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Federico Porcù, Leo Pio D’Adderio, Franco Prodi, and Clelia Caracciolo

1. Introduction After the formulation of a warm rain formation theory ( Langmuir 1948 ), many research activities aimed at gaining deeper knowledge of the main processes that determine the microphysical structures of liquid precipitation. In particular, drop collision/coalescence and breakup were recognized as the main mechanisms to take place in the falling rain and able to define the drop size distribution (DSD) measured at the ground level, if evaporation (below cloud base) and diffusional

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John W. Glendening

-dimensional instability resultsfrom interactions between parallel line vortices, akin toinstability in a vortex sheet but with neighboring circulations having opposite sign. Thorpe (1992) foundthat such interactions predicted along-roll instabilitylengths that agreed reasonably with Langmuir cell observations, so this theory will be quantitatively compared to results from the present simulation. The linear'inviscid theory predicts two different instability mechanisms for three-dimensional disturbances: a pairedvortex

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H. R. Pruppacher and R. L. Pitter

could not be computed bySavic. 6) He neglected the presence of an internal circulation in a falling drop, and its effects on the drop shape.However, Garner and Lane (1959) and Pruppacher andBeard (1970) have shown that water drops falling in airhave well-developed internal circulations. We investigated each of these deficiencies in Savic'smodel and attempted to improve upon them in ours.The complete equation for the balance of forces arounda drop can be found as follows. Using, as illustrated

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Dehai Luo

1. Introduction In Part I of this paper (Luo 2005) , we have established a new model to describe the interaction between synoptic-scale eddies and an incipient block consisting of a dipole soliton and a topographically induced standing wave. This model can describe the relationship between the evolution of synoptic-scale eddies and the development of the blocking anomaly during the life cycle of a blocking circulation, and compares well with features obtained from a composite of many

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Alan J. Faller

-meter diameterrotating tank which was formerly in use at the WoodsHole Oceanographic Institution for these studies. Acirculation was generated by pumping water from thecenter and redistributing it uniformly around the rim.The equilibrium circulation consisted of a circularvortex with a shallow Ekman boundary-layer flow atthe bottom where the required inward transport ofwater took place. The tangential speed U above theboundary layer, in response to a pumping rate S, variedinversely with radius r by

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Tracy Haack and Hampton N. Shirer

dynamically and convectively forced boundary-layer rolls are studiedwith linear and nonlinear analyses of a truncated spectral model of shallow Boussinesq flow. Emphasis is givenhere on the energetics of the dominant roll modes, on the magnitudes of the roll-induced modifications of theinitial basic-state wind and temperature profiles, and on the sensitivity of the linear stability results to the useof modified profiles as basic states. It is demonstrated that the roll circulations can produce substantial

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David Raymond and Marvin Wilkening

convection over an isolated mountain range heated by the sun arepresented. Filter techniques are used to deduce those scales of motion of significance to the circulation.A two-scale process is observed in which a toroidal, heat island circulation -20 km in diameter is drivenby 3-4 km convective eddies. Large negative heat fluxes are found in the upper part of the convectivecore over the mountains.1. Introduction It is well known that in the mountainous westernUnited States thunderstorms form

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J. W. Telford and N. S. C. Thorndike

knowledge is necessary inany theoretical treatment of the coalescence processof rain formation such as was made by Bowcn (1950),Telford (1955) or Twoniey (1959).The term "collection eficiency" is used to suinniarize the complex aerodynamic trajectories followed bytwo colliding droplets and gives the proportion of theprojected area of the drop from which smaller dropletswill be captured. Theoretical studies have been madeby Langmuir and Blodgett (1946), Pearcey and Hill(1957) and Hocking (1959) which

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Huiwen Xue, Alfred M. Moyle, Nathan Magee, Jerry Y. Harrington, and Dennis Lamb

β M,i in Eq. (7) (see Table 2 ). d. Droplet models Most models for atmospheric application fall into two categories: those that treat the growth of individual drops (a Lagrangian approach) and those that treat the growth of entire populations (distributions) of drops (an Eulerian approach). Many of the individual-drop studies were initiated before computer power was sufficient for detailed computations, and most of these studies simply used Langmuir’s (1961) compensated diffusion

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David J. Stensrud and Hampton N. Shirer

. Kayior, 1966: A numerical study of the in stability of the laminar Ekman boundary layer. J. Atmos. Sci., 23, 466-480. Gammelsmd, T., 1975: Instability of Couette flow in a rotating fluid and origin of Langmuir circulations. J. Geophys. Res., 80, 5069 5075.Gelaro, R., 1987a: Linear stability analysis. Nonlinear Hydrodynamic Modeling.',4 Mathematical Introduction, H. N. Shirer, Ed. Lec ture Notes in Physics, 271, Springer-Verlag, 70-85. ,1987b: Bifurcation analysis of stationary

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