Rabah Aider - Academia.edu (original) (raw)

Papers by Rabah Aider

Research paper thumbnail of Symmetry-breaking in periodic gravity waves with weak surface tension and gravity-capillary waves on deep water

Comptes Rendus Mecanique, 2004

The method developed by Debiane and Kharif for the calculation of symmetric gravity-capillary wav... more The method developed by Debiane and Kharif for the calculation of symmetric gravity-capillary waves on infinite depth is extended to the general case of non-symmetric solutions. We have calculated non-symmetric steady periodic gravity-capillary waves on deep water. It is found that they appear via bifurcations from a family of symmetric waves. On the other hand we found that the symmetry-breaking bifurcation of periodic steady class 1 gravity wave on deep water is possible when it approaches the limiting profile, if it is very weakly influenced by surface tension effects. To cite this article: R. Aider, M. Debiane, C. R. Mecanique 332 (2004).La méthode développée par Debiane et Kharif pour le calcul des ondes de gravité-capillarité symétriques en profondeur infinie a été étendue aux cas de vagues à profils non-symétriques. Nous avons calculé des ondes de gravité-capillarité non-symétriques périodiques et de formes permanentes. Elles apparaissent via des bifurcations à partir d'une solution symétrique. D'autre part, nous avons trouvé qu'en présence d'une très faible tension de surface, la brisure de symétrie d'une onde de gravité périodique de classe 1 en profondeur infinie est possible à l'approche de sa forme limite. Pour citer cet article : R. Aider, M. Debiane, C. R. Mecanique 332 (2004).

Research paper thumbnail of A method for the calculation of nonsymmetric steady periodic capillary–gravity waves on water of arbitrary uniform depth

Comptes Rendus Mécanique, 2006

In this Note the method developed by for the calculation of nonsymmetric water waves on infinite ... more In this Note the method developed by for the calculation of nonsymmetric water waves on infinite depth is extended to finite depth. The water-wave problem is reduced to a system of nonlinear algebraic equations which is solved by using Newton's method. Solutions are computed up to their limiting forms by decrementing the depth from the infinity to a value of the depth-wavelength ratio h/λ less than 0.025. It is found that the waves become symmetric when the depth becomes very small. Relations giving some integral properties are derived. To cite this article: R. Aider, M. Debiane, C. R. Mecanique 334 (2006).

Research paper thumbnail of Symmetry-breaking in periodic gravity waves with weak surface tension and gravity-capillary waves on deep water

Comptes Rendus Mécanique, 2004

The method developed by Debiane and Kharif for the calculation of symmetric gravity-capillary wav... more The method developed by Debiane and Kharif for the calculation of symmetric gravity-capillary waves on infinite depth is extended to the general case of non-symmetric solutions. We have calculated non-symmetric steady periodic gravity-capillary waves on deep water. It is found that they appear via bifurcations from a family of symmetric waves. On the other hand we found that the symmetry-breaking bifurcation of periodic steady class 1 gravity wave on deep water is possible when it approaches the limiting profile, if it is very weakly influenced by surface tension effects. To cite this article: R. Aider, M. Debiane, C. R. Mecanique 332 (2004).  2004 Académie des sciences. Published by Elsevier SAS. All rights reserved. Résumé Brisure de symétrie dans les vagues de gravité avec une faible tension de surface et les vagues de gravité-capillarité périodiques en eau profonde. La méthode développée par Debiane et Kharif pour le calcul des ondes de gravité-capillarité symétriques en profondeur infinie a été étendue aux cas de vagues à profils non-symétriques. Nous avons calculé des ondes de gravité-capillarité non-symétriques périodiques et de formes permanentes. Elles apparaissent via des bifurcations à partir d'une solution symétrique. D'autre part, nous avons trouvé qu'en présence d'une très faible tension de surface, la brisure de symétrie d'une onde de gravité périodique de classe 1 en profondeur infinie est possible à l'approche de sa forme limite. Pour citer cet article : R. Aider, M. Debiane, C. R. Mecanique 332 (2004).

Research paper thumbnail of An assessment of Canadian prairie drought: past, present, and future

Climate Dynamics, 2013

Within Canada, the Canadian Prairies are particularly drought-prone mainly due to their location ... more Within Canada, the Canadian Prairies are particularly drought-prone mainly due to their location in the lee of the western cordillera and distance from large moisture sources. Although previous studies examined the occurrence of Canadian Prairie droughts during instrumental, pre-instrumental and to a lesser extent, future periods, none have specifically focused on all time three scales. Using two different drought indicators, namely the Palmer Drought Severity Index (PDSI) and Standardized Precipitation Index (SPI), this investigation assesses the variability of summer drought duration and intensity over a core region of the Prairies during (a) the pre-instrumental record extending back several centuries (inferred from tree rings), (b) the instrumental record , and (c) the twenty-first century using statistically downscaled climate variables from several Atmosphere-Ocean Global climate models with multiple emission scenarios. Results reveal that observed twentieth century droughts were relatively mild when compared to pre-settlement on the Prairies, but these periods are likely to return (and even worsen) in the future due to the anticipated warming during the course of the twenty-first century. However, future drought projections are distinctly different between the two indices. All PDSI-related model runs show greater drought frequency and severity mainly due to increasing temperatures. Conversely, the precipitation-based SPI indicates no significant changes to future summer drought frequency although there tends to be a higher persistence of multi-year droughts in central and southern portions of Canadian Prairies. These findings therefore stress the importance of considering anticipated warming trends when assessing future regional-scale drought, especially given the uncertainties and lack of consistency in future precipitation signals among climate models. This study can be considered an initial step toward quantifying and understanding Canadian Prairie drought occurrence and severity over several centuries as determined from paleo, instrumental, and climate model data sources.

Research paper thumbnail of Symmetry-breaking in periodic gravity waves with weak surface tension and gravity-capillary waves on deep water

Comptes Rendus Mecanique, 2004

The method developed by Debiane and Kharif for the calculation of symmetric gravity-capillary wav... more The method developed by Debiane and Kharif for the calculation of symmetric gravity-capillary waves on infinite depth is extended to the general case of non-symmetric solutions. We have calculated non-symmetric steady periodic gravity-capillary waves on deep water. It is found that they appear via bifurcations from a family of symmetric waves. On the other hand we found that the symmetry-breaking bifurcation of periodic steady class 1 gravity wave on deep water is possible when it approaches the limiting profile, if it is very weakly influenced by surface tension effects. To cite this article: R. Aider, M. Debiane, C. R. Mecanique 332 (2004).La méthode développée par Debiane et Kharif pour le calcul des ondes de gravité-capillarité symétriques en profondeur infinie a été étendue aux cas de vagues à profils non-symétriques. Nous avons calculé des ondes de gravité-capillarité non-symétriques périodiques et de formes permanentes. Elles apparaissent via des bifurcations à partir d'une solution symétrique. D'autre part, nous avons trouvé qu'en présence d'une très faible tension de surface, la brisure de symétrie d'une onde de gravité périodique de classe 1 en profondeur infinie est possible à l'approche de sa forme limite. Pour citer cet article : R. Aider, M. Debiane, C. R. Mecanique 332 (2004).

Research paper thumbnail of A method for the calculation of nonsymmetric steady periodic capillary–gravity waves on water of arbitrary uniform depth

Comptes Rendus Mécanique, 2006

In this Note the method developed by for the calculation of nonsymmetric water waves on infinite ... more In this Note the method developed by for the calculation of nonsymmetric water waves on infinite depth is extended to finite depth. The water-wave problem is reduced to a system of nonlinear algebraic equations which is solved by using Newton's method. Solutions are computed up to their limiting forms by decrementing the depth from the infinity to a value of the depth-wavelength ratio h/λ less than 0.025. It is found that the waves become symmetric when the depth becomes very small. Relations giving some integral properties are derived. To cite this article: R. Aider, M. Debiane, C. R. Mecanique 334 (2006).

Research paper thumbnail of Symmetry-breaking in periodic gravity waves with weak surface tension and gravity-capillary waves on deep water

Comptes Rendus Mécanique, 2004

The method developed by Debiane and Kharif for the calculation of symmetric gravity-capillary wav... more The method developed by Debiane and Kharif for the calculation of symmetric gravity-capillary waves on infinite depth is extended to the general case of non-symmetric solutions. We have calculated non-symmetric steady periodic gravity-capillary waves on deep water. It is found that they appear via bifurcations from a family of symmetric waves. On the other hand we found that the symmetry-breaking bifurcation of periodic steady class 1 gravity wave on deep water is possible when it approaches the limiting profile, if it is very weakly influenced by surface tension effects. To cite this article: R. Aider, M. Debiane, C. R. Mecanique 332 (2004).  2004 Académie des sciences. Published by Elsevier SAS. All rights reserved. Résumé Brisure de symétrie dans les vagues de gravité avec une faible tension de surface et les vagues de gravité-capillarité périodiques en eau profonde. La méthode développée par Debiane et Kharif pour le calcul des ondes de gravité-capillarité symétriques en profondeur infinie a été étendue aux cas de vagues à profils non-symétriques. Nous avons calculé des ondes de gravité-capillarité non-symétriques périodiques et de formes permanentes. Elles apparaissent via des bifurcations à partir d'une solution symétrique. D'autre part, nous avons trouvé qu'en présence d'une très faible tension de surface, la brisure de symétrie d'une onde de gravité périodique de classe 1 en profondeur infinie est possible à l'approche de sa forme limite. Pour citer cet article : R. Aider, M. Debiane, C. R. Mecanique 332 (2004).

Research paper thumbnail of An assessment of Canadian prairie drought: past, present, and future

Climate Dynamics, 2013

Within Canada, the Canadian Prairies are particularly drought-prone mainly due to their location ... more Within Canada, the Canadian Prairies are particularly drought-prone mainly due to their location in the lee of the western cordillera and distance from large moisture sources. Although previous studies examined the occurrence of Canadian Prairie droughts during instrumental, pre-instrumental and to a lesser extent, future periods, none have specifically focused on all time three scales. Using two different drought indicators, namely the Palmer Drought Severity Index (PDSI) and Standardized Precipitation Index (SPI), this investigation assesses the variability of summer drought duration and intensity over a core region of the Prairies during (a) the pre-instrumental record extending back several centuries (inferred from tree rings), (b) the instrumental record , and (c) the twenty-first century using statistically downscaled climate variables from several Atmosphere-Ocean Global climate models with multiple emission scenarios. Results reveal that observed twentieth century droughts were relatively mild when compared to pre-settlement on the Prairies, but these periods are likely to return (and even worsen) in the future due to the anticipated warming during the course of the twenty-first century. However, future drought projections are distinctly different between the two indices. All PDSI-related model runs show greater drought frequency and severity mainly due to increasing temperatures. Conversely, the precipitation-based SPI indicates no significant changes to future summer drought frequency although there tends to be a higher persistence of multi-year droughts in central and southern portions of Canadian Prairies. These findings therefore stress the importance of considering anticipated warming trends when assessing future regional-scale drought, especially given the uncertainties and lack of consistency in future precipitation signals among climate models. This study can be considered an initial step toward quantifying and understanding Canadian Prairie drought occurrence and severity over several centuries as determined from paleo, instrumental, and climate model data sources.