Index absorbing surface, 80 acoustic wave, 214 adiabatic expansion, 14 air density, 147 oversaturated, 151 pressure, sea-level, 148 Airy function, 138 arc length, 119 asymptotic, symbol for, 55 balance between acceleration and pressure force per unit mass, 198 between centripetal acceleration and pressure force, 148 between diffusive transport and absorption, 82 between external and drag forces, 65 between kinetic and potential energies, 250 between load and tension, 119 between nonlinearity and variable-bottom effects, 246 of units, 78, 81 Bernoulli’s theorem, 150 Bessel functions, integral representation of, 111 Boltzmann constant, 65, 149 factor, 65 from minimization of free energy, 66 bore, 231 absorbs characteristics, 239 as energy sink, 233 asymptotic continuity of Riemann invariant across weak bore, see Riemann invariant following precursor trough of tsunami, 255 perturbation analysis of weak bores, 240 propagating into undisturbed ocean, 233 turbulent, 231 wake of, 233, 240 weak, 240 world line of, 238, 241 bore velocity, 232 asymptotic velocity of weak bore, 242 bottom topography, 181, 200 effect on vortices, 202 slowly varying, 246 boundary condition absorbing boundary condition for diffusion, 80, 128 associated with convection PDE, 12 bottom, 187 dynamical, 188, 190 for periodic heating and cooling, 103 kinematic, 187, 189, 199 linearized, 190 looking like initial condition, 163 no penetration, 63, 65, 182 boundary value problem, Neumann, for pressure field of incompressible flow, 166 Brownian motion, 31, 87 as integral of white noise, 121 average exit time, 128–130 distribution of exit times, 129 homogeneity and isotropy of, 33 Brownian particles, 39, 49 259

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