Premium
Weak‐ and strong‐friction limits of parcel models: Comparisons and stochastic convective initiation time
Author(s) -
HernandezDuenas Gerardo,
Smith Leslie M.,
Stechmann Samuel N.
Publication year - 2019
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.3557
Subject(s) - mechanics , convection , drag , buoyancy , limit (mathematics) , physics , limiting , classical mechanics , statistical physics , mathematics , mathematical analysis , mechanical engineering , engineering
For moist convection, models of individual parcel dynamics are valuable for their simple formulation and predictions of cloud properties. Here, two limiting idealized cases of parcel theory are investigated: the weak‐ and strong‐friction limits. The weak‐friction limit is a traditional limit with no momentum drag and the dynamics are a Hamiltonian system for the parcel's height and vertical velocity. A strong‐friction limit is derived and studied here and its limiting form involves a balance between frictional drag and buoyancy, which provides a differential equation for parcel height as a function of time. In the two limiting regimes, analytical formulas are presented and compared for quantities such as maximum vertical velocity and cloud‐top height. For example, in the strong‐friction limit, the cloud‐top height coincides with the level of neutral buoyancy (LNB), whereas in the weak‐friction limit the cloud‐top height is far above the LNB. This comparison suggests that the strong‐friction limit may provide more realistic predictions of some averaged cloud properties. In general, since frictional effects and individual parcel properties can vary even within a single cloud, the predictions of the weak‐ and strong‐friction limits can be viewed as upper and lower bounds for the behavior of more realistic finite‐friction scenarios. Finally, in a stochastic version of the parcel model, in the strong‐friction limit, analytical formulas are derived for convective initiation time. Applications to convective parametrizations are discussed; for example, the formulas for convective initiation time could be applied as stochastic convective triggers.