Vanden-Broeck J.-M. Gravity-capillary free-surface flows (Cambridge; New York, 2010). - ОГЛАВЛЕНИЕ / CONTENTS
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ОбложкаVanden-Broeck J.-M. Gravity-capillary free-surface flows. - Cambridge; New York: Cambridge University Press, 2010. - xi, 318 p.: ill. - (Cambridge monographs on mechanics). - Ref.: p.308-317. - Ind.: p.318. - ISBN 978-0-521-81190-3
 

Оглавление / Contents
 
Preface ........................................................ xi
1  Introduction ................................................. 1
2  Basic concepts ............................................... 7
   2.1  The equations of fluid mechanics ........................ 7
   2.2  Free-surface flows ...................................... 8
   2.3  Two-dimensional flows .................................. 11
   2.4  Linear waves ........................................... 15
        2.4.1  The water-wave equations ........................ 15
        2.4.2  Linear solutions for water waves ................ 17
        2.4.3  Superposition of linear waves ................... 24
3  Free-surface flows that intersect walls ..................... 31
   3.1  Free streamline solutions .............................. 33
        3.1.1  Forced separation ............................... 33
        3.1.2  Free separation ................................. 43
   3.2  The effects of surface tension ......................... 58
        3.2.1  Forced separation ............................... 58
        3.2.2  Free separation ................................. 66
   3.3  The effects of gravity ................................. 73
        3.3.1  Solutions with β1=0 (funnels) ................... 83
        3.3.2  Solutions with β1=0 (nozzles and bubbles) ....... 88
        3.3.3  Solutions with β1= π/2 (flow under a gate
               with gravity) ................................... 94
   3.4  The combined effects of gravity and surface tension .... 98
        3.4.1  Rising bubbles in a tube ........................ 99
        3.4.2  Fingering in a Hele Shaw cell .................. 103
        3.4.3  Further examples involving rising bubbles ...... 108
        3.4.4  Exponential asymptotics ........................ 112
4  Linear free-surface flows generated by moving
   disturbances ............................................... 114
   4.1  The exact nonlinear equations ......................... 115
   4.2  Linear theory ......................................... 116
        4.2.1  Solutions in water of finite depth ............. 116
        4.2.2  Solutions in water of infinite depth ........... 122
        4.2.3  Discussion of the solutions .................... 124
5  Nonlinear waves - asymptotic solutions ..................... 129
   5.1  Periodic waves ........................................ 129
        5.1.1  Solutions when condition (5.55) is satisfied ... 135
        5.1.2  Solutions when condition (5.55) is not
               satisfied ...................................... 138
   5.2  The Korteweg-de Vries equation ........................ 142
6  Numerical computations of nonlinear water waves ............ 148
   6.1  Formulation ........................................... 148
   6.2  Series truncation method .............................. 151
   6.3  Boundary integral equation method ..................... 152
   6.4  Numerical methods for solitary waves .................. 156
        6.4.1  Boundary integral equation methods ............. 157
   6.5  Numerical results for periodic waves .................. 160
        6.5.1  Pure capillary waves (g = 0, T ≠ 0) ............ 160
        6.5.2  Pure gravity waves (g ≠ 0, T = 0) .............. 164
        6.5.3  Gravity-capillary waves (g ≠ 0, T ≠ 0) ......... 175
   6.6  Numerical results for solitary waves .................. 181
        6.6.1  Pure gravity solitary waves .................... 181
        6.6.2  Gravity-capillary solitary waves ............... 186
7  Nonlinear free-surface flows generated by moving
   disturbances ............................................... 191
   7.1  Pure gravity free-surface flows in water of finite
        depth ................................................. 192
        7.1.1  Supercritical flows ............................ 192
        7.1.2  Subcritical flows .............................. 195
   7.2  Gravity-capillary free-surface flows .................. 201
        7.2.1  Results in finite depth ........................ 201
        7.2.2  Results in infinite depth (removal of the
               nonuniformity) ................................. 203
   7.3  Gravity-capillary free-surface flows with Wilton
        ripples ............................................... 206
8  Free-surface flows with waves and intersections with
   rigid walls ................................................ 210
   8.1  Free-surface flow past a flat plate ................... 211
        8.1.1  Numerical results .............................. 212
        8.1.2  Analytical results ............................. 215
   8.2  Free-surface flow past a surface-piercing object ...... 218
        8.2.1  Numerical results .............................. 219
        8.2.2  Analytical results ............................. 221
   8.3  Flow under a sluice gate .............................. 226
        8.3.1  Formulation .................................... 228
        8.3.2  Numerical procedure ............................ 231
        8.3.3  Discussion of the results ...................... 233
   8.4  Pure capillary free-surface flows ..................... 236
        8.4.1  Numerical results .............................. 236
        8.4.2  Analytical results ............................. 239
9  Waves with constant vorticity .............................. 244
   9.1  Solitary waves with constant vorticity ................ 245
        9.1.1  Mathematical formulation ....................... 245
        9.1.2  Numerical procedure ............................ 248
        9.1.3  Discussion of the results ...................... 249
   9.2  Periodic waves with constant vorticity ................ 267
        9.2.1  Mathematical formulation ....................... 268
        9.2.2  Numerical procedure ............................ 270
        9.2.3  Numerical results .............................. 271
        9.2.4  Discussion ..................................... 276
10 Three-dimensional free-surface flows ....................... 278
   10.1 Green's function formulation for two-dimensional
        problems .............................................. 278
        10.1.1 Pressure distribution .......................... 278
        10.1.2 Two-dimensional surface-piercing object ........ 283
   10.2 Extension to three-dimensional free-surface flows ..... 286
        10.2.1 Gravity flows generated by moving
               disturbances in water of infinite depth ........ 286
        10.2.2 Three-dimensional gravity-capillary free-
               surface flows in water of infinite depth ....... 293
   10.3 Further extensions .................................... 298
11 Time-dependent free-surface flows .......................... 301
   11.1 Introduction .......................................... 301
   11.2 Nonlinear gravity-capillary standing waves ............ 301
References .................................................... 308
Index ......................................................... 318


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