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Developing Disturbances in Shear

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  • 1 Harvard University, Cambridge, MA 02138
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Abstract

The origin and growth to moderate amplitude of disturbances in shear flow has been traditionally ascribed to the linear modal instability of the flow. Recent work on initial value problems has suggested that nonmodal growth of perturbations may be of equal and perhaps greater importance, at least in cases of rapid development. Examples of robust growth in model problems which support no instabilities and in baroclinic flows with realistic Ekman damping for which the exponential modes have zero or negative growth rates have been shown. Such examples have focused attention on the perturbations which are configured to tap the energy of mean flows. Here a critical examination of these favorably configured perturbations is given, making use of the simple constant free shear barotropic model which allows construction of exact two-dimensional isolated wave packet solutions.

Abstract

The origin and growth to moderate amplitude of disturbances in shear flow has been traditionally ascribed to the linear modal instability of the flow. Recent work on initial value problems has suggested that nonmodal growth of perturbations may be of equal and perhaps greater importance, at least in cases of rapid development. Examples of robust growth in model problems which support no instabilities and in baroclinic flows with realistic Ekman damping for which the exponential modes have zero or negative growth rates have been shown. Such examples have focused attention on the perturbations which are configured to tap the energy of mean flows. Here a critical examination of these favorably configured perturbations is given, making use of the simple constant free shear barotropic model which allows construction of exact two-dimensional isolated wave packet solutions.

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