J. Fluid Mech. (2013), vol. 731, pp. 545–578. c  Cambridge University Press 2013 545 doi:10.1017/jfm.2013.361 Direct numerical simulations of instability and boundary layer turbulence under a solitary wave Celalettin E. Ozdemir 1, †, Tian-Jian Hsu 1 and S. Balachandar 2 1 Center for Applied Coastal Research, University of Delaware, Newark, DE 19716, USA 2 Mechanical & Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA (Received 19 October 2012; revised 5 May 2013; accepted 11 July 2013; first published online 28 August 2013) A significant amount of research effort has been made to understand the boundary layer instability and the generation and evolution of turbulence subject to periodic/oscillatory flows. However, little is known about bottom boundary layers driven by highly transient and intermittent free-stream flow forcing, such as solitary wave motion. To better understand the nature of the instability mechanisms and turbulent flow characteristics subject to solitary wave motion, a large number of direct numerical simulations are conducted. Different amplitudes of random initial fluctuating velocity field are imposed. Two different instability mechanisms are observed within the range of Reynolds number studied. The first is a short-lived, nonlinear, long- wave instability which is observed during the acceleration phase, and the second is a broadband instability that occurs during the deceleration phase. Transition from a laminar to turbulent state is observed to follow two different breakdown pathways: the first follows the sequence of K-type secondary instability of a near-wall boundary layer at comparatively lower Reynolds number and the second one follows a breakdown path similar to that of free shear layers. Overall characteristics of the flow are categorized into four regimes as: (i) laminar; (ii) disturbed laminar; (iii) transitional; and (iv) turbulent. Our categorization into four regimes is consistent with earlier works. However, this study is able to provide more specific definitions through the instability characteristics and the turbulence breakdown process. Key words: coastal engineering, solitary waves, turbulent flows 1. Introduction Fluid motion of highly transient and skewed characteristics is ubiquitous in nature. Internal waves due to strong tides in the vicinity of complex submarine terrains (Stastna & Lamb 2002; Bogucki, Rodekopp & Barth 2005; Diamessis & Rodekopp 2006) are striking examples of this kind. Tsunami waves (e.g. Voit 1987) and skewed waves in shallow waters are other examples with many coastal engineering applications. Though highly idealized, many studies approximate such transient flow motion using solitary waves (Vittori & Blondeaux 2011). Much of the literature on solitary wave motion is devoted to the dynamics of internal solitary wave motion in a † Current Address: Applied Ocean Physics & Engineering Department, Woods Hole Oceanographic Institution, 02543, Woods Hole, MA, USA. Email address for correspondence: cozdemir@whoi.edu