Generación y y propagación de ondas internas en el Estrecho de Gibraltar: efectos 3-D y de rotación
Resumen Abstract Índice Conclusiones
José Carlos Sánchez Garrido
2010-A
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La presente tesis doctoral pretende ahondar en el conocimiento de la dinámica de ondas internas de gran amplitud generadas en el océano debido a la interacción de corrientes de marea con elementos de la topografía submarina. Se analiza en particular los efectos de de la rotación terrestre sobre en estas ondas, así como efectos tridimensionales derivados. El estudio se centra fundamentalmente en un punto extraordinariamente particular del océano global como es el Estrecho de Gibraltar, dónde ondas internas de más de 100 metros de amplitud son generadas regularmente. No obstante, el documento también contiene algunos capítulos que abordan aspectos generales de la dinámica de ondas no lineales en un contexto eminentemente teórico.
El Capítulo 1 contiene una introducción en la que se pone de manifiesto la importancia de las ondas internas generadas por flujos de marea barotrópica en el océano. Recientes estudios revelan que juegan un papel determinante en los procesos de mezcla, que a su vez dan lugar a la circulación termohalina global según el bien conocido postulado de Sandström. Debido a ello se concluye también que sin mareas, cuya energía es transferida parcialmente a ondas internas y finalmente a mezclas, la vida y el clima que actualmente conocemos no seria posible.
El Capítulo 2 está dedicado a un repaso de teoría de ondas. El Capítulo 3 contiene un estudio publicado en la revista Journal of Geophysical Research-Oceans (Sánchez Garrido, J. C., J. García Lafuente, F. Criado Aldeanueva, A. Baquerizo, and G. Sannino 2008, Time-spatial variability observed in velocity of propagation of the internal bore in the Strait of Gibraltar, J. Geophys. Res., 113, C07034, doi:10.1029/2007JC004624) sobre propiedades cinemáticas de ondas internas en el Estrecho de Gibraltar a partir de datos “in situ” de temperatura y velocidades de corrientes. Se concluye que las componentes de marea diurna modulan significativamente la generación de ondas y su velocidad de propagación por medio de un mecanismo de advección.
Los Capítulos 4 y 5 presentan un estudio numérico de la propagación tridimensional de ondas solitarias a través del Estrecho. Los datos experimentales comentados anteriormente motivaron esta investigación. Los paquetes de ondas observados presentan frecuentemente una estructura anómala: ondas propagándose en la parte delantera de los paquetes de onda presentan mayores amplitudes que las ondas que la suceden, en contra de la teoría clásica que sólo contempla estructuras con amplitudes decrecientes de cabeza a cola del paquete de ondas debido a la dispersión no lineal (ondas de mayor amplitud viajan más rápido). Éste fenómeno es estudiado de forma numérica con el modelo de circulación general del Massachusetts Institute of Technology (MITgcm), que es un modelo 3-D, completamente no lineal y no hidrostático. Se concluye en el estudio, publicado en la revista Journal of Physical Oceanography (Vlasenko V., J.C. Sanchez Garrido, N. Stashchuk, J.G. Lafuente and M. Losada 2009) Three-dimensional evolution of large-amplitude internal waves in the Strait of Gibraltar. Journal of Physical Oceanography, 39(9), 2230-2246) que el anómalo efecto es consecuencia de la generación de ondas secundarias fruto de la interacción de las entrantes al Estrecho con la irregular topografía del fondo. Se concluye también que estas interacciones son más importantes en la costa sur debido a la rotación terrestre.
El capítulo 6 contiene un estudio numérico-teórico sobre los efectos a largo término de la rotación sobre ondas solitarias fuertemente no lineales o de gran amplitud. Según el paradigma establecido por la teoría débilmente no lineal en los últimos 30 años, ondas estables que mantienen su forma, tipo ondas solitarias, no pueden existir bajo efectos de la rotación debido a la dispersión rotatoria: la onda inicial pierde energía a lo largo de su propagación en forma de ondas secundarias (ondas de Poincaré), las cuales son irradiadas hacia atrás debido a su menor velocidad de propagación. El procesos es terminal, es decir, toda la energía inicial se pierde en ondas secundarias en un tiempo finito. En esta investigación se demuestra que este escenario no es aplicable a ondas fuertemente no lineales debido a la formación de ondas secundarias tipo Kelvin, las cuales se propagan más rápido que el solitón inicial para interaccionar con él con el paso del tiempo. Esta interacción da lugar a un paquete de ondas kelvin con escasa pérdida de energía en forma de ondas secundarias, los cuales pueden propagarse durante cientos de kilómetros sin cambia aparente de forma. Constituyen por tanto un objeto quasi-estacionaria.
Este trabajo fue publicado en la revista Nonlinear Processes in Geophysics (Sánchez-Garrido, J. C. and Vlasenko, V.: Long-term evolution of strongly nonlinear internal solitary waves in a rotating channel, Nonlin. Processes Geophys., 16, 587-598, doi:10.5194/npg-16-587-2009, 2009.), y ha sido seleccionada en los EGU (European Geosciences Union) Journal Highlights (ver https://www.egu-media.net/content/view/207/47/).
Finalmente el capítulo 7 aborda el problema de generación de ondas internas no lineales y saltos hidráulicos en el umbral de Camarinal, el principal umbral del Estrecho de Gibraltar. El estudio numérico tridimensional de altísima resolución concluye que bajo forzamientos de marea moderados las ondas internas en el Estrecho de Gibraltar proceden de dos saltos hidráulicos generados aguas arriba del umbral. En términos de teoría hidráulica de flujos bicapa, condiciones supercríticas aguas arriba son producidas por el estrechamiento de la capa de agua atlántica superficial. Estos dos saltos hidráulicos evolucionan hacia ondas cortas tipo ondas solitarias debido a efectos no lineales y dispersivos, que interaccionan a pocos kilómetros al Este del umbral. Durante mareas vivas, los dos saltos hidráulicos se fusionan en uno y es desplazado aguas abajo en la cuenca el Tánger. Bajo este escenario de fuerte forzamiento barotrópico otros importantes saltos hidráulicos se forman aguas abajo en la parte Atlántica del Estrecho, los cuales contribuyen notablemente a la mezcla de aguas Atlánticas y Mediterráneas salientes en profundidad por el Estrecho. Este trabajo ha sido recientemente enviado para publicar a la revista Journal of Geophysical Research-Oceans (J.C Sánchez- Garrido, G. Sannino, L. liberti, and J. García-Lafuente; Generation of Large-Amplitude Internal Waves in the Strait of Gibraltar: a Three-Dimensional Numerical Study, submitted).
Three-dimensional and Earth’s rotation effects on the generation and propagation of internal solitary waves in the Strait of Gibraltar are studied. These tidally generated waves, with horizontal scale of several hundred meters and even one hundred meters amplitude (maximum vertical isopycnal displacement), are the most spectacular phenomenon occurring in the Strait.
The analysis of high temporal resolution observations collected during May 2003 at two different locations of the Strait of Gibraltar is the starting point of the thesis. Data set reveals that during neap tides solitary waves are normally generated during alternative tidal cycles due to the influence of the diurnal tide, which induces a remarkable diurnal inequality. It is shown that diurnal tidal currents in fact considerably modulate the propagation velocity of internal waves.
About half the detected solitary wave packets present an anomalous structure: in contrast with classical theory predictions, waves are not rank-ordered within the packet, that is, they do not show decreasing amplitude from the front to the tail, due to the nonlinear dispersion. This fact is investigated within the framework of a three-dimensional, fully nonlinear, non-hydrostatic numerical model. It is shown that this unexpected behaviour is the result of the interaction of internal waves with the irregular bottom topography and lateral boundaries of the Strait, that favour the leakage of energy from the leading wave to the waves behind.
The effect of rotation on the dynamics of internal solitary waves in a rectangular channel is also numerically investigated. As it happens in the open ocean, rotation plays a fundamental role in the long-term. When a two-dimensional internal solitary wave enters a rotating channel it evolves into a Kelvin solitary wave that losses energy due to the continuous radiation of Poincar\’e waves. Eventually secondary Kelvin waves may arise at the tail as a result of reflections from the lateral boundaries, and finally reach the leading wave to produce a quasi-stable wave packet.
Finally the numerical model has been used to investigate the generation process of internal waves at Camarinal sill, in the Strait of Gibraltar. Several scenarios of wave generation, which depends on the barotropic tidal forcing, are identified. Rotation and 3D effects related to local variations of the bottom topography are also evaluated.
1.- Some aspects of internal solitary waves (ISWs) kinematics have been derived from the analysis of high time-resolution observations in the Strait of Gibraltar. Although tides are mainly semidiurnal in the Strait, diurnal tidal currents play a significant role in the generation and subsequent propagation of ISWs. It has been observed that normally during neap tides ISWs are generated during alternative tidal cycles due to the diurnal inequality. Moreover, due to the importance of tidal advection on the propagation velocity of ISWs, there exists a remarkable diurnal inequality on it. The phase speed of two consecutives wave packets of ISWs can differ as much as 0.4 m/s between the western section of Tarifa Narrows and the entrance of the Alboran Sea. The diurnal inequality is even more noticeable when observing the arrival time (relative to high water) of ISWs to the latter location: consecutives wave packets can arrive with a maximum time difference as high as 6 hours at this point with respect to the high water time at Ceuta.
2.- Observation of temperature records reveals that ISWs packets quite often present an irregular structure. Statistical analysis of all recorded wave trains (46 well defined packets) reveals that only 46.5% of them can be identified as well rank-ordered wave trains (decreasing wave amplitude from the front to the tail). The rest, i.e. 53.5% of packets, was either partly rank-ordered (23.3%) or chaotic rather than organized (30.2%). This abnormal fact was investigated within the framework of a high resolution, fully nonlinear, non-hydrostatic numerical model. It was found that the interaction of the ISWs with the complex bottom topography and lateral boundaries of the Strait leads to wave reflections and formation of secondary waves which in turn produces such irregular ISWs packets structure. The energy reflected back from the boundaries is partially absorbed by the smaller ISWs propagating at the rear of the packet, this making these smaller waves increase their amplitude. This mechanism is responsible for the formation of non rank-ordered wave packets.
3.- Coriolis force plays a significant role on the ISWs dynamics in the Strait of Gibraltar, a result that is not unexpected since the first internal Rossby radius if about the Strait width. Because of rotation ISWs tend to accumulate energy at the Southern coast of the Strait (to the right of the direction of the wave propagation in the northern hemisphere), a fact that enhances wave-topography interactions on this shore, such as wave reflection, wave breaking, and derived mixing processes.
4.- Motivated by recent interesting results concerning long-term processes induced by rotation on ISWs dynamics in an open ocean (Helfrich 2007), an analogous study has been carried out for a rectangular channel of constant depth. It was found that an initial straight soliton evolves rapidly into a Kelvin wave-like soliton, with exponential cross-channel distribution of amplitude. This evolution, which agrees with the weakly nonlinear theory predictions, takes place through the continuous radiation of Poincaré modes, responsible of the fast energy damping of the leading Kelvin mode. As a result of multiple reflections with the lateral boundaries, a Mach stem system is formed behind the leading soliton, which eventually transform into a secondary Kelvin wave that collides with the leading perturbance. At the end, a quasi-steady wave packet of Kelvin waves is formed with few energy damping by radiation.
This mechanism of secondary wave formation and final collision with the leading perturbance is enhanced, as either the amplitude of the initial soliton, or the effect rotation, or the channel width increase.
5.- A tidally forced model has been run in order to investigate 3D characteritiscs of the generation mechanism of ISWs over Camarinal Sill. The model is 3D, high resolution, fully nonlinear, and fully non-hydrostatic. A first scrutiny of the vast information it provides has allowed us to distinguish four different scenarios of internal waves generation, which depend on the intensity of the tidal forcing. In terms of the maximum value of the internal Froude number during the tidal cycle, they are the following:
Frmax < 1.0: Generation of internal tides (long wavelength tidal wave).
Frmax = 1.0: Generation of ISWs as a result of the nonlinear evolution of the long wavelength internal tide.
1.0 < Frmax < 1.6: Generation of ISWs as a result of the evolution of a double internal bore generated in Camarinal Sill. One leewards, the other just over Camarinal crest. It is argued that local ondulatory variations of the bottom topography at Camarinal Sill favour such structure.
Frmax > 1.6 : Generation of a huge internal bore trapped at the lee side of Camarinal Sill, which evolves into a series of energetic unsteady Lee waves. The further evolution of this baroclinic structure leads to the formation of ISWs of more than 150 meters nearby Tarifa Narrows.
6.- Transversal (across channel) variations of the baroclinic response at Camarinal Sill are mainly driven by rotation effects and local variations of the bottom topography. Due to the influence of rotation on the barotropic (external) tides, amplitude of semidiurnal tidal currents (dominant in the Strait) are smaller at the northern section of the channel, and phases are delayed. Because of it, the baroclinic bore trapped by tidal currents at Camarinal is locally released before at the northern section, which induces a regular pattern on the shape of the generated ISWs wave front: at the beginning of its evolution it goes ahead in the north of the Strait. Eventually this asymmetry tends to fade out as the influence of rotation starts exerting influence directly on the internal dynamics. Solitary waves accumulate energy at the southern section and the wave front tilts anticlockwise, compensating the initial inclination.
7.- The numerical experiments do not predict the generation of ISWs propagating westward of the Strait. This is in agreement with observations, and the idea that this »western» bore, must be linked to a shallower second pycnocline formed during the summer season.