ALBERT

Description: Do tidal channels have a characteristic length? Given the sediment characteristics, the inlet conditions and the degree of channel convergence, can we predict it? And how is this length affected by the presence of tidal flats adjacent to the channel? We answer the above questions on the basis of a fully analytical treatment, appropriate for the short channels typically observed in coastal wetlands. The equilibrium length of non-convergent tidal channels is found to be proportional to the critical flow speed for channel erosion. Channel convergence causes concavity of the bed profile. Tidal flats shorten equilibrium channels significantly. Laboratory and field observations substantiate our findings. © 2009 Cambridge University Press.

Description: We study the occurrence of the multiple steady states that flows in a collapsible tube can develop under the effect of: (i) geometrical alterations (e.g. stenosis), (ii) variations of the mechanical properties of the tube wall, or (iii) variations of the external pressure acting on the conduit. Specifically, if the approaching flow is supercritical, two steady flow states are possible in a restricted region of the parameter space: one of these flow states is wholly supercritical while the other produces an elastic jump that is located upstream of the variation. In the latter case the flow undergoes a transition through critical conditions in the modified segment of the conduit. Both states being possible, the actual state is determined by the past history of the system, and the parameter values show a hysteretic behaviour when shifting from one state to the other. First we set up the problem in a theoretical framework assuming stationary conditions, and then we analyse the dynamics numerically in a one-dimensional framework. Theoretical considerations suggest that the existence of multiple states is associated with non-uniqueness of the steady-state solution, which is confirmed by numerical simulations of the fully unsteady problem. © 2014 Cambridge University Press.

Description: We study the conditions under which discontinuous mechanical properties of a collapsible tube can induce transcritical flows, i.e. the transition through the critical state where the speed index (analogous to the Mach or the Froude numbers for compressible and free surface flows, respectively) is one. Such a critical transition may strongly modify the flow properties, cause a significant reduction in the crosssectional area of the tube, and limit the flow. General relationships are obtained for a short segment using a one-dimensional model under steady flow conditions. Marginal curves delimiting the transcritical regions are identified in terms of the speed index and the cross-sectional area ratio. Since there are many examples of such flows in physiology and medicine, we also analyse the specific case of prosthesis (graft or stent) implantation in blood vessels. We then compute transcritical conditions for the case of stiffness and reference area variations, considering a collapsible tube characterized by physiological parameters representative of both arteries and veins. The results suggest that variations in mechanical properties may induce transcritical flow in veins but is unrealistic in arteries. © Cambridge University Press 2013.

Description: We present a new equation describing the hydrodynamics in infinitely long tidal channels (i.e., no reflection) under the influence of oceanic forcing. The proposed equation is a simple relationship between partial derivatives of water level and velocity. It is formally derived for a progressive wave in a frictionless, prismatic, tidal channel with a horizontal bed. Assessment of a large number of numerical simulations, where an open boundary condition is posed at a certain distance landward, suggests that it can also be considered accurate in the more natural case of converging estuaries with nonlinear friction and a bed slope. The equation follows from the open boundary condition and is therefore a part of the problem formulation for an infinite tidal channel. This finding provides a practical tool for evaluating tidal wave dynamics, by reconstructing the temporal variation of the velocity based on local observations of the water level, providing a fully local open boundary condition and allowing for local friction calibration.

Description: Water temperature in lakes is governed by a complex heat budget, where the estimation of the single fluxes requires the use of several hydro-meteorological variables that are not generally available. In order to address this issue, we developed Air2Water, a simple physically based model to relate the temperature of the lake superficial layer (epilimnion) to air temperature only. The model has the form of an ordinary differential equation that accounts for the overall heat exchanges with the atmosphere and the deeper layer of the lake (hypolimnion) by means of simplified relationships, which contain a few parameters (from four to eight in the different proposed formulations) to be calibrated with the combined use of air and water temperature measurements. The calibration of the parameters in a given case study allows for one to estimate, in a synthetic way, the influence of the main processes controlling the lake thermal dynamics, and to recognize the atmospheric temperature as the main factor driving the evolution of the system. In fact, under certain hypotheses the air temperature variation implicitly contains proper information about the other major processes involved, and hence in our approach is considered as the only input variable of the model. In particular, the model is suitable to be applied over long timescales (from monthly to interannual), and can be easily used to predict the response of a lake to climate change, since projected air temperatures are usually available by large-scale global circulation models. In this paper, the model is applied to Lake Superior (USA–Canada) considering a 27 yr record of measurements, among which 18 yr are used for calibration and the remaining 9 yr for model validation. The calibration of the model is obtained by using the generalized likelihood uncertainty estimation (GLUE) methodology, which also allows for a sensitivity analysis of the parameters. The results show remarkable agreement with measurements over the entire data period. The use of air temperature reconstructed by satellite imagery is also discussed.

Description: The effect of river discharge on tidal damping in estuaries is explored within one consistent theoretical framework where analytical solutions are obtained by solving four implicit equations, i.e. the phase lag, the scaling, the damping and the celerity equation. In this approach the damping equation is obtained by subtracting the envelope curves of high water and low water occurrence, taking into account that the flow velocity consists of a tidal and river discharge component. Different approximations of the friction term are considered in deriving the damping equation, resulting in as many analytical solutions. In this framework it is possible to show that river discharge affects tidal damping primarily through the friction term. It appears that the residual slope, due to nonlinear friction, can have a substantial influence on tidal wave propagation when including the effect of river discharge. An iterative analytical method is proposed to include this effect, which significantly improved model performance in the upper reaches of an estuary. The application to the Modaomen and Yangtze estuaries demonstrates that the proposed analytical model is able to describe the main tidal dynamics with realistic roughness values in the upper part of the estuary where the ratio of river flow to tidal flow amplitude is substantial, while a model with negligible river discharge can be made to fit observations only with unrealistically high roughness values.

Description: The effect of river discharge on tidal damping in estuaries is explored within one consistent theoretical framework where analytical solutions are obtained by solving four implicit equations, i.e., the phase lag, the scaling, the damping and the celerity equation. In this approach the damping equation is obtained by subtracting the envelope curves of high water and low water occurrence, taking into account that the flow velocity consists of a tidal and river discharge component. Different approximations of the friction term are considered in deriving the damping equation, resulting in as many analytical solutions. In this framework it is possible to show that river discharge affects tidal damping primarily through the friction term. The application to the Modaomen and Yangtze estuaries demonstrates that the influence of river discharge on tidal damping can be significant in the upstream part of an estuary where the ratio of river flow to tidal flow amplitude is substantial. The analytical model is able to describe the main tidal dynamics with realistic roughness values in the upper part of the estuary, while a model with negligible river discharge can be made to fit observations only with unrealistically high roughness values. Moreover, the damping equation can be used to estimate river discharge on the basis of observed tidal damping, which makes the proposed analytical model a tool to obtain indirect information about quantities that are difficult to measure in the tidal region.

Description: Water temperature in lakes is governed by a complex heat budget, where the single fluxes are hardly assessable over long time periods in the absence of high accuracy data. In order to address this issue, we developed Air2Water, a simple physically-based model to relate the temperature of the lake superficial layer (epilimnion) to air temperature only. The model accounts for the overall heat exchanges with the atmosphere and the deeper layer of the lake (hypolimnion) by means of simplified relationships, which contain a few parameters (from four to eight in the different proposed formulations) to be calibrated with the combined use of air and water temperature measurements. In particular, the calibration of the parameters in a given case study allows one to estimate, in a synthetic way, the influence of the main processes controlling the lake thermal dynamics, and to recognize the atmospheric temperature as the main factor driving the evolution of the system. In fact, the air temperature variation implicitly contains proper information about the variation of other major processes, and hence in our approach is considered as the only input variable of the model. Furthermore, the model can be easily used to predict the response of a lake to climate change, since projected air temperatures are usually available by large-scale global circulation models. In this paper, the model is applied to Lake Superior (USA – Canada) considering a 27-yr record of measurements, among which 18 yr used for calibration and the remaining 9 yr for model validation. The results show a remarkable agreement with measurements, over the entire data period. The use of air temperature reconstructed by satellite imagery is also discussed.