L. Tejedor

Simulation of the semidiurnal tides in the Strait of Gibraltar

The M2 and S2 surface tides in the Strait of Gibraltar are simulated using a two-dimensional, nonlinear, boundary-fitted coordinate model with a nominal resolution of ∼0.5 km. Good agreement is achieved with tide gauge and bottom pressure observations, as well as with current measurements made during the Gibraltar Experiment. The cotidal charts and the maps of tidal current ellipse parameters, which have been constructed on the basis of the model results, reproduce all of the known features of the spatial structure of the M2 and S2 tidal waves. These results also show that a ∼90° phase difference between tidal velocity and elevation is detected in much of the Strait of Gibraltar, thus suggesting a small mean tidal energy flux through the strait. The model results give evidence of the general direction for the M2 and S2 net tidal energy fluxes to the west. This finding is consistent with an observed southwestern tidal phase propagation and remains qualitatively unchanged when varying the straits geometry as well as boundary and astronomical forcings.

Non-linear interaction between tidal and subinertial barotropic flows in the Strait of Gibraltar

Abstract The present work establishes clear relationships of the amplitude and phase variation of the barotropic M 2 signal in the velocity of the current with the barotropic subinertial flow in the Strait of Gibraltar. The analytical procedure is applied on data from Gibraltar Experiment in order to obtain barotropic subinertial series and the amplitude and phase variation of the M 2 signal series involves harmonic analysis, empirical orthogonal function analysis and complex demodulation. In addition, cross-spectral analysis has been applied to study these relationships, concerning which non-linear interaction between M 2 and the subinertial oscillation is proposed as the responsible physical mechanism. An analytical solution characterizing this type of non-linear interaction is offered in explanation of the experimental results.

Vertical structure of the semidiurnal tidal currents at Camarinal Sill, the strait of Gibraltar

Abstract The dynamical mode decomposition (DMD) technique is applied to the data of currentmeter and CTD measurements taken during the 1985–1986 Gibraltar Experiment and the 1989 survey so as to clarify features of the vertical structure of the M2 and S2 tidal currents at the Camarinal Sill. It is shown that in conformity with the inference made on the basis of the empirical orthogonal function (EOF) decomposition technique, these currents are mainly due to the M2 and S2 barotropic modes. At the same time the first three baroclinic modes are responsible not only for the vertical variability of the tidal currents but also for the velocity and density amplitude variances at semidiurnal frequencies. Certain quantitative discrepancies between the values of barotropic tidal current characteristics as deduced from DMD and EOF decomposition techniques are revealed. In order to eliminate these, new currentmeter data are required with a finer vertical resolution than those which are available.

A note on sea-breeze-induced seasonal variability in the K1 tidal constants in Cádiz Bay, Spain

Abstract The response of Cadiz Bay to sea-breeze wind stress and tidal boundary forcing—individually and in combination—is studied using a 2D depth-averaged, non-linear, high-resolution hydrodynamic model. Linear superposition of the solution for the K 1 and S 1 constituents, like the solution obtained with an allowance for both the input functions together, is shown to give rise to a modulation of the K1 tidal dynamics. It is precisely this modulation which is responsible for the observed seasonal variations in the K 1 tidal constants in Cadiz Bay.

Weak wave–tide interaction formulation and its application to Cádiz bay

Abstract Using a single-point, one-equation ( k – l ) model for an oscillatory turbulent bottom boundary layer (BBL) above a hydrodynamically rough bottom and varying the external determining parameters over a wide range, we show that nonlinear wave/low-frequency current interaction effects are smaller, the greater are the ratio of near-bottom wave orbital velocity amplitude to friction-free, low-frequency current velocity amplitude and the ratio between frequencies of wave and low-frequency components of motion. Specifically, in shallow waters the bottom stress oscillations with wave and tidal frequencies are, with fair accuracy, weakly correlated, thereby suggesting that wave-tide interaction is substantially weak interaction. A new weak wave–tide interaction formulation is proposed. It involves a relationship for the drag coefficient in a wave-affected tidal flow and the surface Rossby number dependences for the scaled wave and tidal friction velocity amplitudes inferred from the resistance law for an oscillatory turbulent BBL over a hydrodynamically rough surface. This formulation is implemented within a 2D nonlinear, finite-difference, high-resolution, hydrodynamic model and the modified model is applied to quantify the wave-induced changes in the tidal dynamics and energetics of Cadiz Bay. The model results reveal one unexpected feature in the fields of maximum tidal velocity and mean tidal energy flux. Namely, wave–tide interaction responsible for enhancing the mean bottom stress throughout the bay tends to increase the maximum tidal velocities and the mean tidal energy fluxes at deeper depths and to reduce them at shallower depths. The reason for appearing this feature is an overall amplification of the mean tidal energy transport into the bay from Gulf of Cadiz. Based on the sensitivity study to varying wave parameters, the wave-induced seasonal variability in the M 2 tidal characteristics is found to be not pronounced in Cadiz Bay. This, however, does not rule out a clearly defined manifestation of such a variability in other shallow basins and/or in other tidal frequency bands. Special attention is given to identify the regions of potential suspended sediment transport and their wave-induced changes.

TIDES AND TIDAL ENERGETICS OF THE STRAIT OF GIBRALTAR : A MODELLING APPROACH

Abstract The main semidiurnal (M2 and S2) and diurnal (O1 and K1) tidal waves in the Strait of Gibraltar are simulated by employing a 2D high-resolution, non-linear, boundary-fitted coordinate model. Agreement between observational evidence and model results is good for the M2 and S2 tidal waves and satisfactory for the O1 and K1 tidal waves. The model reproduces all the known features of the spatial structure of these waves and predicts some new ones, namely, the general direction of the M2 and S2 mean tidal energy fluxes to the west, with a clear increase at the Camarinal Sill; the O1 amphidrome with anticlockwise rotation of cotidal lines in the Tarifa Narrows; and small-scale eddies in the M2, S2 and O1 mean tidal energy flux fields in the vicinity of the western and eastern boundaries of the Strait.

Weak wave/tide interaction in suspended sediment-stratified flow: a case study

Abstract The formulation of weak wind-wave/low-frequency current interaction is extended to the case of suspended sediment-stratified flow. The influence of suspended sediment stratification on flow dynamics is described in terms of a sediment stratification parameter defined as von Karmans constant times a depth-independent function of the relative friction velocity and the relative settling velocity of suspended particles that is specified by a solution for the problem on the vertical structure of the suspended sediment-stratified near-bottom logarithmic layer. This ‘extended’ formulation is inserted in a two-dimensional non-linear, finite-difference, high-resolution hydrodynamic model and the modified model is applied to clarify the roles of wind-wave/tide interaction and suspended sediment stratification—individually and in combination—in the formation of the M4 and M6 overtides in Cadiz Bay. It is shown that the predictions for the M4 and M6 overtides have much in common and much in contrast with the M2 tide. For the M2 tide the influence of suspended sediment stratification shows up most vividly in the spatial variability of the tidal characteristics, but is not evident in changes in the M4 and M6 overtides. On the other hand, the influence of wave-induced changes on the M2 tidal amplitude and phase is only of minor importance, but for the M4 and M6 overtides these changes are quite significant. When taken together, the effects of the two factors under investigation are very nearly balanced. This, however, does not mean that the conventional assumption of ignoring these factors is valid in shallow-water dynamics. Simply, that their resulting effect vanishes.

Weak wind-wave/tide interaction over a moveable bottom: results of numerical experiments in Cádiz Bay

Abstract The formulation of weak wind-wave/low-frequency current interaction is extended to the moveable rough bottom case using the bottom roughness predictors of Nielsen (Coastal Eng. 7 (1983) 233) and Tolman (J. Phys. Oceanogr. 24 (1994) 994). This “extended” formulation is then implemented in a 2D non-linear, high-resolution hydrodynamic model and the modified model is applied to study the changes in the tidal dynamics of Cadiz Bay due to wind-wave/tide interaction and bottom mobility. It is shown that an agreement between the observed and predicted tidal elevation amplitudes and phases at the tide-gauge and bottom-pressure measurement locations within the bay tend to be improved if both of these factors are accounted for. Distinctions between the solutions derived when employing Nielsens and Tolmans bottom roughness predictors are considerable though not so much as might be expected. The sensitivity of the solution to the mean sediment grain size turns out to be either moderate or low depending on which of the above-mentioned bottom roughness predictors is adopted and much less than the sensitivity to the tidal reference bottom roughness length. Accordingly, if the wave and tidal reference bottom roughness lengths are set equal to each other, the changes in the fields of tidal characteristics become unreasonable, thereby eliminating the possibility of prescribing a single reference bottom roughness length.