Estuarine Circulation in Well-Mixed Tidal Inlets
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Estuarine Circulation in well-mixed tidal inlets Dissertation zur Erlangung des akademischen Grades doctor rerum naturalium (Dr. rer. nat.) der Mathematisch-Naturwissenschaftlichen Fakult¨at der Universit¨atRostock vorgelegt von Johannes Becherer geb. am 11. August 1983 in Rostock Rostock, 19. Dezember 2013 Abstract Estuarine dynamics in well-mixed tidal inlets is studied based on data of two measure- ment campaigns, carried out in the German Wadden Sea. We present the first direct observations of tidal straining in the Wadden Sea, a process that is supposed to be a ma- jor driver of estuarine circulation in this system. In contradiction to this theory, we also observe strong late flood stratification. This late flood stratification is found to be due to asymmetric lateral circulation, which is generated by a systematic interplay of horizontal density gradients and centrifugal forcing. By applying a consistent theoretical framework this newly discovered process is found to be also responsible for a large fraction of the residual estuarine exchange flow. Finally, an idealized model is developed to study the relevance of this process for other systems. Zusammenfassung Die ¨astuarineDynamik von gut durchmischten Gezeitenkan¨alen wird an Hand der Daten zweier Messkampagnen untersucht, die im deutschen Wattenmeer unternommen wurden. Wir pr¨asentieren die ersten direkten Beobachtungen von tidal straining im Wattenmeer, einem Prozess von dem man vermutet, dass er hauptverantwortlich f¨urdie ¨astuarineZirku- lation in diesem System ist. Im Widerspruch zu dieser Theorie stehend, beobachten wir allerdings auch starke Flutschichtung. Diese Flutschichtung wird durch asymmetrische Lateralzirkulation hervorgerufen, die wiederum durch ein systematisches Zusammenspiel von horizontalem Dichtegradient und Zentrifugalkraft verursacht wird. Durch den Ge- brauch eines konsistenten theoretischen Modells wird gezeigt, dass dieser neu entdeckte Prozess ebenfalls f¨ureinen Großteil der residualen ¨astuarinenAustauschstr¨omung verant- wortlich ist. Abschließend wird ein idealisiertes Modell entwickelt, um die Relevanz dieses Mechanismus f¨urandere Systeme zu untersuchen. 3 Contents 1. Structure of this thesis 1 2. Basic equations 3 2.1. Momentum equations . 3 2.2. Density equations . 3 2.3. Turbulence in the boundary layer . 4 2.3.1. Law-of-the-wall . 4 2.3.2. Turbulent fluxes . 4 3. Introduction: Circulating Estuaries 7 3.1. What is estuarine circulation? . 7 3.2. Why is estuarine circulation important? . 9 3.3. How does estuarine circulation work? . 10 3.3.1. Direct drivers of estuarine circulation . 10 3.3.2. Indirect drivers of estuarine circulation . 11 4. Sylt inlet: Tidal straining and flood tide stratification 19 4.1. Introduction . 19 4.2. Field observations . 20 4.2.1. Study site . 20 4.2.2. Instrumentation and data analysis . 20 4.2.3. Field work . 22 4.3. Results . 24 4.4. Discussion and conclusions . 26 5. Spiekeroog inlet: Asymmetric lateral circulation 29 5.1. Introduction . 29 5.2. Field campaign . 31 5.2.1. Study site . 31 5.2.2. Instrumentation . 31 5.2.3. Measurements . 33 5.2.4. Basic data-processing . 33 5.3. Theoretical framework . 35 5.3.1. Potential energy anomaly Φ . 35 5.3.2. Framework for along- and across-channel circulation . 37 5.4. Observations . 41 5.4.1. General conditions . 41 5.4.2. Tidal variation of stratification . 41 i Contents 5.4.3. Tidal velocities . 45 5.5. Mechanisms (Discussion) . 48 5.5.1. Generation of vertical stratification . 48 5.5.2. Generation of lateral circulation . 52 5.5.3. Implications for estuarine circulation . 56 5.6. Conclusions . 59 6. Vorticity-Model: Jump and circulate 61 6.1. Introduction . 61 6.2. Model description . 61 6.2.1. Model assumptions . 62 6.2.2. Vertical gradients . 63 6.2.3. Lateral gradients . 64 6.2.4. Turbulence closure . 65 6.2.5. Model parameters . 66 6.2.6. Non-dimensional numbers . 67 6.3. Model Validation . 69 6.3.1. Model setup . 69 6.3.2. Results . 70 6.3.3. Discussion . 74 6.4. Influence of channel shapes . 76 6.4.1. Model setups . 76 6.4.2. Results . 76 6.4.3. Discussion . 81 6.5. Parameter study . 84 6.5.1. Model setup . 84 6.5.2. Results . 85 6.5.3. Discussion . 89 6.6. Conclusions . 95 7. Summary and Conclusions 97 8. Future perspectives 99 A. Vorticity-Model 101 A.1. Basic relations . 101 A.1.1. Along-channel vorticty . 101 A.1.2. Across-channel vorticty . 101 A.1.3. Continuty equation . 102 A.2. Derivation of model equations . 102 A.2.1. [!x]....................................102 A.2.2. [!y]....................................103 A.2.3. [N 2] ...................................103 A.2.4. [@yb] ...................................103 A.2.5. [@yu]...................................104 A.3. [Φ] . 105 ii Contents A.4. Turbulence closure . 106 A.5. Periodicity of a signal . 106 iii 1. Structure of this thesis The studies for this thesis have been carried out in the framework of the ECOWS1 project of the German Research Foundation (DFG). The major aim of this thesis is to study estuarine circulation in a highly energetic tidal environment with small horizontal density gradients. Examples for such environments are for instance the tidal inlets of the German Wadden Sea, where two measurement campaigns have been conducted. The results of the first campaign carried out in the Lister Deep have been published in Becherer et al. (2011). Chapter 4 is based on that publication and studies indications for mixing asymmetries like tidal straining and their implication for vertical stratification and sediment transport. A second substantially refined measurement campaign was carried out in the tidal inlet between the islands of Langeoog and Spiekeroog, a similar study site as Lister Deep. The obtained data set is more comprehensive in terms of instrumentation and data coverage than the first campaign and provides a whole new perspective on the estuarine dynamics in the Wadden Sea. The analysis of those results are the core of another publication (Becherer et al., submitted), which is the basis of chapter 5. In this chapter we identify a whole new mechanism that is able to explain a large fraction of the estuarine dynamics in the tidal inlet. In order to test the general relevance of the newly discovered process for other systems and to connect the findings of chapter 4 and chapter 5, we provide an idealized modelling study in chapter 6. Despite its simplicity, the self-developed vorticity model is able to capture most of the dynamics that appear in the observations and allows at the same time projections of the investigated processes on other systems. Chapter 6 is written in such a way that it can be used with small modification as a third independent article, which will be submitted to a peer-review journal in the near future. Chapter 4, 5, and 6, which are the core of this thesis, are in the form of independent manuscripts, which is why each of them have their own introduction and conclusion. Nevertheless, all three chapters are strongly related to each other, and are surrounded by a thematic introduction in chapter 3 and final conclusions in chapter 7. This thesis closes with some future perspectives in chapter 8. As mentioned above, parts of this thesis have already been published in two articles: Becherer, J., H. Burchard, G. Fl¨oser,V. Mohrholz, and L. Umlauf, 2011: Evidence of tidal straining in well-mixed channel flow from micro-structure observations. Geo- phys. Res. Lett., 38 Becherer, J., M. T. Stacey, L. Umlauf, and H. Burchard, submitted: Asymmetric lateral circulation in a well-mixed tidal inlet: Mechanisms and inplications. J. Phys. 1Exploring the role of estuarine circulation for transport of suspended particulate matter (SPM) in the Wadden Sea by means of field observations and numerical modelling 1 1. Structure of this thesis Oceanogr. These articles would not have been possible in this form without the help of the co-authors, whose contributions are listed below : Hans Burchard Leibniz-Institute for Baltic Sea Research, Warnem¨unde,Germany, de- partment of Physical Oceanography. Principal investigator of the ECOWS project. Support and supervision of this thesis and of the publications. Lars Umlauf Leibniz-Institute for Baltic Sea Research, Warnem¨unde,Germany, depart- ment of Physical Oceanography. Support of data analysis, measurements and manuscript revision. Mark T. Stacey Civil and Environmental Engineering Department, University of Cali- fornia, Berkeley, California, USA. Support of data analysis, theoretical framework, article concept and manuscript revision. Volker Mohrholz Leibniz-Institute for Baltic Sea Research, Warnem¨unde,Germany, de- partment of Physical Oceanography. Support of data analysis and measurements. G¨otzFl¨oser Institute for Coastal Research, Helmholtz Centre Geesthacht, Geesthacht, Germany. Support of data analysis and measurements. 2 2. Basic equations In this chapter we present the most important equations used throughout the entire thesis. More specific equations related to the different topics will be introduced in the corresponding chapters. 2.1. Momentum equations The basis of almost any geophysical flow analysis are the the Reynolds averaged Navier Stokes (RANS) equations. Applying the Boussinesq and hydrostatic assumptions, the two horizontal components in a curved coordinate system are (Huijts et al., 2009) 1 @tu = −u@xu − v@yu − w@zu + fv − R uv (2.1) R η 0 0 0 −g@xη + z @xbdz − @z hu w i , 1 2 @tv = −u@xv − v@yv − w@zv − fu + R u (2.2) R η 0 0 0 −g@yη + z @ybdz − @z hv w i , where here and after @t, @x, @y, and @z denote partial derivative with respect to time and space , R is the radius of curvature, f the Coriolis parameter, η the surface elevation, and b the buoyancy. The underlying coordinate system is aligned with the curved channel, where y is parallel and x perpendicular to the radius of curvature, and z points vertically upwards.