Baroclinic Tides Theoretical Modelling And Observational Evidence

0521843952......Page 1
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Tables......Page 12
Preface......Page 13
Acknowledgements......Page 15
Symbols......Page 17
Abbreviations......Page 21
Preamble......Page 23
1.1 Introduction......Page 29
1.2 Governing equations: basic assumptions and hypotheses......Page 34
Nonadiabatic processes......Page 39
Equations for wave disturbances......Page 40
Boussinesq approximation......Page 41
Reynolds equations......Page 42
1.3 Problem formulation: boundary and initial conditions......Page 45
Problem formulation......Page 47
Boundary and initial conditions......Page 48
1.4 Linear wave equation......Page 50
1.5.1 Formulation of the boundary value problem......Page 54
1.5.2 Linear vertical mode analysis......Page 56
1.6 Nonlinear wave problem......Page 62
2 Linear baroclinic tides over variable bottom topography......Page 66
2.1 Analytical solution for “small” bottom features......Page 69
Zeroth-order solution......Page 74
First-order solution......Page 75
2.1.2 Scattering of internal waves by a bottom obstacle......Page 81
2.2 Numerical model for large bottom obstacles......Page 85
Step 1: Introduction of the grid......Page 91
Step 2: Finding the recurrence relation......Page 92
Step 4: Orthogonalization......Page 93
Step 5: Downstream procedure and orthogonalization......Page 94
Step 6: Truncation......Page 95
2.3 Wave dynamics over oceanic ridges: applicability of the perturbation method......Page 96
2.3.1 Generation of internal waves......Page 97
2.3.2 Internal wave scattering......Page 101
2.4.1 Generation of baroclinic tides......Page 107
2.4.2 Transformation of baroclinic tides......Page 110
2.5 Internal waves near steep bottom topography......Page 116
2.6 Internal waves near the critical latitude......Page 122
3 Combined effect of horizontal density gradient and bottom topography on the dynamics of linear baroclinic tides......Page 126
3.1 Semianalytical two-layer model......Page 132
3.2 Wave characteristics derived from the two-layer model......Page 139
3.2.1 Generation of internal waves......Page 140
3.2.2 Internal wave scattering......Page 144
3.3 Applicability of layer models......Page 145
3.4 Riemann method for a continuously stratified fluid......Page 149
3.5 Propagation of internal waves through a frontal zone......Page 155
3.6 Generation of baroclinic tides in the presence of a frontal zone......Page 164
4 Topographic generation of nonlinear baroclinic tides......Page 168
4.1 Experimental evidence for nonlinear baroclinic tides......Page 170
4.2 Numerical model for the description of nonlinear waves......Page 178
First semistep......Page 181
Second semistep......Page 182
4.3 Qualitative analysis of the excitation mechanism......Page 185
4.4 Generation mechanism at low Froude numbers: baroclinic tides......Page 187
4.5 Influence of the intensity of the tidal forcing and dissipation......Page 190
4.6 Critical Froude numbers: excitement of unsteady lee waves......Page 199
5.1 Analytical models for the evolution of baroclinic tides......Page 204
5.2 Solitary internal waves as manifestations of the coherent structure of baroclinic tides......Page 210
5.2.1 Long’s equation......Page 213
5.2.2 First-order weakly nonlinear theory......Page 214
5.2.3 Second-order weakly nonlinear theory......Page 219
5.3 Structure of large-amplitude solitary internal waves......Page 223
5.3.1 Numerical model for stationary wave solutions......Page 225
5.3.2 Characteristics of large waves......Page 226
5.3.3 Observational evidence of large waves......Page 233
5.4 Interaction of large-amplitude SIWs with bottom topography......Page 238
5.4.1 Scenarios of wave–topography interaction......Page 239
Scenario 1: Wave adjustment when aΞ /(H – HΞ ) << 1......Page 242
Scenario 2: Wave transformation at aΞ /(H – HΞ ) ～ 1......Page 244
Scenario 3: Wave breaking at aΞ /(H – HΞ ) > 1......Page 248
5.4.2 Strong wave–topography interaction: breaking criterion......Page 250
Kinematics of wave breaking......Page 252
Breaking criterion......Page 260
Experimental setup and measuring technique......Page 266
The experiments......Page 267
Typical experimental data......Page 268
Results of the numerical modeling......Page 270
6.1 Effects related to the rotation of the Earth......Page 282
6.1.1 Barents Sea Polar Front experiment......Page 283
6.1.2 Baroclinic tides......Page 286
6.1.3 Short internal waves......Page 288
6.1.4 Dependence on the rotation of the Earth......Page 293
6.2 Influence of the fluid stratification......Page 296
6.2.1 Variation of the vertical position of the pycnocline......Page 301
6.2.2 Effect of horizontal density gradients......Page 306
6.3 Baroclinic tides over steep bottom features: “mode” and “beam” approaches......Page 311
6.4 Strong high-mode baroclinic response over steep bottom topography......Page 316
6.5 Generation mechanism at large Froude numbers......Page 323
6.6 Summary of generation mechanism......Page 326
7 Three-dimensional effects of baroclinic tides......Page 330
7.1.1 Observations of SIWs on the Portuguese Shelf......Page 332
7.1.2 Generation of waves at the Oporto Seamount......Page 335
7.1.3 Far-field generation from a shelf edge......Page 337
7.2 Baroclinic tides in narrow channels and straits......Page 340
7.2.1 Modification of the model for straits......Page 343
7.2.2 Dynamics of internal waves in the Skarnsund Strait......Page 345
7.2.3 Residual currents produced by nonlinear waves......Page 349
7.2.4 Experiments on the dynamics of a passive admixture......Page 351
References......Page 357
Index......Page 370