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Computation of finite-amplitude dispersive waves
OLR(1987)34 (12)
A. PhysicalOceanography
87:6719 Dewar, W.K., 1987. Planetary shock waves. J. phys. Oceanogr., 17(4):470-482. The evolution of a thermal anomaly is considered in the absence of wind forcing. In this case, the planetary geostrophic equations can be reduced to a first-order equation, the Planetary Geostrophic Wave Equation. Arbitrary initial conditions governed by the equation tend to steepen and form shock waves. The evolution of an initially columnar eddy is obtained, and four different phases of shock propagation are identified. Implications for heat transport, potential vorticity transport and thermocline ventilation are discussed. Dept. of Oceanogr., Florida State Univ., Tallahassee, FL 32306, USA. 87:6720 Hara, Tetsu and C.C. Mei, 1987. Bragg scattering of surface waves by periodic bars: theory and experiment. J. Fluid Mech., 178:221-241. A recent linearized theory is extended to include second-order effects of the free surface and the bars. New experiments are performed to verify the existence of the cutoff detuning frequency, the dispersive nature of the first-order wave envelope, and the radiation of second-order long waves. Measured transient and quasi-steady responses to incident wave packets and uniform wavetrains are compared with corresponding theoretical results. For quasi-steady incident waves of relatively small steepness it is necessary to improve the theory to the second order in bar slope, so that the calculated short-wave envelopes agree with those measured over the bars. Dept. of Civil Engng, Univ. of Tokyo, Japan. 87:6721 Katopodes, N.D. and C.-T. Wu, 1987. Computation of finite-amplitude dispersive waves. J. War Way Port coast. Ocean Engng, Am. Soc. civ. Engrs, 113(4):327-346. An explicit finite element model is developed and applied to problems in one and two space dimensions. It uses linear chapeau functions for interpolation, is simple to formulate and inexpensive to execute. The model is sufficiently accurate so that the cumulative effect of numerical errors does not affect the results even at very long times of computation. The method is applied to the computation of solitary waves of various amplitudes and undular bores propagating through two-dimensional channel transitions. It is as accurate as the best available methods and superior in eliminating spurious oscillatory tails often encountered near
1025
computed nonlinear dispersive waves. Dept. of Civ. Engng, Univ. of Michigan, Ann Arbor, MI 48109, USA. 87:6722 Kienle, JOrgen, Zygmunt Kowalik and T.S. Murty, 1987. Tsunamis generated by eruptions from Mount St. Augustine Volcano, Alaska. Science, 236(4807): 1442-1447. During an eruption in 1986, there was the possibility that a tsunami might be generated by the collapse of a portion of the volcano. A similar collapse of the volcano and ensuing sea wave occurred in 1883. Mount St. Augustine remained intact during this eruptive cycle, but a possible recurrence spurred a numerical simulation of the 1883 sea wave. This simulation, which yielded a forecast of potential wave heights and travel times, was based on a method applicable generally to other coastal volcanos. @1987 by AAAS. Geophysical Inst., Univ. of Alaska, Fairbanks, AK 99775-0800, USA. 87:6723 Lambert, F., M. Musette and E. Kesteloot, 1987. Soliton resonances for the good Bonssinesq equation. Inverse Problem.v, 3(2):275-288. Vrije Univ. Brussel, Theoretische Natuurkunde, Pleinlaan 2, B-1050 Brussels, Belgium. 87:6724 Lepelletier, T.G. and Fredric Raichlen, 1987. Harbor oscillations induced by nonlinear transient long waves. J. WatWay Port coast. Ocean Engng, Am. Soc. cir. Engrs, 113(4):381-400, Excitation of harbors and bays is investigated theoretically and experimentally. A numerical method is used to solve the weakly nonlinear-dispersivedissipative equations of motion for variable depth. Several dissipative effects also are included. Open sea conditions are simulated using a time varying radiative boundary condition imposed at a finite distance from the harbor entrance. Experiments are conducted using continuous waves incident upon a narrow constant depth rectangular harbor. Results show that, for the lowest resonant mode, a linear dissipative solution is sufficient to describe the wave dynamics. For higher resonant modes nonlinear convective effects must be included. Using transient waves, good agreement is obtained between experimental and theoretical results for a rectangular harbor with a linearly sloping bottom and a constant depth harbor with a trapezoidal planform. Setec Travaux Publics, Paris, France.
A. PhysicalOceanography
87:6719 Dewar, W.K., 1987. Planetary shock waves. J. phys. Oceanogr., 17(4):470-482. The evolution of a thermal anomaly is considered in the absence of wind forcing. In this case, the planetary geostrophic equations can be reduced to a first-order equation, the Planetary Geostrophic Wave Equation. Arbitrary initial conditions governed by the equation tend to steepen and form shock waves. The evolution of an initially columnar eddy is obtained, and four different phases of shock propagation are identified. Implications for heat transport, potential vorticity transport and thermocline ventilation are discussed. Dept. of Oceanogr., Florida State Univ., Tallahassee, FL 32306, USA. 87:6720 Hara, Tetsu and C.C. Mei, 1987. Bragg scattering of surface waves by periodic bars: theory and experiment. J. Fluid Mech., 178:221-241. A recent linearized theory is extended to include second-order effects of the free surface and the bars. New experiments are performed to verify the existence of the cutoff detuning frequency, the dispersive nature of the first-order wave envelope, and the radiation of second-order long waves. Measured transient and quasi-steady responses to incident wave packets and uniform wavetrains are compared with corresponding theoretical results. For quasi-steady incident waves of relatively small steepness it is necessary to improve the theory to the second order in bar slope, so that the calculated short-wave envelopes agree with those measured over the bars. Dept. of Civil Engng, Univ. of Tokyo, Japan. 87:6721 Katopodes, N.D. and C.-T. Wu, 1987. Computation of finite-amplitude dispersive waves. J. War Way Port coast. Ocean Engng, Am. Soc. civ. Engrs, 113(4):327-346. An explicit finite element model is developed and applied to problems in one and two space dimensions. It uses linear chapeau functions for interpolation, is simple to formulate and inexpensive to execute. The model is sufficiently accurate so that the cumulative effect of numerical errors does not affect the results even at very long times of computation. The method is applied to the computation of solitary waves of various amplitudes and undular bores propagating through two-dimensional channel transitions. It is as accurate as the best available methods and superior in eliminating spurious oscillatory tails often encountered near
1025
computed nonlinear dispersive waves. Dept. of Civ. Engng, Univ. of Michigan, Ann Arbor, MI 48109, USA. 87:6722 Kienle, JOrgen, Zygmunt Kowalik and T.S. Murty, 1987. Tsunamis generated by eruptions from Mount St. Augustine Volcano, Alaska. Science, 236(4807): 1442-1447. During an eruption in 1986, there was the possibility that a tsunami might be generated by the collapse of a portion of the volcano. A similar collapse of the volcano and ensuing sea wave occurred in 1883. Mount St. Augustine remained intact during this eruptive cycle, but a possible recurrence spurred a numerical simulation of the 1883 sea wave. This simulation, which yielded a forecast of potential wave heights and travel times, was based on a method applicable generally to other coastal volcanos. @1987 by AAAS. Geophysical Inst., Univ. of Alaska, Fairbanks, AK 99775-0800, USA. 87:6723 Lambert, F., M. Musette and E. Kesteloot, 1987. Soliton resonances for the good Bonssinesq equation. Inverse Problem.v, 3(2):275-288. Vrije Univ. Brussel, Theoretische Natuurkunde, Pleinlaan 2, B-1050 Brussels, Belgium. 87:6724 Lepelletier, T.G. and Fredric Raichlen, 1987. Harbor oscillations induced by nonlinear transient long waves. J. WatWay Port coast. Ocean Engng, Am. Soc. cir. Engrs, 113(4):381-400, Excitation of harbors and bays is investigated theoretically and experimentally. A numerical method is used to solve the weakly nonlinear-dispersivedissipative equations of motion for variable depth. Several dissipative effects also are included. Open sea conditions are simulated using a time varying radiative boundary condition imposed at a finite distance from the harbor entrance. Experiments are conducted using continuous waves incident upon a narrow constant depth rectangular harbor. Results show that, for the lowest resonant mode, a linear dissipative solution is sufficient to describe the wave dynamics. For higher resonant modes nonlinear convective effects must be included. Using transient waves, good agreement is obtained between experimental and theoretical results for a rectangular harbor with a linearly sloping bottom and a constant depth harbor with a trapezoidal planform. Setec Travaux Publics, Paris, France.