On the Fourier approximation method for steady water waves

Zhao, Hongjun; Song, Zhiyao; Li, Ling; Kong, Jun

doi:10.1007/s13131-014-0470-1

Cited by 5 publications

(8 citation statements)

References 21 publications

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“…Hypoxia was observed at stations H12 and 32 during sampling in August (table 1). In June, as a result of the intrusion of the cold water mass from the Yellow Sea (Zhao 1987), the temperature of sample H15-1-B was the lowest. are shown in figure 2.…”

Section: Environmental Characterizationmentioning

confidence: 97%

Temporal distribution of bacterial community structure in the Changjiang Estuary hypoxia area and the adjacent East China Sea

Liu

Xiao

et al. 2012

Environ. Res. Lett.

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Bacterial community structure and the effects of environmental factors on the microbial community distribution were investigated in the Changjiang Estuary hypoxia area and its adjacent area in the East China Sea (ECS) in June, August and October, 2006. Profiles of bacterial communities were generated by denaturing gradient gel electrophoresis (DGGE) of 16S rRNA genes followed by DNA sequence analysis. The dominant bacterial groups were affiliated to Gammaproteobacteria, Cytophaga-Flavobacteria-Bacteroides (CFB), Deltaproteobacteria, Cyanobacteria and Firmicutes, which were mostly from the marine seawater ecosystem. Effects of environmental factors on the bacterial community distribution were analyzed by the ordination technique of canonical correspondence analysis (CCA). The environmental factors significantly influencing bacterial community structure were different in the three months; dissolved organic carbon (DOC) and temperature in June and nitrite in August. No environmental variables displayed significant influence on the bacterial community at the 5% level in October. The seasonal environmental heterogeneity in the Changjiang Estuary and the adjacent ECS, such as seasonal hydrodynamic conditions and riverine input of nutrients, might be the reason for the difference in the key environmental factors determining the bacterial community in the three months.

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Section: Environmental Characterizationmentioning

confidence: 97%

Temporal distribution of bacterial community structure in the Changjiang Estuary hypoxia area and the adjacent East China Sea

Liu

Xiao

et al. 2012

Environ. Res. Lett.

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“…DI was better matched to gradient‐changing salinities in this season. On the contrary, in winter, the CDW flowed southward under the influence of the EAWM and low CR discharge (Figure 1a) (Zhao, 1991), and the LCDs may not be sufficiently mixed. Besides, the salinity values at the same stations in the CRE and offshore area were higher in winter than those in summer due to the decrease in the CDW discharge (Table S2 in Supporting Information ).…”

Section: Discussionmentioning

confidence: 99%

“…A large volume of terrigenous material was deposited near the CRE because of the low intensity of the ZFCC in summer (Gong et al., 2011). In winter, CDW flowed southward along the Zhemin coast under the influence of the East Asian winter monsoon (EAWM; Zhao, 1991). The enhanced ZFCC, driven by the EAWM, transported sediments that were previously stored near the CRE southward (Li et al., 2007; Figure 1a).…”

Section: Methodsmentioning

confidence: 99%

Seasonal Variation of Long‐Chain Alkyl Diols Proxies in Suspended Particulate Matter of the Changjiang River Estuary

et al. 2022

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Long‐chain alkyl diols (LCDs) were applied as indicators of salinity, sea surface temperature (SST), upwelling, and nutrient conditions in marine settings. While increasing the body of most applications of LCDs proxies reconstructed paleo‐environment information, few studies reported seasonal variation in LCDs and evaluated their applicability as environmental indicators in modern marine environments. Here, the composition and distribution of LCDs in suspended particulate matter (SPM) in three seasons in the Changjiang River Estuary (CRE) were analyzed to evaluate seasonal influence on the application of LCDs as environmental indicators. We found that the reconstructed temperature based on the long‐chain diol index (LDI; LDI = C30 1,15‐diol/(C28 1,13‐diol + C30 1,13‐diol + C30 1,15‐diol)) was not consistent with satellite‐measured SST, likely due to vertical mixing of LCDs in this region. The 1,14‐diols previously used to indicate upwelling conditions, did not reflect the nutrient distribution of this region due to the Changjiang River (CR) nutrients discharge. Our results showed that the mean relative proportions of FC32 1,15‐diol (FC32 1,15‐diol = C32 1,15‐diol × 100%/(C28 1,13‐diol + C30 1,13‐diol + C30 1,15‐diol + C32 1,15‐diol)) gradually decreased from nearshore to offshore (71.1%, 37.4%, and 16.5%, respectively), suggesting that FC32 1,15‐diol was a reliable proxy for riverine input to the CRE. We found that the diol index (DI; DI = C30 1,15‐diol × 100/(C30 1,15‐diol + C32 1,15‐diol)) values were correlated strongly with salinities in spring (R2 = 0.82) and summer (R2 = 0.94), indicating that DI can be considered as a useful indicator for salinity construction in this estuary.

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“…No results are output. The number of terms that can be converged when calculating high waves using the Fourier series method is 41 (Zhao et al [47]). When N > 40, the FSA not converging for high waves on deep water is an interesting mathematical problem.…”

Section: Error Sources Of Fsamentioning

confidence: 99%

“…Rienecker and Fenton [22] concluded that the FSA is essentially a numerical technique for the approximation of continuous periodic functions and is valid for almost waves at all depths. After using Fourier series to represent the surface wave profile, Newton's iteration method associated with relaxation technology was used to solve the unknowns of the simultaneous nonlinear equations by Zhao et al [47]. The application of the FSA to the shoaling of nonlinear waves over a gently sloping bottom was studied by Chang [48] and Eldrup and Andersen [49].…”

Section: Introductionmentioning

confidence: 99%

Accuracy Examination of the Fourier Series Approximation for Almost Limiting Gravity Waves on Deep Water

Chen,

Chang

2024

MCA

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A permanent gravity wave propagating on deep water is a classic mathematical problem. However, the Fourier series approximation (FSA) based on the physical plane was examined to be valid for almost waves at all depths. The accuracy of the FSA for almost-limiting gravity waves remains unevaluated, which is the purpose of this study. We calculate some physical properties of almost-limiting waves on deep water using the FSA and compare them with other studies on the complex plane. The comparison results show that the closer the wave is, the greater the difference. We find that the main reason for this difference is that the wave profile in the FSA retains an original implicit form and is not represented by Fourier series. Therefore, the kinematic and dynamic conditions of the free surface around the wave crest cannot be satisfied at the same time.

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On the Fourier approximation method for steady water waves

Cited by 5 publications

References 21 publications

Temporal distribution of bacterial community structure in the Changjiang Estuary hypoxia area and the adjacent East China Sea

Temporal distribution of bacterial community structure in the Changjiang Estuary hypoxia area and the adjacent East China Sea

Seasonal Variation of Long‐Chain Alkyl Diols Proxies in Suspended Particulate Matter of the Changjiang River Estuary

Accuracy Examination of the Fourier Series Approximation for Almost Limiting Gravity Waves on Deep Water

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