Spectral Modelling of Current Induced Wave-Blocking

Abstract

Waves travelling against an increasing opposing current tend to dissipate energy and part of the energy reflects back (in blocking conditions). The kinematic behaviour of these waves can be approximated with the linear theory for surface gravity waves. This theory has been implemented for random, short-crested waves in the third-generation wave model SWAN with numerical schemes that are fully implicit. Ad hoc assumptions that are made in other, similar models for blocking conditions are therefore not required and the model is consistent with the underlying theory. To represent the dissipation of the breaking waves in these blocking conditions, the pulse-based model of Hasselmann (1974) as adapted by Komen et al. (1984) has been chosen. Computations have been compared with the flume observations of Lai et al. (1989) in which random waves are blocked with violent breaking by an increasing counter current in relatively deep water. The computations underestimate the dissipation considerably but the addition of the bore-based model of Battjes and Janssen (1978) for steep, breaking waves in deep water improves the agreement with the observations significantly although some discrepancy remains. INTRODUCTIONField and laboratory observations of random waves in an opposing current show that the wave spectrum changes considerably, often accompanied with (currentinduced) wave breaking. These changes take place rapidly at the moment that waves are blocked by the current. The third-generation spectral SWAN wave model (Holthuijsen et al., 1993;Ris et al., 1994;Holthuijsen et al., 1996) can be used to simulate these wave-blocking conditions in a linear approach as it is fully consistent with the linear wave theory for surface gravity waves. The model includes the thirdgeneration formulation for deep-water wave breaking of Hasselmann (1974) as adapted by Komen et al. (1984). The flume experiments of Lai et al. (1989) offer an excellent opportunity to test this formulation against observations.

Study on Locally Varying Inundation Characteristics Induced by Super Typhoon Haiyan. Part 1: Dynamic Behavior of Storm Surge and Waves Around San Pedro Bay

“…17 assumes the constant value of γ b in Eq. (5) although this value may decrease with the increasing opposing current velocity [Chawla and Kirby, 2002;Ris and Holthujisen, 1996]. Besides breaking, opposing current has significant impact on wave blocking on the shallow water.…”

“…(5) to compute breaking wave-height as functions of breaking water depth, h b , wave period, T , and current velocity component in the wave propagation direction, U c . Although Chawla and Kirby [2002] and Ris and Holthujisen [1996] apply the smaller value of γ b in the case of strong opposing current, this study used the constant value, γ b = 0.6, regardless of the magnitude of opposing current velocity since it is not well known how the value of γ b should vary with the opposing current velocity. In this study, therefore, the influence of opposing current appears only in the evaluation of the wave number and corresponding wave steepness obtained through Eqs.…”

“…While the value of γ b used in the original Miche's [1951] criterion corresponds to γ b = 0.88, Chawla and Kirby [2002] applied the smaller value, γ b = 0.6, to obtain the best predictions of breaking points observed in their experiment of breaking waves against the opposing current. Ris and Holthujisen [1996] also applied the smaller value, γ b = 0.5, for their computations of wave deformation against strong opposing current. This study applied Eq.…”

Waves and Currents at a River Mouth: The Role of Macrovortices, Sub-Grid Turbulence and Seabed Friction

“…A common and easily detectable feature of interacting waves and currents is wave blocking, an occurrence in which the incoming waves are gradually blocked (with part of their energy reflected back to the open sea) by a current flowing in the opposite direction [1,2]. Wave blocking can considerably reduce the energy of sea waves penetrating the river mouth or estuary, since it leads to local wave steepening and breaking and global energy dissipation.…”

Wave-, wind-, and tide-driven circulation at a well-mixed ocean inlet

“…In particular, the observations suggest flood enhancement in the deep channel (Wargula et al, 2014), whereas the model suggests ebb enhancement in the deep channel ( Figure 2.9b, red and blue curves are negative for 600 < cross-shore distance < 900 m), similar to previous modeling studies (Olabarrieta et al, 2011 and. There are several potential sources for this difference, including the smoothing of the observed bathymetry to reduce spurious circulation (the model assumes gradual spatial changes) (Rogowski et al, 2014;Chen et al, 2015), unresolved vertical variability in flows (Spydell et al, 2015), insufficient blocking of the ebb jet (Olabarrieta et al, 2014), an overestimation of set-up inside the inlet (e.g., owing to unresolved exchanges with the ICW), and an underestimation of wave radiation-stress gradients (e.g., owing to incorrectly parameterized dissipation, (Ris and Holthuijsen, 1996)). …”