Paul Boudreau

A two-dimensional finite element drying-wetting shallow water model for rivers and estuaries

A new finite element model has been developed to simulate two-dimensional free surface flow in rivers and estuaries. The variables of the model are the specific discharge and the water level. The algorithm takes into account the natural boundaries of the flow, defined by the contour lines of zero depth, with a new approach that accepts positive and negative values for the water depth. In this way, we consider a wet or dry area when the water depth is positive or negative respectively. A 6-node triangular element and an implicit Euler scheme are respectively used for spatial and time discretization of the mathematical model. The solution procedure is based on the inexact Newton-GMRES type solver with incomplete factorization as preconditioning. The numerical results of the proposed approach are in good agreement with an analytic solution and also with the classical approach.

NUMERICAL METHOD FOR MODELLING SPAWNING HABITAT DYNAMICS OF LANDLOCKED SALMON, SALMO SALAR

The stability of habitat conditions determined by the hydrological regime of a river can play a major part in fish spawning success. Application of the classical IFIM approach (Instream Flow Incremental Methodology) does not usually take into account this dynamic aspect of the habitat. We developed a numerical method to simulate the rate of variation in spawning habitat conditions using two-dimensional hydrodynamic modelling coupled with a fish model based on habitat suitability indices (HSI). The approach assumes that, under natural conditions, fish spawning success is maximized under the most common rates of habitat variation. This method was applied during the feasibility study phase of a Hydro-Quebec hydroelectric project on Ashuapmushuan River (St-Jean Lake region, Quebec, Canada). The aim was to evaluate the environmental impact of different exploitation regimes on the rearing and spawning habitats of the landlocked salmon (Ouananiche) of this river. Only the spawning aspect is addressed here. After the hydrodynamic model was well established on a representative reference reach of the river, two spawning areas were identified within this reach and delimited for computational purposes. The per cent usable areas (PUA) were estimated on these two zones for 36 different flow discharges representing a wide rate of the usual hydrological conditions in summer and autumn. In addition, a time series of daily rate of variation of normalized PUA (dPUA′) were obtained from a 35 year habitat time series. Finally, some relevant statistics of dPUA′ (mean and exceedance probabilities of 50, 20, 10, 5 and 2%) were obtained for the natural flow regime. They were then compared with a hypothetical peak exploitation flow pattern currently in use on a neighbouring river. According to our model, this regime would induce a 10–20-fold increase in the rate of variation compared with the most extreme natural conditions (dPUA exceeded 2% of the time). This regime was considered to obtain a contrasting image of different options that were never seriously envisaged by Hydro-Quebec for this river.

Integrated two-dimensional macrophytes-hydrodynamic modeling

Lake Saint-Francois is the first fluvial lake downstream of the Great Lakes. Aquatic macrophytes are abundant because of water level stabilization and increased nutrient loads. The influence of plants on flow modification is very important and must be considered in order to simulate hydrodynamic conditions. The spatial distribution of plant species is linked to their instream flow preferences. Several abiotic variables are of importance: light penetration, wave energy, current velocity, nutrients in substrate and physical characteristics of the substrate are controlling the species and their biomass. Field characterization of macrophytes was performed using echosounder transects in association with a submersible video camera. This technique allowed the calibration of each echofacies for species identification and their relative proportion, height and density. The main eleven assemblages appear to be strongly correlated with abiotic conditions. A basic interpretation key was set up in order to describe plant distribution over the entire lake. Species, relative proportion, density and plant height were interpolated between transects. This information is used to adjust the Mannings friction coefficient for each assemblage. Simulations of the flow fields with plants and in absence of plants show a contrasted pattern. During the summer (with plants), the flow is mainly concentrated in deep channels where velocities are clearly increased by approximately 20% compared to spring-fall simulation (without plants).

Pristine Lake Saint-François, St. Lawrence River: Hydrodynamic Simulation and Cumulative Impact

Abstract Lake Saint-Francois is a fluvial lake of the St. Lawrence system which is used for hydropower production and commercial navigation. For 150 years, it was dredged and dammed regularly without any impact analysis being made. The cumulative impact of dredging and damming on large rivers such as the St. Lawrence is an issue with only qualitative answers. Bidimensional hydrodynamics was used to simulate ancient flow conditions and to produce quantitative descriptors. Two Numerical Field Models (NFM) were prepared, one representing present state geometry, which contains 300,000 sounding points, and the other representing pristine state, based on 1900 and 1870 measurements and containing 70,000 soundings. These two NFMs were compared, showing important changes in the morphology of the lake. The NFMs were then used for bidimensional hydrodynamic simulations of both actual and pristine states for 3 different discharges: 5,000 m 3 /s, 7,500 m 3 /s, and 10,000 m 3 /s. Results highlight the cumulative physical transformation of the system. Hydrodynamic simulations and velocity differences show an increase of velocities over shoals for discharge under 8,800 m 3 /s, and a decrease of velocities in deeper water for the same range of discharge. Dredging and straightening around Cornwall Island resulted in changes from 64% to 71% of the total river flow passing through the south channel while the flow in the north channel decreased from 36% to 29%. These hydrodynamic transformations had a definitive impact on sedimentation and most probably on aquatic plant distribution.

Dynamic tracking of flow boundaries in rivers with respect to discharge

A new Eulerian approach is proposed to track the dynamic position of flow boundaries in rivers with respect to flow discharge or tides. Associated to a two dimensional (2D) transient horizontal hydrodynamic model, it allows to define the configuration of watercourses in a broad hydrological register varying from dry conditions to severe flooding. The finite element method is used to develop the numerical prediction tool. It is employed to estimate not only the classical flow variables such as water surface level and velocity field, but also the position of the shorelines. In this paper, the strategy followed for building this «drying-wetting» model consists in letting the water surface move freely, everywhere in the domain including the dry zones, allowing it to plunge under the ground. Two practical applications on rivers of Quebec (Canada) are presented. The first one deals with steady state situations on St. Marguerite River. The second one deals with the reconstitution of flood propagation on Chicoutimi River according to the extreme flooding events of July 96 in the Saguenay region.