The last one or two decades have witnessed an increased interest in to pographic Rossby waves, both from a theoretical computational as well as an observational point of view. However, even though long periodic pro cesses were observed in lakes and ocean basins with considerable detail, it appears that interpretation in terms of physical models is not suffi ciently conclusive. The reasons for this lack in understanding may be sought both, in the insufficient spatial resolution or the brevity of the time series of the available data and the inadequacy of the theoretical understanding of long periodic oscillating processes in lakes and ocean bays. Advancement will emerge from intensified studies of both aspects, but it is equally our believe that the understanding of long per'iodic oscillations in lakes is presently likely to profit most from a theore tical-computational study of topographic Rossby waves in enclosed basins. With this tractate we aim to provide the reader with the basic concepts of wave motion in shallow waters at subinertial frequencies. Our ques tions throughout this monogra~h are essentially: How can the solutions to this topographic wave equation in a prescribed idealized domain be construced; what are the physical properties of these solutions; are their features identifiable by observations; how reliable are such in terpretations, etc.
Table of Contents1. Introduction.- 1.1 Preamble.- 1.2 Waves in waters.- 1.3 Observations Their interpretations.- a) Lake Michigan.- b) Lake of Lugano (North basin).- c) Lake of Zurich.- d) Lake Ontario.- e) Other iakes and ocean basins.- 1.4 Aim of this work.- 2. Governing equations.- 2.1 Equations of adiabatic fluid flow.- 2.2 Vorticity, potential vorticity, topographic Rossby waves.- 2.3 Baroclinic coupling the two-layer model.- a) Prerequisites.- b) Two-layer equations.- c) Approximations.- d) Scaie anaiysis.- e) Boundary conditions.- 2.4 Continuous stratification.- a) Modal equations.- b) Scaie anaiysis.- 2.5 TW-equation in orthogonal coordinate systems.- a) Preparation.- b) Cyiindricai coordinates.- c) Eiiipticai coordinates.- d) Natural coordinates.- e) Cartesian-coordinate correspondence principle.- 3. Some known solutions of the TW-equation in various domains.- 3.1 Circular basin with parabolic bottom.- 3.2 Circular basin with a power-law bottom profile.- 3.3 Elliptic basin with parabolic bottom.- 3.4 Elliptic basin with exponential bottom.- a) Basin with central island.- b) Basin without island.- 3.5 Topographic waves in infinite domains.- a) Straight channel.- b) Channel with one-sided topography.- c) Shelf.- d) Trench.- e) Single-step shelf.- f) Elliptic island.- 4. The Method of Weighted Residuals.- 4.1 Application to the TW-equation.- 4.2 Symmetrization.- 5. Topographic waves in infinite channels.- 5.1 Basic concept.- 5.2 Dispersion relation.- 5.3 Channel solutions.- 5.4 Velocity profiles.- 5.5 Alternative solution procedures.- 5.6 Hyperbolically curved channels.- 6. Topographic waves in rectangular basins.- 6.1 Crude lake model.- 6.2 Lake model with non-constant thalweg.- a) Numerical method.- b) New types of topographic waves.- c) Convergence and parameter dependence.- d) The bay-type.- 7. Reflection of topographic waves.- 7.1 Reflection at a vertical wall.- 7.2 Reflection at an exponential shore.- 7.3 Reflection at a sin2-shore.- a) Numerical method.- b) Reflection patterns.- 8. Review and outlook: Review and outlook: Restrictions of this study A list of unsolved problems.- 8.1 A brief summary.- 8.2 Validity of TW-equations.- 8.3 Single or multivalued dispersion relation.- 8.4 Bay-type modes.- 8.5 A list of unsolved problems.- a) On the computational side.- b) On the physical side.- 8.6 Measurements, observations.- Appendix A.- Appendix B.- Appendix C.- References.- Author Index.