A theoretical solution to dispersion coefficients in wave field

• Published in: Ocean engineering 2014-09, Vol.88, p.342-356
• Main Authors: Shen, L.D., Zou, Z.L.
• Format: Article
• Language: English
• Subjects: Approximation; Computational fluid dynamics; Deviation; Dispersion coefficient; Dispersions; Earth, ocean, space; Exact sciences and technology; External geophysics; Frequency dispersion; Mathematical models; Ocean engineering; Orbital velocity; Physics of the oceans; River flow; Stokes drift; Surface waves, tides and sea level. Seiches; Water wave
• ISSN: 0029-8018; 1873-5258
• DOI: 10.1016/j.oceaneng.2014.07.002

Dispersion of mass concentration due to ocean waves has characteristics different from that induced by river flows. Theoretical formulae of first and second order dispersion coefficients, including both mean and oscillating parts, are derived by successive approximation for flow field composed of tidal current, Stokes drift and first order wave orbital velocity, in which the second order dispersion coefficient is first introduced. The significant contribution of wave orbital velocity is investigated. It is found that the source of this contribution is the interaction between the velocity components and the concentration deviations from its depth-mean value. The validation of the time-mean coefficient is made against the related numerical and experimental results. The effects of the second order dispersion coefficient and the dispersion coefficient oscillation on concentration transport are discussed. •The first and second order dispersion coefficients in wave field are derived.•The interaction between wave and current (Stokes drift) is considered.•The higher order effect of wave motion on the result is included.•Both mean and oscillating part of dispersion coefficient are obtained.•Validation is made against numerical results and laboratory measurements.