Boris A. Kagan

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.

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.

Earth—Moon tidal evolution: model results and observational evidence

Abstract There are five datasets which can be used to verify models of the Earth—Moon tidal evolution. Those are: (1) geological evidence of the age of earth and lunar rocks; (2) paleontological and sedimentological data of growth increments in marine invertebrate fossils, stromatolite growth patterns and cyclically laminated, thin-bedded sediments; (3) astronomical data of the secular lunar orbit motion acceleration; (4) lunar laser ranging and satellite tracking data; and (5) estimates of tidal energy dissipation derived from global paleotide models. It is shown that models of the Earth—Moon tidal evolution come into conflict with one or the other dataset if they do not take into account the fluctuating effects of continental drift and their associated changes in resonance properties of the ocean on geological timescales. The simplest of all possible ways out is to parameterize the response of the ocean to the tide-generating force by a multi-mode resonance approximation with time-dependent frequencies of resonance modes and to assume that the ocean resonance lifetime is much shorter than the duration of the cycle of consolidation—disintegration of continents.

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.

Numerical simulation of tides in the World Ocean: 3. A solution to the spectral problem

The spectral problem is formulated as an initial boundary-value problem for free oscillations excited by an arbitrary initial disturbance. Numerical solution to this problem shows that the spectrum of eigenoscillations of the World Ocean in a range of periods from 8 hours and above contains more than 30 energetically significant modes. In particular, in semi-diurnal and diurnal spectral bands, there are modes with periods 11.96; 12.50; 12.68; 12.82 and 22.50; 23.87; 25.90 h quite close to the periods of main harmonics of the tide-generating potential. This fact, together with qualitative similarity of spatial pattern of these modes and observed tides, can be a direct proof of the resonance origin of semi-diurnal and diurnal tides in the World Ocean.

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.

Numerical simulation of tides in the World Ocean: 1. Parameterization of the shelf effects

Two methods of shelf parameterization are proposed: one of the local and the other of the integral type. The paper gives the results of testing these methods using a calculation of tides according to Webbs [1976] and von Trepkas [1967] model oceans as an example. The proposed methods of shelf effect parameterization provide a quite acceptable accuracy of simulation of semi-diurnal tides in the open ocean, but in some cases they underestimate the tidal energy dissipation on the shelf. The latter circumstance is caused by the ignored effect of edge waves with a longitudinal scale of the order of the shelf width.

Numerical simulation of tides in the World Ocean: 2. Experiments of the sensitivity of the solution to choice of the shelf effect parameterization and to variations in shelf parameters

A numerical solution to the problem of tides in the World Ocean taking into account the shelf effects is described. Results of the numerical experiments show that the spatial structure and energetics of global semi-diurnal tides are quite sensitive to the choice of the shelf effect parameterization and to the variations in shelf parameters. This fact can be regarded as indirect evidence of the resonant nature of semi-diurnal tides in the World Ocean.

A reconstruction of the tides in the paleocean: Results of a numerical simulation

Results of a calculation of the spectrum of eigenoscillations, spatial structure and energy characteristics of the M2-tidal wave in the paleocean for nine periods of the Phanerozoic are discussed. It has been shown that consolidation of the continents causes attenuation of the semi-diurnal and amplification of the diurnal eigenoscillations and vice versa, isolation of the continents contributes to amplification of the semi-diurnal oscillations and attenuation of the diurnal ones. Changes in the resonant properties of the World Ocean result in a reconstruction of spatial structure of the tides and in evolution of the tidal energy dissipation. As it retreats to the past, the tidal energy dissipation first decreases and then, beginning from the period between the Late Carboniferous — Early Permian, increases reaching its maximum in the Early Cambrian.

Modelling of global ocean tides with allowance for island effects

Parameterization schemes for single islands, island chains and archipelagos are described. It is shown that their utilization within the framework of a global tidal model leads not only to local peculiarities in the spatial structure of tidal characteristics, but also to cardinal restructuring of the tidal pattern far beyond the islands and an appreciable increase (about 0.5·1012W) of the global tidal energy dissipation. The latter is commensurable by the order of magnitude with the imbalance between estimates of tidal energy dissipation in the World Ocean as a whole and on the continental shelf.