Julie D. Pietrzak

Wind and waves in extreme hurricanes

Waves breaking at the ocean surface are important to the dynamical, chemical and biological processes at the air-sea interface. The traditional view is that the white capping and aero-dynamical surface roughness increase with wind speed up to a limiting value. This view is fundamental to hurricane forecasting and climate research but it has never been verified at extreme winds. Here we show with observations that at high wind speeds white caps remain constant and at still higher wind speeds are joined, and increasingly dominated, by streaks of foam and spray. At surface wind speeds of ?40 m/s the streaks merge into a white out, the roughness begins to decrease and a high-velocity surface jet begins to develop. The roughness reduces to virtually zero by ?80 m/s wind speed, rendering the surface aero-dynamically extremely smooth in the most intense part of extreme (or major) hurricanes (wind speed > 50 m/s). A preliminary assessment shows that cross swell, dominant in large regions of hurricanes, allows the roughness under high wind conditions to increase considerably before it reduces to the same low values.

A three-dimensional hydrostatic model for coastal and ocean modelling using a generalised topography following co-ordinate system

Abstract A three-dimensional hydrostatic model is presented that combines a generalised vertical co-ordinate system with an efficient implicit solution technique for the free surface. The model is capable of maintaining high resolution in the surface and/or bottom boundary layers as well as dealing with steep topography. Horizontal diffusion is calculated using the Smagorinsky formulation and a k–e turbulence model is used in the vertical. In addition the model uses higher-order advection routines. An important aspect in three-dimensional models is the choice of vertical discretisation. If one is mostly interested in problems which are governed by boundary layer flows, a terrain following or sigma co-ordinate system seems attractive. This paper focuses on the development of a generalised sigma-type grid in a three-dimensional hydrostatic model. The generalised grid offers a wide range of possibilities including grid refinement toward the bed or surface, a mixed layer transformation, and a constant layer transformation where the lowermost or uppermost grid cells can be specified to have a constant height above the bed or below the surface. A number of tests are presented which show that the model is capable of simulating both shallow nearshore, estuarine flows as well as large-scale geophysical flows. These include an extreme flooding event in the shallow North Sea and the Odden ice tongue formation in the Greenland Sea.

On the pressure gradient error in sigma coordinate ocean models: A comparison with a laboratory experiment

Boundary-fitted vertical coordinates are frequently used in three-dimensional primitive equation models. The sigma coordinate transformation, in which the water column is divided into a number of layers independently of the water depth, is commonly used. Unfortunately, it is well known that this transformation can produce an error in the calculation of the pressure gradient terms. The error can be significant in regions with steep topography and large density gradients. The importance of this error in simulations of coastal currents is difficult to test in reality. The competing effects of the models dynamics, its sensitivity, for example, to the chosen grid resolution or numerical techniques, are hard to separate. In the following we first identify the pressure gradient error and assess its magnitude in relation to two analytical reference solutions. A number of commonly used techniques to reduce the error are compared. Of these techniques, z-level based pressure gradient calculations are shown to improve the simulation results. We then take a step in the direction of a more realistic simulation and use a laboratory experiment as our reference solution. The results demonstrate that a sigma coordinate model can be used in a region such as the Skagerrak where steep topography and large density gradients are present. Errors do exist which need to be taken into account when interpreting the model results. This is important, as the Skagerrak dominates the North Sea and Baltic Sea system, and models that run with a coarse grid resolution may lead to artificial flows.

The Effects of the Internal Flow Structure on SPM Entrapment in the Rotterdam Waterway

Field measurements are presented, which are the first to quantify the processes influencing the entrapment of suspended particulate matter (SPM) at the limit of saltwater intrusion in the Rotterdam Waterway. The estuarine turbidity maximum (ETM) is shown to be maintained by the trapping of fluvial SPM at the head of the salt wedge. The trapping process is associated with the raining out of fluvial SPM from the upper, fresher part of the water column, into the layer below the pycnocline. The dominant mechanisms responsible are baroclinic shear flows and the abrupt change in turbulent mixing characteristics due to damping of turbulence at the pycnocline. This view contrasts with the assumption of landward transport of marine SPM by asymmetries in bed stress. The SPM transport capacity of the tidal flow is not fully utilized in the ETM, and the ETM is independent of a bed-based supply of mud. This is explained by regular exchange of part of the ETM with harbor basins, which act as efficient sinks, and that the Rotterdam Waterway is not a complete fluvial SPM trap. The supply of SPM by the freshwater discharge ensures that the ETM is maintained over time. Hence, theETMis an advective phenomenon. Relative motion between SPM and saltwater occurs because of lags introduced by resuspension. Moreover,SPM that lags behind the salt wedge after high water slack (HWS) is eventually recollected at the head. Hence, SPM follows complex transport pathways and the mechanisms involved in trapping and transport of SPM are inherently three-dimensional.

Advection of the Salt Wedge and Evolution of the Internal Flow Structure in the Rotterdam Waterway

An analysis of field measurements recorded over a tidal cycle in the Rotterdam Waterway is presented. These measurements are the first to elucidate the processes influencing the along-channel current structure and the excursion of the salt wedge in this estuary. The salt wedge structure remained stable throughout the measuring period. The velocity measurements indicate decoupling effects between the layers and that bed-generated turbulence is confined below the pycnocline. The barotropic M4 overtide structure is imposed at the mouth of the estuary, and the generation of M4 overtides within the estuary is found to be relatively small. Internal tidal asymmetry does not make a significant contribution to the M4 velocity frequency band. Instead, the combination of barotropic and baroclinic forcing, in conjunction with the suppression of turbulence at the interface, provides the main explanation for the time dependence and mean structure of the flow in the Rotterdam Waterway. This gives rise to the observed differences in the length of the flood and ebb, in the magnitudes of the flood and ebb velocities, in the length of the slack water periods, and in the timing of the onset of slack water at the surface and near the bed. It results in the formation of distinct exchange flow profiles at the head of the salt wedge around slack water and the creation of maximal velocities at the pycnocline during flood. Advection governs the displacement and structure of the salt wedge since turbulent mixing is suppressed. The tidal displacement of the salt wedge controls the height of the pycnocline above the bed at a particular site. Hence, it controls the height to which bed-generated turbulence can protrude into the water column. Consequently, the authors find asymmetries in the structure of the internal flow, turbulent mixing, and bed stresses that are not related to classical internal tidal asymmetry.

The impact of storms and stratification on sediment transport in the Rhine region of freshwater influence

We present measurements of along and across-shore sediment transport in a region of the Dutch coast 10 km north of the Rhine River mouth. This section of the coast is characterized by strong vertical density stratification because it is within the midfield region of the Rhine region of freshwater influence, where processes typical of the far-field, such as tidal straining, are modified by the passage of distinct freshwater lenses at the surface. The experiment captured two storms, and a wide range of wind, wave, tidal and stratification conditions. We focus primarily on the mechanisms leading to cross-shore sediment flux at a mooring location in 12 m of water, which are responsible for the exchange of sediment between the nearshore and the inner shelf. Net transport during storms was directed offshore and influenced by cross-shelf winds, while net transport during spring tides was determined by the mean state of stratification. Tidal straining dominated during neap tides; however, cross-shore transport was negligible due to small sediment concentrations. The passage of freshwater lenses manifested as strong pulses of offshore transport primarily during spring tides. We observe that both barotropic and baroclinic processes are relevant for cross-shore transport at depth and, since transport rates due to these competing processes were similar, the net transport direction will be determined by the frequency and sequencing of these modes of transport. Based on our observations, we find that wind and wave-driven transport during storms tends move fine sediment offshore, while calmer, more stratified conditions move it back onshore.

Cross‐shore transport of nearshore sediment by river plume frontal pumping

We present a new mechanism for cross-shore transport of fine sediment from the nearshore to the inner shelf resulting from the onshore propagation of river plume fronts. Onshore frontal propagation is observed in moorings and radar images, which show that fronts penetrate onshore through the nearshore and surf zone, almost to the waterline. During frontal passage a two-layer counterrotating velocity field characteristic of tidal straining is immediately set up, generating a net offshore flow beneath the plume. The seaward flow at depth carries with it high suspended sediment concentrations, which appear to have been generated by wave resuspension in the nearshore region. These observations describe a mechanism by which vertical density stratification can drive exchange of material between the nearshore region and the inner shelf. To our knowledge these are the first observations of this frontal pumping mechanism, which is expected to play an important role in sediment transport near river mouths.

Simultaneous measurements of tidal straining and advection at two parallel transects far downstream in the Rhine ROFI

This study identifies and unravels the processes that lead to stratification and destratification in the far field of a Region of Freshwater Influence (ROFI). We present measurements that are novel for two reasons: (1) measurements were carried out with two vessels that sailed simultaneously over two cross-shore transects; (2) the measurements were carried out in the far field of the Rhine ROFI, 80 km downstream from the river mouth. This unique four dimensional dataset allows the application of the 3D potential energy anomaly equation for one of the first times on field data. With this equation, the relative importance of the depth mean advection, straining and nonlinear processes over one tidal cycle is assessed. The data shows that the Rhine ROFI extends 80 km downstream and periodic stratification is observed. The analysis not only shows the important role of cross-shore tidal straining but also the significance of along-shore straining and depth mean advection. In addition, the nonlinear terms seem to be small. The presence of all the terms influences the timing of maximum stratification. The analysis also shows that the importance of each term varies in the cross-shore direction. One of the most interesting findings is that the data are not inline with several hypotheses on the functioning of straining and advection in ROFIs. This highlights the dynamic behaviour of the Rhine ROFI, which is valuable for understanding the distribution of fine sediments, contaminants and the protection of coasts.

Accurate vertical profiles of turbulent flow in z-layer models

Three-dimensional hydrodynamic z-layer models, which are used for simulating the flow in rivers, estuaries, and oceans, suffer from an inaccurate and often discontinuous bottom shear stress representation, due to the staircase bottom. We analyze the governing equations and clearly show the cause of the inaccuracies. Based on the analysis, we present a new method that significantly reduces the errors and the grid dependency of the results. The method consists of a near-bed layer-remapping and a modified near-bed discretization of the k − e turbulence model. We demonstrate the applicability of the approach for uniform channel flow, using a schematized two-dimensional vertical model and for the flow over a bottom sill using the Delft3D modeling system.

Chapter 25 SPM variations in a harbour basin

Abstract This paper deals with suspended particulate matter (SPM) variations in the Botlek Harbour basin located along the meso-tidal Rotterdam Waterway at the limit of saline water intrusion. Observations of the vertical structure of velocity, salinity and turbidity from a 7 hour boat survey in Rotterdam Waterway just down-estuary of Botlek Harbour and long-term time series of salinity and turbidity near the bed acquired with a measuring rig in the Botlek Harbour basin are presented. These data have been analyzed to determine the possible causes of the pattern of SPM variations. The existence of an estuarine turbidity maximum (ETM) in this part of Rotterdam Waterway is deduced from both data sets. On a tidal timescale, the ETM in Rotterdam Waterway is associated with a continuous cycle of processes that include settling, deposition, re-entrainment and advection of SPM near the head of saline water intrusion. High near-bed SPM concentration layers are observed due to tidal advection of the ETM towards the Botlek Harbour region during flood and low near-bed SPM concentration layers are observed at slack tide as a result of settling of background SPM. Recurring salinity and SPM increases around local HW in the long-term data records are attributed to advection of a part of the ETM into Botlek Harbour by salinity-induced density currents. The persistence of this pattern indicates that the supply of SPM to the ETM is sufficient to keep it maintained over time. Modifications of the “regular or periodic” siltation pattern correlate with changes in the hydrodynamic forcing at the sea and river boundaries, respectively, due to mean water level changes during and after rough weather episodes and fresh water discharges below the threshold value of the Haringvliet sluicing program. The aforementioned cycle of processes, the occurrence of non-capacity transport conditions and the fact that dredged material in Rotterdam Waterway hardly contains any mud indicate that the amount of SPM in the ETM is not stored in the sandy bed. This implies that significant change of the amount of SPM in the ETM is determined by advection of SPM from the sea and river boundaries, which has a larger timescale than the tidal period. Modifications of the “regular or periodic” siltation pattern are therefore attributed to displacements of the salt intrusion limit and ETM relative to Botlek Harbour and/or to a different functioning of the dominant (density driven) exchange mechanism of SPM due to temporary storage of saline water in the basin, but at timescales exceeding the tidal period.