the Mahakam River and four tributaries is coupled to the 2D unstructured mesh model implemented on the Mahakam Delta, the adjacent Makassar Strait, and three lakes in the central part of the river catchment. Using observations of water elevation at five stations, the bottom friction for river and tributaries, lakes, delta, and adjacent coastal zone is calibrated. Next, the model is validated using another period of observations of water elevation, flow velocity, and water discharge at various stations. Several criteria are implemented to assess the quality of the simulations, and a good agreement between simulations and observations is achieved in both calibration and validation stages. Different aspects of the flow, i.e., the division of water at two bifurcations in the delta, the effects of the lakes on the flow in the lower part of the system, the area of tidal propagation, are also quantified and discussed.     

On the behaviour of the residence time at the bottom of the mixed layer

To understand why the findings of Deleersnijder et al. [(2006), Environ Fluid Mech 6: 25–42]—the residence time in the mixed layer in not necessarily zero at the pycnocline—are consistent with those of Delhez and Deleersnijder [(2006), Ocean Dyn 56:139–150]—the residence time in a control domain vanishes at the open boundaries of this control domain—, it is necessary to consider a control domain that includes part of the pycnocline, in which the eddy diffusivity is assumed to be zero. Then, depending on the behaviour of the eddy diffusivity near the bottom of the mixed layer, the residence time may be seen to exhibit a discontinuity at the interface between the mixed layer and the pycnocline. If such a discontinuity exists, the residence time is non-zero in the former and zero in the latter. This is illustrated by analytical solutions obtained under the assumption that the eddy diffusivity is constant in the mixed layer.     

Assessing the parameterisation of the settling flux in a depth-integrated model of the fate of decaying and sinking particles, with application to fecal bacteria in the Scheldt Estuary

The fate of reactive tracers is often modelled by depth-averaged equations. When integrating the depth-resolved equations, it appears that the term describing the settling of particles is dependent on the concentration just above the bottom. Because in a depth-averaged framework this quantity is not available, the settling term needs to be parameterised. The most natural choice is to make the settling flux dependent on the average concentration. This approximation is acceptable if the water column is well mixed, but these conditions are not necessarily met in real applications. Therefore, this study aims at assessing and understanding the error made by using a depth-averaged model in a range of realistic conditions. For the definition of these conditions, typical values for the Scheldt Estuary and the Dutch-Belgian coast were taken. The realistic inspiration for the reactive tracer in this study is the fecal bacterium Escherichia coli, whose own dynamics are characterised by settling and gradual decay by mortality. In an attempt to understand the relative importance of several factors like settling, mortality, mixing and stratification on the error made by a depth-averaged approach, a number of simplified test cases were investigated. It follows that, as expected, the error is acceptable if the situation is mixing-dominated. However, the effect of mortality and stratification was less obvious in advance. For instance, it appeared that errors can also be significant if settling and mortality have the same characteristic timescales. Stratification often has the effect to increase the error made by the depth-averaged model.     

An implicit wetting–drying algorithm for the discontinuous Galerkin method: application to the Tonle Sap,Mekong River Basin

Environmental Fluid Mechanics - The accurate simulation of wetting–drying processes in floodplains and coastal zones is a challenge for hydrodynamic modelling, especially for long time...     

The Residence Time of Settling Particles in the Surface Mixed Layer

The transport from the upper mixed layer into the pycnocline of particles with negative buoyancy is considered. Assuming the hydrodynamic parameters to be time- independent, an adjoint model is resorted to that provides a general expression of the residence time in the mixed layer of the constituent under study. It is seen that the residence time decreases as the settling velocity increases or the diffusivity decreases. Furthermore, it is demonstrated that the residence time must be larger than z/w and smaller than h/w, where z, h and w denote the distance to the pycnocline, the thickness of the mixed layer and the sinking velocity. In the vicinity of the pycnocline, the residence time is not necessarily zero; its behaviour critically depends on the eddy diffusivity profile in this region. Closed-form solutions are obtained for constant and quadratic diffusivity profiles, which allows for an analysis of the sensitivity of the residence time to the Peclet number. Finally, an approximate value is suggested of the depth-averaged value of the residence time.     

Analysis of Wind-Induced Thermocline Oscillations of Lake Tanganyika

An analysis is presented of the wind-induced thermocline oscillations of Lake Tanganyika, East Africa. The region undergoes a four month dry season and the wet season for the rest of the year. The dry season is characterised by nearly constant high southeasterly winds, while for the rest of the year mild wind blows generally from the northeast. Observations show that the dry season high winds cause tilting of the thermocline, being higher/lower than normal at the southern/northern ends of the lake. The thermocline tries to restabilise itself after the cessation of dry season winds and oscillates for the rest of the year. A non-linear reduced-gravity model is used to study the thermocline oscillations of the lake. The numerical simulations satisfactorily represent the oscillations, their period and amplitude. Different forcing conditions (thermocline depth, wind stress and stability) are used in the model and their effect on the period and amplitude of the oscillations are studied. The amplitude of oscillations ranges from 15 to 45 m, while their period varies from 3 to 4 weeks according to the variation in the model parameters. Wavelet transform is used to study the evolution of periods of oscillations with depth in the time series of observations and along the length of the lake using model simulations. Wavelet spectra presents several dominant modes including the semidiurnal, diurnal, synoptic, intraseasonal variability, besides the modes representing the wind-induced thermocline oscillations.