A Synoptic Study of Deformation Fields

VUORELA, L.

doi:10.3402/tellusa.v5i3.8577

TellusA

1953

DOI: 10.3402/tellusa.v5i3.8577

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A Synoptic Study of Deformation Fields

L. VUORELA

Abstract: An attempt has been made to compute thc field of horizontal deformation for a few synoptic situations. Some reasons for the rather high lalues of dilatation obtained arc discussed and criticism over the method is p;esented.ERNEST, 1952: A Comparison between Observed and Computed Winds with Respect to their Applicability for Vorticity Coniputations. Tr,llus, 4. PANOFSKY, H. A,, 1946: Mcthods of Computing Vertical Motion in the Atniosphcre. J . hlefeor, 3, 45-49. 126-134.

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Studies on the General Development of Motion in a Two-Dimensional, Ideal Fluid

Welander¹

1955

Tellus

103

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The purpose of this paper is to discuss qualitatively certain kinds of asymptotic motion in a two‐dimensional, ideal fluid by help of methods of statistical mechanics. It is stressed that the final development of such a fluid cannot be adequately described by use of the ordinary equations of motion, but that a “coarse grain” representation should be used. In this representation, the development is characterized by the forming of a single, large vortex accompanied by a certain non‐viscous dissipation. The final equilibrium is probably reached almost explosively after a finite time. Some experiments which are carried out seem to support this result. In the earlier stages of development we may expect to have some kind of a quasi‐equilibrium motion. It is attempted to find conditions under which such a motion can exist, by studies of a point‐vortex model.

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Studies on the General Development of Motion in a Two-Dimensional, Ideal Fluid

Welander¹

1955

Tellus

103

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Contraction Rate and Its Relationship to Frontogenesis, the Lyapunov Exponent, Fluid Trapping, and Airstream Boundaries

Cohen

Schultz

2005

Monthly Weather Review

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Although a kinematic framework for diagnosing frontogenesis exists in the form of the Petterssen frontogenesis function and its vector generalization, a similar framework for diagnosing airstream boundaries (e.g., drylines, lee troughs) has not been constructed. This paper presents such a framework, beginning with a kinematic expression for the rate of change of the separation vector between two adjacent air parcels. The maximum growth rate of the separation vector is called the instantaneous dilatation rate and its orientation is called the axis of dilatation. Similarly, a maximum decay rate is called the instantaneous contraction rate and its orientation is called the axis of contraction. These expressions are related to the vector frontogenesis function, in that the growth rate of the separation vector corresponds with the scalar frontogenesis function, and the rotation rate of the separation vector corresponds with the rotational component of the vector frontogenesis function.Because vorticity can rotate air-parcel pairs out of regions of deformation, the instantaneous dilatation and contraction rates and axes may not be appropriate diagnostics of airstream boundaries for fluid flows in general. Rather, the growth rate and orientation of an airstream boundary may correspond better to the so-called asymptotic contraction rate and the asymptotic axis of dilatation, respectively. Expressions for the asymptotic dilatation and contraction rates, as well as their orientations, the asymptotic dilatation and contraction axes, are derived. The asymptotic dilatation rate is related to the Lyapunov exponent for the flow. In addition, a fluid-trapping diagnostic is derived to distinguish among adjacent parcels being pulled apart, being pushed together, or trapped in an eddy. Finally, these diagnostics are applied to simple, idealized, steady-state flows and a nonsteady idealized vortex in nondivergent, diffluent flow to show their utility for determining the character of air-parcel trajectories and airstream boundaries.

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Studies on the General Development of Motion in a Two-Dimensional, Ideal Fluid

Welander

1955

TellusA

114

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The purpose of this paper is to discuss qualitatively certain kinds of asymptotic motion in a two-dimensional, ideal fluid by help of methods of statistical mechanics. It is stressed that the final development of such a fluid cannot be adequately described by use of the ordinary equations of motion, but that a "coarse grain" representation should be used. In this representation, the development is characterized by the forming of a single, large vortex accompanied by a certain non-viscous dissipation. The final equilibrium is probably reached almost explosively after a finite time. Some experiments which are carried out seem to support this result. In the earlier stages of development we may expect to have some kind of a quasi-equilibrium motion. It is attempted to find conditions under which such a motion can exist, by studies of a point-vortex model.

show abstract

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A Synoptic Study of Deformation Fields

Cited by 3 publications

References 2 publications

Studies on the General Development of Motion in a Two-Dimensional, Ideal Fluid

Studies on the General Development of Motion in a Two-Dimensional, Ideal Fluid

Contraction Rate and Its Relationship to Frontogenesis, the Lyapunov Exponent, Fluid Trapping, and Airstream Boundaries

Studies on the General Development of Motion in a Two-Dimensional, Ideal Fluid

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