scholarly journals ENGINEERING DESIGN IN THE PRESENCE OF WAVE GROUPS

2011 ◽  
Vol 1 (32) ◽  
pp. 68
Author(s):  
Thomas D. Shand ◽  
William L. Peirson ◽  
Ronald J. Cox
Keyword(s):  
Water Level ◽  
Deep Water ◽  
Group Development ◽  
Design Guidelines ◽  
Wave Group ◽  
Non Linear ◽  
Present Design ◽  
Wave Trains ◽  
Monochromatic Waves ◽  
Group Effects

Determining the largest wave height, H which can occur in water of depth, d without breaking is a fundamental reference quantity for the design of coastal structures. Current design guidelines, used to predict the ratio of breaking height to depth (Hb/d), also known as the breaker index, are based on investigations which predominantly used monochromatic waves, thereby implicitly neglecting group effects. Groupiness or height modulation in wave trains is an inherent characteristic of freely propagating waves in deep water and has been shown within previous studies to induce breaker indices substantially exceeding those predicted by design guidelines. Additionally, the raw data upon which present design guidelines have been based exhibit considerable scatter. This scatter is surprising given the monochromatic and uniform nature of the laboratory waves. A physical investigation at the Water Research Laboratory using new techniques for data extraction and visualisation has yielded new insights into the shoaling and breaking processes of regular and grouped waves and revealed deficiencies in the present design techniques. Monochromatic waves trains were found to develop amplitude modulation with distance along the flume due to non-linear instabilities. These instabilities are well recognized in deep-water waves and contribute to group development and the occurrence of low-probability extreme waves. These modulations induced variation in breaking wave heights, locations and derived breaker indices. Such modulation of initially regular wave trains is proposed as a possible cause of the scatter observed in raw laboratory breaker index data. Wave group testing has revealed evolutionary cycles in local energy density during deep water propagation and that the spatial phasing of this evolution with the initiation of shoaling yielded considerably different shoaling and breaking regimes. Critically, smaller waves within the group, particularly those occurring at the front of the wave group were, at times, able to propagate into shallower water before breaking than is presently predicted by existing design guides. Causes for this discrepancy, including differences in definitions of water level and depth are investigated. However, discrepancies between observed and predicted values are found to remain. Revision to present design guidelines to directly incorporate non-linear group effects and group-induced water level variation are presented.

The Focusing of Uni-Directional Gaussian Wave-Groups in Finite Depth: An Approximate NLSE Based Approach

2010 ◽  
Author(s):  
Thomas A. A. Adcock ◽  
Shiqiang Yan
Keyword(s):  
Analytical Model ◽  
Deep Water ◽  
Finite Depth ◽  
Full Potential ◽  
Wave Group ◽  
Freak Waves ◽  
Wave Groups ◽  
Non Linear ◽  
Cubic Nonlinear Schrödinger Equation ◽  
Linear Interactions

The non-linear changes to a NewWave type wave-group are helpful in developing our understanding of the non-linear interactions which can lead to the formation of freak waves. In addition, Gaussian wave-groups are used in model tests where it is useful to have a simple model for their non-linear dynamics. This paper derives a simple analytical model to describe the nonlinear changes to a wave-group as it focuses. This paper is an extension to finite depth of the theory developed for deep water in Adcock & Taylor (2009) (Proc. Roy. Soc. A 465(2110)). The model is derived using the conserved quantities of the cubic nonlinear Schrodinger equation (NLSE). In deep water there are substantial changes to the group shape and spectrum as the wave-group focuses, and the characteristics of these changes are governed by the Benjamin-Feir Index. However, in finite depth the characteristics of the non-linear interactions change, reducing the non-linear changes to the group shape. The analytical model is validated against simulations using the NLSE and against full potential flow solutions using a QALE-FEM numerical scheme. We also compare its predictions against experiments in a physical wavetank. We find that the NLSE, and thus analytical theories derived from it, capture the dominant physics in the evolution of narrowbanded wave-groups.

scholarly journals Effects of Water Depth on the Growth of the Submerged Macrophytes Vallisneria natans and Hydrilla verticillata: Implications for Water Level Management

Water ◽  
2021 ◽  
Vol 13 (18) ◽  
pp. 2590
Author(s):  
Qisheng Li ◽  
Yanqing Han ◽  
Kunquan Chen ◽  
Xiaolong Huang ◽  
Kuanyi Li ◽  
...  
Keyword(s):  
Water Level ◽  
Water Depth ◽  
Deep Water ◽  
Submerged Macrophytes ◽  
Hydrilla Verticillata ◽  
Water Level Fluctuations ◽  
Total Biomass ◽  
Intermediate Water ◽  
Factors Affecting ◽  
Vallisneria Natans

Water level is one of the most important factors affecting the growth of submerged macrophytes in aquatic ecosystems. The rosette plant Vallisneria natans and the erect plant Hydrilla verticillata are two common submerged macrophytes in lakes of the middle and lower reaches of the Yangtze River, China. How water level fluctuations affect their growth and competition is still unknown. In this study, three water depths (50 cm, 150 cm, and 250 cm) were established to explore the responses in growth and competitive patterns of the two plant species to water depth under mixed planting conditions. The results show that, compared with shallow water conditions (50 cm), the growth of both submerged macrophytes was severely suppressed in deep water depth (250 cm), while only V. natans was inhibited under intermediate water depth (150 cm). Moreover, the ratio of biomass of V. natans to H. verticillata gradually increased with increasing water depth, indicating that deep water enhanced the competitive advantage of V. natans over H.verticillata. Morphological adaptation of the two submerged macrophytes to water depth was different. With increasing water depth, H. verticillata increased its height, at the cost of reduced plant numbers to adapt to poor light conditions. A similar strategy was also observed in V. natans, when water depth increased from 50 cm to 150 cm. However, both the plant height and number were reduced at deep water depth (250 cm). Our study suggests that water level reduction in lake restoration efforts could increase the total biomass of submerged macrophytes, but the domination of key plants, such as V. natans, may decrease.

Weakly non-linear, slowly varying waves and their instabilities

1972 ◽  
Vol 72 (1) ◽  
pp. 95-104 ◽  
Author(s):  
R. Grimshaw
Keyword(s):  
Variational Principle ◽  
Gordon Equation ◽  
Transport Equations ◽  
Linear Wave ◽  
Leading Order ◽  
Non Linear ◽  
Klein Gordon ◽  
Wave Trains ◽  
Klein Gordon Equation

AbstractA non-linear Klein–Gordon equation is used to discuss the theory of slowly varying, weakly non-linear wave trains. An averaged variational principle is used to obtain transport equations for the slow variations which incorporate the leading order modulation and non-linear terms. Linearized transport equations are used to discuss instabilities.

Ocean Wave Non-Linearity and Wind Input in Directional Seas: Energy Input During Wave-Group Focussing

2018 ◽  
Author(s):  
Thomas A. A. Adcock ◽  
Paul H. Taylor
Keyword(s):  
Energy Input ◽  
Wind Waves ◽  
Rogue Waves ◽  
Wave Group ◽  
Spectral Evolution ◽  
Wave Groups ◽  
Small Influence ◽  
Non Linear ◽  
Linear Effects ◽  
Wind Input

There has been speculation that energy input (wind) can play an important role in the formation of rogue waves in the open ocean. Here we examine the role energy input can play by adding energy to the modified non-linear Schrödinger equation. We consider NewWave type wave-groups with spectra which are realistic for wind waves. We examine the case where energy input is added to the group as the wave-group focuses. We consider whether this energy input can cause significant non-linear effects to the subsequent spatial and spectral evolution. For the parameters considered here we find this to have only a small influence.

The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains

2000 ◽  
Vol 275 (5-6) ◽  
pp. 386-393 ◽  
Author(s):  
Alfred R Osborne ◽  
Miguel Onorato ◽  
Marina Serio
Keyword(s):  
Nonlinear Dynamics ◽  
Gravity Wave ◽  
Deep Water ◽  
Rogue Waves ◽  
Wave Trains

Finite-amplitude deep-water waves on currents

1979 ◽  
Vol 292 (1392) ◽  
pp. 371-390 ◽  
Keyword(s):  
Wave Propagation ◽  
Deep Water ◽  
Water Waves ◽  
Large Scale ◽  
Finite Amplitude ◽  
The Other ◽  
Wave Trains ◽  
Deep Water Waves

Accurate integral properties of plane periodic deep-water waves of amplitudes up to the steepest are tabulated by Longuet-Higgins (1975). These are used to define an averaged Lagrangian which, following Whitham, is used to describe the properties of slowly varying wave trains. Two examples of waves on large-scale currents are examined in detail. One flow is that of a shearing current, V ( x ) j , which causes waves to be refracted. The other flow, U ( x ) i , varies in the direction of wave propagation and causes waves to either steepen or become more gentle. Some surprising features are found.

Sign in / Sign up

Export Citation Format

Share Document