Undular bottom topography as a salt intrusion mitigation measure

Undular bottom topography as a salt intrusion mitigation measure: A study on the potential of trapped internal waves to enhance vertical mixing

Wegman, Tess (TU Delft Civil Engineering and Geosciences)

Pietrzak, J.D. (mentor)
Labeur, R.J. (graduation committee)
Verlaan, M. (graduation committee)
Kranenburg, Wouter (graduation committee)

Delft University of Technology

Civil Engineering | Hydraulic Engineering

2021-01-25

Due to climate change and human interventions, saltwater intrusion is becoming a topic of increasing concern worldwide. Salt water intrudes into the Rotterdam Waterway (RWW) by an exchange flow, where the denser sea water propagates landwards at the bottom. The main competing mechanism for this stratified exchange flow is vertical mixing, which can be realised by internal wave induced shear instabilities or wave breaking. The goal of this study is to investigate whether internal waves generated over undular bottom topography in the RWW can generate additional vertical mixing. The underlying assumption is that a decrease in stratification decreases salt intrusion.   The approach to answer the main research question is a combination of an analytical and a numerical analysis. The analytical study is based on frictionless linear theory. Internal wave behaviour is further analysed with FinLab, a finite element model which includes the non-hydrostatic processes and effects of density differences. FinLab is evaluated for the application of this study by means of a validation case.  In the analytical study, linear theory is applied to obtain a relation between the bed wave parameters and average internal wave energy density E for internal waves generated over sinusoidal bottom topography in a linearly stratified fluid. The derived expression describes that the bottom topography amplitude h0 and bed wave number kT both have a positive quadratic relation with the energy. Additionally, kTkinfluences the resonance conditions.  To validate FinLab for internal wave breaking and mixing an experiment in a wave tank, according to an example from literature, is simulated. The validation case reveals a shortcoming in the turbulent mixing parameterization. However, on scales relevant for the RWW the effect of this will not have the same significance. The validation case offers a suggestion for a subgrid closure of diffusion, where density effects are taken into account.  Numerical simulations of a 2D channel stretch with sinusoidal bottom topography, a linearly stratified fluid and a linearly varying background velocity, show generation of resonant trapped internal waves for the first two resonant modes. These occurrences correspond to the highest values of kinetic energy as function of vertical velocity averaged over the bed wave domain. The vertical buoyancy flux b is downward directed during occurrences of internal waves and becomes upward directed for increasing background flow. Vertical mixing is associated with an increase in average potential energy Ep, which is 17% higher for the base case (containing bed waves) than for a similar case without bed waves. This increase is larger when bottom shear stress increases. Richardson numbers below 0.25, associated with shear instabilities and mixing, are only observed near the bed, mainly when internal waves are present. The effect of variations in bottom topography wavelength LT and amplitude h0 on internal wave energy can be explained by the analytical formulation. The effect of bed wave parameter changes on b and relative increase in Ep can be related to the effect of the changed amount of bed friction rather than the difference in wave energy.   The first resonant mode is the most energetic, however, the average energy density found for these waves is only 0.4% to 6.7% of the potential energy anomaly (PEA); the energy required to fully mix a stratified water column. In the simulations the only mechanism that could transfer internal wave energy to turbulent kinetic energy are shear instabilities near the bed. Over the full simulation, the net vertical buoyancy transport is of negligible magnitude, where Ep shows significant increases between 6% and 99% compared to similar cases without bed waves and is enhanced during the presence of internal waves.  The main discussion point is that the quantification of vertical mixing requires improvement, particularly to determine the importance of mixing by internal wave-induced shear instabilities and by bed shear. Mixing by local shear instabilities (of which the relevant scales cannot be resolved with the current grid resolution) does not have an adequate parameterization, because density effects are not included in the turbulence closure. The bed friction parameter, which greatly influences the behaviour of the system, has to be validated. Furthermore, cases where internal waves might break in practice (e.g. at banks) were not considered. Finally, the observed internal wave energy is of small magnitude, however field measurements by Pietrzak(1991) shows that turbulence production by internal waves was significant.   

Salt Intrusion
Internal waves
Turbulent mixing
Stratified flows
Estuarine circulation
FinLab

http://resolver.tudelft.nl/uuid:c7516ec1-3698-4127-af4a-096f0b3500f1

Student theses

master thesis

© 2021 Tess Wegman