A hydrodynamical perspective on the turbulent transport of bacteria in rivers

The transport of bacteria in river systems is a phenomenon which occurs on a multitude of length scales
ranging from the size of individual microbes up to the size of an entire estuary.
At the same time the understanding of the spreading of microbial populations after a localised contamination
event such as a combined sewer overflow is crucial for the prediction of the water quality downstream of
the source, which is in turn essential to managing public health.
It is well-established that microbial populations in fluvial systems may preferably be found on the surface
of small particles rather than solely freely suspended in the water body. The attachment to particles
provides an environment beneficial to the survival of bacteria due to the improved access to nutrients and
the shielding from environmental stressors, but also alters their dispersion characteristics as the transport of
bacteria is then coupled to the trajectories of heavy particles.

The importance in the distinction between the particle-attached and the freely-suspended mode of transport
has been recognised in the mechanistic modelling of bacteria fate and transport. ... mehrHowever, due to the multiscale
nature of the problem, the mechanisms which govern the transport of particles in river-like flows are
never resolved explicitly, and hence, the models profoundly rely upon the availability of accurate descriptions thereof.
The associated problem of particles settling in a turbulent carrier flow is an active topic of research by itself,
and is rich in emerging phenomena such as the emergence of spatial inhomogeneities or non-trivial modifications of the
settling characteristics compared to quiescent environments.
In particular, the transient settling of particles in horizontal open channels, which serves as an abstraction of particle-attached
bacteria transport in rivers, has hitherto received only little attention in the literature.
As a consequence, the knowledge on the impact of its defining features such as boundedness, anisotropy and vertical inhomogeneity
on the settling characteristics is limited and needs to be addressed to enable the formulation of reliable models thereof.

The aim of this thesis is to fill the knowledge gap on the transport characteristics of heavy particles in turbulent horizontal
open channel flows, and to identify phenomena which may be of importance in the context of bacteria transport modelling.
For this purpose, the incompressible Navier--Stokes equations and the momentum balance equations for dispersed particles
are solved using direct numerical simulations and the immersed boundary method. This approach resolves all relevant scales
of turbulence and the microscopic flow around each particle explicitly, and thus, describes the particle-fluid interaction from
fundamental principles of physics without the need of additional modelling.
Apart from the contaminated particles, which are introduced near the free surface of the flow, the simulation domain includes
approximately 100,000 fully resolved particles at the bottom of the domain, which form a realistic sediment bed, and enable the
examination of the interaction between contaminated particles and mobile sediments.

Concerning the parameter space, the value of the friction Reynolds number is varied within the range $Re_{\tau} \in [241,838]$,
while the contaminant parameter space is chosen such that the resulting relative turbulence intensities---defined as the ratio
between the friction velocity and the undisturbed terminal velocity---lie within the range $I_{\tau} \in [0.47,2.88]$.
Moreover, two types of sediment bedforms are investigated in order to assess their effect on contaminant transport, namely
a macroscopically flat bed and a bed featuring ripples.

The analysis of the simulation data shows that the settling velocity of the contaminant particles is enhanced in the ensemble-averaged
sense, yet, the time from beginning of the settling until the initial deposition is prolonged when compared to the ratio between
the channel height and the terminal velocity. The enhancement is demonstrated to be a result of the preferential sampling of turbulent sweep
events, which also implies that the streamwise component of the particle velocity is increased compared to the mean fluid
velocity at the same position. A closer examination of the spatial organisation of contaminated particles reveals that
they tend to accumulate in large-scale high-speed velocity streaks in the outer region of turbulence.
Due to this focusing mechanism, the mean-squared lateral displacement of the settling particles stagnates in the lower half of the
channel such that contaminants are not further dispersed in cross-stream direction until shortly before deposition.
The same behaviour could be reproduced using a time-invariant exact coherent flow state resembling a hairpin vortex as a proxy
for turbulence, and an extended parameter sweep in this setup suggests that this transport barrier effect persists even at
high relative turbulence intensities. It is speculated that this phenomenon might confine contaminated particles to a
region close to the river bank over a considerable downstream distance in the aftermath of a combined sewer overflow event,
which might seriously impact decisions regarding public health measures.

Near the sediment bed, the barrier effect of the large-scale motions is inactive and contaminants are found to disperse laterally
at a rate which presumably depends on the Shields parameter. The interaction between the sediment and the contaminants is
distinct for the two bed topologies under investigation. In the case of macroscopically flat beds, the contaminated particles
are transported towards sediment ridges which are in turn known to be a result of the action of large-scale fluid motions, and
the mixing of contaminants and sediment particles is restricted to the thin layer of sediment near the interface.
In contrast, the presence of ripples leads to a capturing effect where contaminated particles are preferentially deposited
in the trough of the ripple, and subsequently buried by a thick layer of sediment due to the propagation of the bed feature.
This mechanism temporarily immobilises a large share of all contaminated particles until the displacement of the ripple has
sufficiently progressed for them to be eroded on the windward side. During the immobilisation, the associated bacteria
are shielded from solar radiation to a substantial degree, which likely has a significant impact on their inactivation,
especially in shallow waters.
Moreover, the cyclic nature of this phenomenon may provide one of many explanations for bacteria storages which are known to
exist in river sediments and may cause bursts in fecal bacteria indicator levels even in absence of immediate
contamination events.

It is concluded that direct numerical simulation can be a valuable tool for the analysis of bacteria transport,
and recommendations are made on how the conjectures compiled in this thesis can be targeted in laboratory experiments
to examine their relevance.