The island-scale internal wave climate of Moorea, French Polynesia

Analysis of five-year records of temperatures and currents collected at Moorea reveal strong internal wave activity at predominantly semi-diurnal frequencies impacting reef slopes at depths 30m around the entire island. Temperature changes of 1.5C to 3C are accompanied by surges of upward and onshore flow and vertical shear in onshore currents. Superimposed on annual temperature changes of approximately 3C, internal wave activity is high from Oct-May and markedly lower from Jun-Sep. The offshore pycnocline is broadly distributed with continuous stratification to at least 500m depth, and a subsurface fluorescence maximum above the strong nutricline at approximately 200m. Minimum buoyancy periods range from 4.8 to 6min, with the maximum density gradient occurring at 50 to 60m depth in summer and deepening to approximately 150 to 200m in winter. The bottom slope angle around all of Moorea is super-critical relative to the vertical stratification angle suggesting that energy propagating into shallow water is only a portion of total incident internal wave energy. Vertical gradient Richardson numbers indicate dominance by density stability relative to current shear with relatively limited diapycnal mixing. Coherence and lagged cross-correlation of semi-diurnal temperature variation indicate complex patterns of inter-site arrival of internal waves and no clear coherence or lagged correlation relationships among island sides. Semi-diurnal and high frequency internal wave packets likely arrive on Moorea from a combination of local and distant sources and may have important impacts for nutrient and particle fluxes in deep reef environments. © 2012 American Geophysical Union. All Rights Reserved.

Una perspectiva de análisis de las transformaciones geométricas en curvas de la función f(x)=e^ax utilizando el GeoGebra

Con el propósito de superar algunas dificultades de los profesores en la integración de tecnologías en la enseñanza de las matemáticas, se presenta una secuencia de análisis de las trasformaciones geométricas de la función exponencial natural, definida por f(x)=e^ax, que se apoya en el uso del GeoGebra. Tal secuencia permite caracterizar familias de curvas asociadas a la expresión anterior, a partir del análisis de las transformaciones geométricas “deformación” y “reflexión” experimentadas por estas curvas tras la variación del parámetro a. En el diseño de la secuencia se tomó en cuenta aspectos de teóricos, instrumentales y didácticos, que se consideran pertinentes para realizar el análisis. El uso de esta secuencia favorece el desarrollo de las capacidades para la integración eficiente de las tecnologías en la enseñanza de la Matemática.