Jeffreys' Drag Instability Applied to Waves in the Lower Atmosphere: Linear and Nonlinear Growth Rates

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  • 1 School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, Georgia
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Abstract

In a geostrophically balanced region of the atmosphere the horizontal pressure gradients do no work since they are aligned at right angles to the winds, but near the earth's surface where friction destroys geostrophic balance these large-scale pressure gradients can feed energy into smaller-scale flows. One mechanism through which this occurs is Jeffreys' drag instability, a mechanism normally associated with the formation of waves on a sloping sheet of water but equally capable of generating a variety of waves in the lower atmosphere. This study examines Jeffeys' drag instability, as a source of large amplitude boundary layer waves that fall off exponentially above a shallow surface layer, and large amplitude gravity wave modes ducted in the overlying troposphere. jeffreys' formulation is modified to the atmospheric context and modeled to compute conditions that support the linear and nonlinear growth of various waves. Several regimes of instability are identified, but the greatest growth rates are associated with waves propagating upstream in boundary layer jets, a wind form that is characteristic of the Ekman layer. Analysis of some observed waves of remarkable amplitude indicates that they occurred under conditions that strongly favored Jeffreys' drag mechanism. It is also suggested that the drag mechanism allows waves in the boundary layer to generate turbulence and drive mixing at the expense of the available potential energy in the larger scales.

Abstract

In a geostrophically balanced region of the atmosphere the horizontal pressure gradients do no work since they are aligned at right angles to the winds, but near the earth's surface where friction destroys geostrophic balance these large-scale pressure gradients can feed energy into smaller-scale flows. One mechanism through which this occurs is Jeffreys' drag instability, a mechanism normally associated with the formation of waves on a sloping sheet of water but equally capable of generating a variety of waves in the lower atmosphere. This study examines Jeffeys' drag instability, as a source of large amplitude boundary layer waves that fall off exponentially above a shallow surface layer, and large amplitude gravity wave modes ducted in the overlying troposphere. jeffreys' formulation is modified to the atmospheric context and modeled to compute conditions that support the linear and nonlinear growth of various waves. Several regimes of instability are identified, but the greatest growth rates are associated with waves propagating upstream in boundary layer jets, a wind form that is characteristic of the Ekman layer. Analysis of some observed waves of remarkable amplitude indicates that they occurred under conditions that strongly favored Jeffreys' drag mechanism. It is also suggested that the drag mechanism allows waves in the boundary layer to generate turbulence and drive mixing at the expense of the available potential energy in the larger scales.

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