Numerical modeling of surf zone dynamics under weakly plunging breakers with SPH method

• Refined 2-D SPH spatial resolution, smaller than integral turbulence length scales, similarly to a pseudoLES approach.
• Combination of heuristic approaches for the discrimination of fluctuating hydrodynamics from ordered wave motion.
• Good quantitative agreement of numerical results against experimental data for characteristic wave features.
• Plausibly simulated wave-induced mean flows (e.g. undertow) and “streaming” effect near the bed.
• Identification of coherent structures that define the weak plunging mechanism.

The wave breaking of weak plungers over a relatively mild slope is investigated in this paper. Numerical modeling aspects are studied, concerning the propagation and breaking of shore-normal, nonlinear and regular waves. The two-dimensional (2-D) kinematics and dynamics (fluctuating flow features and large 2-D eddies) of the wave-induced flow on a vertical cross-section over the entire surf zone are simulated with the use of Smoothed Particle Hydrodynamics (SPH). The academic ‘open source’ code SPHysics v.2 is employed and the viscosity treatment is based on a Sub-Particle Scale (SPS) approach, similarly to the Large Eddy Simulations (LES) concept. Thorough analysis of the turbulent flow scales determines the necessary refinement of the spatial resolution. The initial particle discretization reaches down to the demarcation point between integral turbulence length scales and Taylor micro-scales. A convolution-type integration method is implemented for the transformation of scattered Lagrangian particle data to Eulerian values at fixed gauges. A heuristic technique of ensemble-averaging is used for the discrimination of the fluctuating flow components from coherent structures and ordered wave motion. Comparisons between numerical and experimental data give encouraging results for several wave features. The wave-induced mean flows are simulated plausibly, and even the ‘streaming’ effect near the bed is reproduced. The recurring vorticity patterns are derived, and coherent 2-D structures inside the surf zone are identified. Fourier spectral analysis of velocities reveals isotropy of 2-D fluctuating dynamics up to rather high frequencies in shear intensified regions. The simulated Reynolds stresses follow patterns that define the characteristic mechanism of wave breaking for weak plungers. Persisting discrepancies at the incipient breaking region confirm the need for fine, massively ‘parallel’ 3-D SPS-SPH simulations.