Generalized characteristics and Lax–Oleinik operators: global theory

Piermarco Cannarsa; Wei Cheng

doi:10.1007/s00526-017-1219-4

Generalized characteristics and Lax–Oleinik operators: global theory

Calculus of Variations and Partial Differential Equations ◽

10.1007/s00526-017-1219-4 ◽

2017 ◽

Vol 56 (5) ◽

Cited By ~ 6

Author(s):

Piermarco Cannarsa ◽

Wei Cheng

Keyword(s):

Global Theory ◽

Generalized Characteristics

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Field Observations of a Multilevel Beach Cusp System and Their Swash Zone Dynamics

Geosciences ◽

10.3390/geosciences11040148 ◽

2021 ◽

Vol 11 (4) ◽

pp. 148

Author(s):

Siegmund Nuyts ◽

Zili Li ◽

Kieran Hickey ◽

Jimmy Murphy

Keyword(s):

Morphological Evolution ◽

Swash Zone ◽

Storm Events ◽

Survey Period ◽

Similarity Parameter ◽

Global Theory ◽

Astronomical Tide ◽

Tidal Cycles ◽

Aerial Vehicle ◽

Beach Cusp

This paper presents the observed morphological evolution of a multilevel beach cusp system in Long Strand, Co. Cork, Ireland. The surveys were carried out with an Unmanned Aerial Vehicle (UAV) system between March and September 2019. From this site, three levels of beach cusps on the beachface (i.e., lower beach level, mid beach level and upper beach level), and critical cusp parameters are reported, including cusp spacing, cusp elevation, cusp depth, and cusp amplitude. Thus far, such an extensive dataset has not previously been reported in the literature from a single site. The evolution of the different cusp parameters is then linked with the hydrodynamics in the study area, and new prediction theories are proposed for the different cusp parameters. The Lower beach level cusps (1 < z < 2.5 m Irish Transverse Mercator (ITM)) changed with every tide and appeared when surf-similarity parameter -ξ0 < 1.55. These cusps had a mean cusp spacing of λmean = 11.09 m, which are closely linked with the predictions of the self-organisation theory (p < 0.05). In contrast, the Mid beach level cusps (2.5 < z < 3.5 m ITM) are less dynamic compared to the Lower beach level cusps and can persist between spring tidal cycles. They had a mean cusp spacing of λmean = 18.17 m. The Upper beach level cusps (approximately z = 6 m ITM) are above astronomical tide levels and have a mean cusp spacing of λmean = 40.26 m. They did not change significantly over the survey period due to a lack of major storm events. These findings give a better understanding of the evolution of different cusp parameters for a multilevel beach cusp system and can be used to formulate a global theory regarding their change over time.

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