Abstract
The dynamic state index (DSI) is a scalar field that combines variational information on the total energy and vorticity of a flow field with the second law of thermodynamics. Its magnitude is a combined local measure for non-stationarity, diabaticity, and dissipation in the flow, and it has been shown to provide good qualitative indications for the onset and presence of precipitation and the organization of storms. The index has been derived thus far for ideal fluid models only, however, so that one may expect more detailed insights from a revised definition of the quantity that includes more complex aerothermodynamics. The present paper suggests definitions of DSI-like indicators for flows of moist air with phase changes and precipitation. In this way, the DSI is generalized to signal deviations from a variety of different types of balanced states. A comparison of these indices evaluated with respect to one and the same flow field enables the user to test whether the flow internally balances any combination of the physical processes encoded in the generalized DSI-indices.
Highlights
The Dynamic State Index (DSI) is a parameter based on first principles of fluid mechanics that indicates local deviations of the atmospheric flow field from a stationary, adiabatic, and inviscid solution of the non-hydrostatic compressible governing equations
The point of departure for the present developments is the observation that the original dry air DSI has a representation in terms of the mass flow divergence of Schär’s13 “steady wind,” vst, 62, 123101-13
We considered water vapor together with phase changes to account for cloud formation, and third, we have included the fallout of precipitation
Summary
The Dynamic State Index (DSI) is a parameter based on first principles of fluid mechanics that indicates local deviations of the atmospheric flow field from a stationary, adiabatic, and inviscid solution of the non-hydrostatic compressible governing equations. In this way, the DSI can be evaluated on a given atmospheric flow field to detect atmospheric developments, such as fronts or hurricanes. The originally introduced DSI by Névir is based on the adiabatic non-hydrostatic compressible governing equations for dry air without consideration of thermodynamical sources and sinks, such as solar forcing, in the basic state In this case, regarding (1), ψ corresponds to the potential temperature, B is the Bernoulli function (or total enthalpy) (see Ref. 16, Sec. 1.10), and Π is Ertel’s potential vorticity formed with the potential temperature as the advected scalar (see Ref. 16, Sec. 4.5). This DSI concept can be applied to indicate non-steady, diabatic, and frictional atmospheric processes across all scales: Weber and Névir showed how the characteristic dipole structure of the dynamic state index can be used to diagnose the evolution of highand low-pressure areas on the synoptic scale or hurricanes on the meso-scale. Several authors have shown that the DSI is strongly correlated with intensive precipitation processes; see, e.g., the work of Claussnitzer et al., Gaßmann, and Weijenborg et al.
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