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  • Author or Editor: Katharine M. Kanak x
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Katharine M. Kanak
and
Douglas K. Lilly

Abstract

An investigation in made of the linear stability and structure of convection embedded in a mean shear flow with a circular hodograph. This can he considered an extension of Asai's work, but with emphasis on the rotational and helicity features of the disturbances. It also examines the relevance of the Beltrami flow solutions presented previously by Lilly and Davics-Jones, which could not be directly extended to consider the effects of buoyancy. The Boussinesq equations we applied to neutrally and unstably stratified fluids, with emphasis placed on the inviscid solutions. Upper and lower boundary conditions are free slip and rigid. Lateral conditions are periodic, which allows casting the disturbance equations into a horizontally periodic normal-mode structure. The growth rates and disturbance forms are generally fairly similar to the results presented by Asai, except that the most unstable modes are nearly always oriented transverse to the shear component at the channel center. The most rapidly growing modes at small Richardson number are found to be highly helical, with the helicity obtained from the Beltrami mean state. The helicity transfer efficiency and disturbance relative helicity decrease rapidly, however, for negative, Richardson numbers greater than about 1.

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Alan Shapiro
and
Katharine M. Kanak

Abstract

The rise of an isolated dry thermal bubble in a quiescent unstratified environment is a prototypical natural convective flow. This study considers the rise of an isolated dry thermal bubble of ellipsoidal shape (elliptical in both horizontal and vertical cross sections). The azimuthal asymmetry of the bubble allows the vorticity tilting mechanism to operate without an environmental wind. The dry Boussinesq equations of motion are solved analytically as a Taylor series in time for the early time behavior of the bubble (involving derivatives of up to the third order in time). The analytic results are supplemented with numerical simulations to examine the longer-time behavior. The first nonzero term in the Taylor expansion for the vertical vorticity is a third-order term, and appears as a four-leaf clover pattern with lobes of alternating sign. The horizontal flow associated with this vorticity pattern first appears as a sheared stagnation point-type flow, but eventually organizes into vertical vortices that fill the bubble. The vortices induce large structural changes to the bubble and eventually reverse the sense of the azimuthal asymmetry.

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Katharine M. Kanak
,
Jerry M. Straka
, and
David M. Schultz

Abstract

Mammatus are hanging lobes on the underside of clouds. Although many different mechanisms have been proposed for their formation, none have been rigorously tested. In this study, three-dimensional numerical simulations of mammatus on a portion of a cumulonimbus cirruslike anvil are performed to explore some of the dynamic and microphysical factors that affect mammatus formation and evolution. Initial conditions for the simulations are derived from observed thermodynamic soundings. Five observed soundings are chosen—four were associated with visually observed mammatus and one was not. Initial microphysical conditions in the simulations are consistent with in situ observations of cumulonimbus anvil and mammatus. Mammatus form in the four model simulations initialized with the soundings for which mammatus were observed, whereas mammatus do not form in the model simulation initialized with the no-mammatus sounding. Characteristics of the modeled mammatus compare favorably to previously published mammatus observations.

Three hypothesized formation mechanisms for mammatus are tested: cloud-base detrainment instability, fallout of hydrometeors from cloud base, and sublimation of ice hydrometeors below cloud base. For the parameters considered, cloud-base detrainment instability is a necessary, but not sufficient, condition for mammatus formation. Mammatus can form without fallout, but not without sublimation. All the observed soundings for which mammatus were observed feature a dry-adiabatic subcloud layer of varying depth with low relative humidity, which supports the importance of sublimation to mammatus formation.

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