Tidal Spectroscopy of the English Channel with a Numerical Model

Provost, C. Le; Fornerino, M.

doi:10.1175/1520-0485(1985)015<1008:tsotec>2.0.co;2

Cited by 60 publications

(25 citation statements)

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“…-analytical analysis based on perturbation methods applied to the shallow-water equations (Le Provost 1974, 1976, 1991Kabbaj and Le Provost 1980); -physical modeling with a large (14 m) rotating platform with an astonishing vertical precision of 0.02 mm, corresponding to cm-level precision in the real world (Chabert d'Hières and Le Provost , 1979; -time stepping numerical modeling with both finitedifference and finite-element formulations (Le Provost and Fornerino 1985); -spectral numerical modeling, i.e., the frequency domain analog to the time-stepping codes (Le Poncet 1977, 1978;Le Provost et al 1981); and -data analysis (Chabert d'Hières and Le Provost 1979;Le Provost 1991;Ponchaut et al 2001).…”

Section: Introductionmentioning

confidence: 99%

“…1 and 2 are more significant in giving rise to which tidal effects. The work by Le Provost and Fornerino (1985), Pingree and Maddock (1978), and Walters and Werner (1991) demonstrated how the nonlinearities in the continuity equation dominate the generation of the M 4 , MS 4 and other tides in the English Channel. They also quantified the contribution from advection around capes and bottom friction to this constituent.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Mapping nonlinear shallow-water tides: a look at the past and future

Andersen¹,

Egbert

Erofeeva

et al. 2006

Ocean Dynamics

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Overtides and compound tides are generated by nonlinear mechanisms operative primarily in shallow waters. Their presence complicates tidal analysis owing to the multitude of new constituents and their possible frequency overlap with astronomical tides. The science of nonlinear tides was greatly advanced by the pioneering researches of Christian Le Provost who employed analytical theory, physical modeling, and numerical modeling in many extensive studies, especially of the tides of the English Channel. Le Provost's complementary work with satellite altimetry motivates our attempts to merge these two interests. After a brief review, we describe initial steps toward the assimilation of altimetry into models of nonlinear tides via generalized inverse methods. A series of barotropic inverse solutions is computed for the M 4 tide over the northwest European Shelf. Future applications of altimetry to regions with fewer in situ measurements will require improved understanding of error covariance models because these control the tradeoffs between fitting hydrodynamics and data, a delicate issue in coastal regions.While M 4 can now be robustly determined along the Topex/Poseidon satellite ground tracks, many other compound tides face serious aliasing problems.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mapping nonlinear shallow-water tides: a look at the past and future

Andersen¹,

Egbert

Erofeeva

et al. 2006

Ocean Dynamics

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“…The English Channel is well known for its tide-dominated hydrodynamic regime, associated with current fields which are quasi-homogeneous from surface to bottom. Hence, accurate simulations of instantaneous current fields can be obtained with the help of 2-dimensional horizontal hydrodynamic models (Le Provost & Fornerino 1985, Salomon & Breton 1991. However, as far as modelling nutrient cycling in the Channel as a whole is concerned, it seems reasonable to cope with time scales of several days or weeks, that is to say to highlight the long-term drift of water masses and to consider tidal oscillations a s dispersive processes.…”

Section: The Modelmentioning

confidence: 99%

Modelling the biogeochemical cycles of elements limiting primary production in the English Channel:I. Role of thermohaline stratification

Ménesguen¹,

Hoch²

1997

Mar. Ecol. Prog. Ser.

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This paper presents the general framework of a n ecological model of the English Channel. The model is a result of combining a physical sub-model with a biological one. In the physical submodel, the Channel is divided into 71 boxes and water fluxes between them are calculated automatically. A 2-layer, vertical thermohaline model was then linked with the horizontal circulation scheme. This physical sub-model exhibits thermal stratification in the western Channel during spring and summer and haline stratification in the Bay of Seine due to high flow rates from the river The biological sub-model takes 2 elements, nitrogen and silicon, into account and divides phytoplankton into diatoms and dinoflagellates. Results from this ecological model emphasize the influence of stratification on chlorophyll a concentrations a s well as on primary production. Stratified waters appear to be much less productive than well-mixed ones. Nevertheless, when simulated production values are compared with literature data, calculated production is shown to be underestimated. This could be attributed to a lack of refinement of the 2-layer box-model or processes omitted from the biological model, such as production by nanoplankton.

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“…Later, Inoue and Garrett (2007) used a novel approach to determine the Fourier coefficients of u|u|, which allows the magnitude of the effective friction coefficient to be determined for many tidal constituents. For the general two-dimensional tidal wave propagation, the expansion of quadratic bottom friction using a Fourier series was first proposed by Le Provost (1973) and subsequently applied to spectral models for regional tidal currents (Le Provost et al, 1981;Le Provost and Fornerino, 1985;Molines et al, 1989). Building on the previous work by Le Provost (1973), the importance of quadratic bottom friction in tidal propagation and damping was discussed by Kabbaj and Le Provost (1980) and reviews of friction terms in models were presented by Le Provost (1991).…”

Section: Introductionmentioning

confidence: 99%

Frictional interactions between tidal constituents in tide-dominated estuaries

et al. 2018

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Abstract. When different tidal constituents propagate along an estuary, they interact because of the presence of nonlinear terms in the hydrodynamic equations. In particular, due to the quadratic velocity in the friction term, the effective friction experienced by both the predominant and the minor tidal constituents is enhanced. We explore the underlying mechanism with a simple conceptual model by utilizing Chebyshev polynomials, enabling the effect of the velocities of the tidal constituents to be summed in the friction term and, hence, the linearized hydrodynamic equations to be solved analytically in a closed form. An analytical model is adopted for each single tidal constituent with a correction factor to adjust the linearized friction term, accounting for the mutual interactions between the different tidal constituents by means of an iterative procedure. The proposed method is applied to the Guadiana (southern Portugal-Spain border) and Guadalquivir (Spain) estuaries for different tidal constituents (M 2 , S 2 , N 2 , O 1 , K 1 ) imposed independently at the estuary mouth. The analytical results appear to agree very well with the observed tidal amplitudes and phases of the different tidal constituents. The proposed method could be applicable to other alluvial estuaries with a small tidal amplitude-to-depth ratio and negligible river discharge.

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Tidal Spectroscopy of the English Channel with a Numerical Model

Cited by 60 publications

References 0 publications

Mapping nonlinear shallow-water tides: a look at the past and future

Mapping nonlinear shallow-water tides: a look at the past and future

Modelling the biogeochemical cycles of elements limiting primary production in the English Channel:I. Role of thermohaline stratification

Frictional interactions between tidal constituents in tide-dominated estuaries

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