Topographic Waves in Channels and Lakes on the f-Plane

Topographic Waves in Channels and Lakes on the f-Plane

by Thomas Stocker, Kolumban Hutter

Paperback(Softcover reprint of the original 1st ed. 1987)

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Product Details

ISBN-13: 9783540176237
Publisher: Springer Berlin Heidelberg
Publication date: 04/06/1987
Series: Coastal and Estuarine Studies , #21
Edition description: Softcover reprint of the original 1st ed. 1987
Pages: 176
Product dimensions: 6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

1. 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.

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