Frictional interactions between tidal constituents in tide-dominated estuaries

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 (M2, S2, N2, O1, K1) 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.

THE NUMERICAL MODELLING OF TIDES IN A SHALLOW SEMI-ENCLOSED BASIN BY A MODIFIED ELLIPTIC METHOD

A numerical model which renders possible the numerical solution of the nonlinear tidal equations by obtaining a solution for each individual tidal component is developed. For this purpose, a set of time independent non-linear equations for each tidal constituent is constructed. Each of these sets of equations is interrelated through the non-linear frictional terms, the approximation of which is accomplished by an iterative scheme. The method is tested for several models before it is applied to the real basin (Bight of Abaco). In order to evaluate the model and to construct the boundary conditions along the opening, a series of tidal observations were undertaken. The viability of the method is indicated by the fact that the results of computations using a coefficient of friction r = 0.0034 give good agreement with observations for all components and over all stations.

Frictional interactions between tidal constituents in tide-dominated estuaries

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 the Guadalquivir (Spain) estuaries for different tidal constituents (M2, S2, N2, O1, K1) 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.

EFFECT OF LONG TERM TIDAL CONSTITUENTS ON MEAN SEA LEVEL TREND DURING EL-NINO AND LA-NINA PHENOMENA

There are many factors that influence the change of the tidal constituent pattern. The factors can be classified as astronomical factors and non- astronomical factors. The astronomical factors involve the gravitational force attraction by the moon and sun. The distance of sun and moon influence the gravitational attractions that are produced by the moon and sun towards earth surface. Non-astronomical factors involved the movements of currents, waves, temperature and so on which is cause by the phenomenon such as El-Nino, La-Nina. This study was conducted to investigate the effect of these phenomena towards the pattern of tidal constituent during the phenomenon on several stations that have been chosen. The difference stations were chose due to the change in the position of celestial body. In addition, tidal data for several stations were processed using the UTM Tidal Analysis and Prediction Software (μ-TAPS). Based on the tidal data that has been processed, the graphs were plotted for the predicted data and observed data to compare the different pattern between the data. The tidal data that has been processed were used to analyse the pattern of tidal constituents based on the changing amplitude of M₂, S₂, K₁, O₁, S_a, S_sa, Mm, Mf and MSf.

The Influence of Subinertial Internal Tides on Near-Topographic Turbulence at the Mendocino Ridge: Observations and Modeling

Shipboard measurements of velocity and density were obtained in the vicinity of a small channel in the Mendocino Ridge, where flows were predominantly tidal. Measured daily inequalities in transport are much greater than those predicted by a barotropic tide model, with the strongest transport associated with full depth flows and the weakest with shallow, surface-confined flows. A regional numerical model of the area finds that the subinertial K1 (diurnal) tidal constituent generates topographically trapped waves that propagate anticyclonically around the ridge and are associated with enhanced near-topographic K1 transports. The interaction of the baroclinic trapped waves with the surface tide produces a tidal flow whose northward transports alternate between being surface confined and full depth. Full depth flows are associated with the generation of a large-amplitude tidal lee wave on the northward face of the ridge, while surface-confined flows are largely nonturbulent. The regional model demonstrates that, consistent with field observations, near-topographic dissipation over the entire ridge is diurnally modulated, despite the semidiurnal tidal constituent having larger barotropic velocities. It is concluded that at this location it is the bottom-trapped subinertial internal tide that governs near-topographic dissipation and mixing. The effect of the trapped wave on regional energetics is to increase the fraction of converted barotropic–baroclinic tidal energy that dissipates locally.

Inversion of Tidal Open Boundary Conditions of the M2 Constituent in the Bohai and Yellow Seas

Open boundary conditions (OBCs) of the M2 tidal constituent in the Bohai and Yellow Seas (BYS) were inverted successfully through assimilation of TOPEX/Poseidon (T/P) altimeter data. An improved independent points (IPs) scheme was employed in the inversion. Under the assumption that the OBC was spatially varying, values at a set of IPs along the open boundary were inverted using the adjoint method and those at other points were calculated by the spline interpolation. The OBC inverted with the improved scheme was closer to reality in terms of smoothness than that inverted with the Cressman interpolation. The scheme was calibrated in twin experiments. Practical experiments showed that the misfits between simulated results and observations were smaller when the spline interpolation was used.

HIGH AND LOW WATER PREDICTION AT LAGOS HARBOUR, NIGERIA

In this work, 500 hourly water level tidal data were used to perform least squares tidal harmonic analysis. Eleven tidal constituents were used for the harmonic analysis. Astronomical arguments (v + u) and the nodal factor (f) were computed for each tidal constituent and at each observational period with a programme written in Matlab environment. The harmonic constants determined from the least squares tidal harmonic analysis were substituted into a tidal prediction model to predict hourly tidal data and tidal predictions at 5 minutes’ intervals. Series of high and low water heights from the tidal predictions made at 5 minutes’ intervals were determined and matched with their corresponding times. Autocorrelation at lags 1 to 30 for the residuals of the observed and predicted tidal data shows that there is no significant correlation in the range of the 30 lags. The series of residuals of the observed and predicted tidal data is therefore white noise.   http://dx.doi.org/10.4314/njt.v36i3.39

On Tidal Inference in the Diurnal Band

Standard methods of tidal inference should be revised to account for a known resonance that occurs mostly within the K1 tidal group in the diurnal band. The resonance arises from a free rotational mode of Earth caused by the fluid core. In a set of 110 bottom-pressure tide stations, the amplitude of the P1 tidal constituent is shown to be suppressed relative to K1, which is in good agreement with the resonance theory. Standard formulas for the K1 nodal modulation remain essentially unaffected. Two examples are given of applications of the refined inference methodology: one with monthly tide gauge data and one with satellite altimetry. For some altimeter-constrained tide models, an inferred P1 constituent is found to be more accurate than a directly determined one.

Extraction of Internal Tidal Currents and Reconstruction of Full-Depth Tidal Currents from Mooring Observations

To obtain internal tidal currents and full-depth tidal currents from limited mooring observations, a method is put forward combining harmonic analysis and modal decomposition. Harmonic analysis is used to separate tidal currents of different constituents, and modal decomposition is used to calculate full-depth tidal currents of each mode. By adding the barotropic tidal currents to all the baroclinic ones, the full-depth tidal currents of each constituent are reconstructed. The feasibility and accuracy of the proposed method is tested by twin experiments. Then, the method is used to extract tidal currents of each mode and to reconstruct full-depth tidal currents for M2 and K1 from a 3-month-long time series of acoustic Doppler current data observed at a station in the northern South China Sea. Results indicate that the total kinetic energy (KE) of M2 is 25% larger than that of K1. For M2, the first baroclinic mode is the dominant one, followed by the barotropic one, and the sum of these modes accounts for more than 90% of the total M2 KE. Tidal constituent K1 is dominated by the barotropic mode, which accounts for more than 90% of the total K1 KE.