O. Álvarez

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.

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.

Characterization of wave climate and extreme events into the SW Spanish and Wales coasts as a first step to define their wave energy potential

ABSTRACT Rangel- Buitrago, N., Anfuso, G., Alvarez, O., Phillips, M., Thomas, T., M. Forero. 2013. Characterization of wave climate and extreme events into the SW Spanish and Wales coasts as a first step to define their wave energy potential. Proceedings 13th International Coastal Symposium (Durban, South Africa), Journal of Coastal Research, Special Issue No. 70, pp. 314–319, ISSN 0749-0208. The characterization of wave climate and extreme events is a key issue for planning coastal and offshore activities. The energy sector is obliged to use alternative sources directed towards environment friendly renewable energy. Ocean waves constitute a potential source of this kind of energy and detailed knowledge of site specific wave climates constitutes the first step in developing a wave energy system. Consequently, this work deals with the analysis of wave climate at Cadiz (SW Spanish Atlantic coast) and Tenby (S Wales, UK). At the former site, wave records include 22 years of data covering the period between 1987 and 2008. Offshore wave climate showed clear cyclic variations in average monthly significant wave height (Hs). Waves were usually low (Hs<0.8 m, Cadiz - Hs<1.0 m, Tenby) from May to August (late spring to summer), reaching minimum values in August (Hs = 0.6 m Cadiz - Hs = 1.0 m Tenby). Winter waves rapidly increased in height, reaching peak values (Hs = 1.2 m, Cadiz, Hs = 2.1 m, Tenby) between December and January. Energy patterns calculated using the equation of wave energy flux, showed monthly averages at Cadiz and Tenby of circa 5 kW/m and 15 kW/m respectively that reached average values of 37 kW/m and 155 kW/m respectively, during winter. Despite this, Atlantic coastal locations receive less attention when compared with other coastlines around the world since they are considered to be relatively calm areas. Wave power values recorded in this research suggest that the SW Spanish Atlantic and South Wales coastal areas are potential sources of renewable energy.

Synthetic aperture radar image analysis as a tool for validation of baroclinic internal wave 3D modeling in Algeciras Bay (Strait of Gibraltar)

This paper presents the main results obtained from the application of synthetic aperture radar (SAR) sea surface image analysis to the validation of the baroclinic internal wave 3D modeling in the Strait of Gibraltar and Algeciras Bay. Appropriate SAR images, showing the occurrence of short-wavelength oscillations in the sea surface in this area, were selected and compared with the modeled spatial fields of the M2 free-surface elevation at the corresponding tidal stages, sometimes corrected for the consideration of neap or spring episodes. A good agreement between SAR images and model fields was found. The analysis of SAR images has showed to be a powerful tool for the study of the internal wave phenomena in the Strait of Gibraltar and Algeciras Bay, providing a holistic way for the validation of 3D model experiments in that matter.