Distributions of void fraction under breaking waves in the surf zone Ashabul Hoque a, * , Shin-ichi Aoki b a Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh b Department of Architecture and Civil Engineering, Toyohashi University of Technology, Toyohashi 441-8580, Japan Received 20 August 2004; accepted 19 November 2004 Available online 1 April 2005 Abstract Void fractions under breaking waves have been measured by a conductivity probe. Empirical coefficients k 0 and C 0 have been determined through the experimental results and found to be function of the local wave height and relative distance, respectively. The results indicate that the distributions of void fraction follow closely analytical solution of the diffusion equation. q 2005 Elsevier Ltd. All rights reserved. Keywords: Void fraction; Surf zone; Breaking waves; Diffusion equation 1. Introduction The rate of air bubble transport is needed for various purposes such as the gas exchanges, wave energy transferred, sediment transport and sound generation (e.g. Koga, 1982; Wu, 1988; Lamarre and Melville, 1991; Waniewski et al., 2001). In shallow water, the sloping bottom causes the breaking process, where a large amount of air bubble entrains into water near the breaking point. With the mixing of air bubbles, the flow fields of broken waves are turbulent and complicated. The injected air bubbles beneath a breaking wave are rapidly broken up by turbulence, producing an initial size spectrum proportional to (radius) K10/3 (Garrett et al., 2000). This tiny air bubbles are not always visible to the naked eye, yet they play a very important role in the surf zone. Ocean Engineering 32 (2005) 1829–1840 www.elsevier.com/locate/oceaneng 0029-8018/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2004.11.013 * Corresponding author. E-mail addresses: ashabulh@yahoo.com (A. Hoque), aoki@jughead.tutrp.tut.ac.jp (S.-i. Aoki).