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A. K. Azad
and
J. Latham

Abstract

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A. K. Azad
and
J. Latham

Abstract

In order to assess quantitatively the role of drop disintegrations in producing the electrification of warm clouds, it is necessary to establish the electrohydrodynamical equations governing the stability of drops subjected to electrical forces. In the present paper a theoretical and experimental study is presented of the disintegration of drops raised to equal and opposite potentials.

In his theoretical treatment of the deformation and disintegration of individual water drops of undistorted radius R 0 raised to a potential V, Taylor assumed that the drop retained a spheroidal shape until the instability point was reached and that the equations of equilibrium between the stresses due to surface tension T, the potential V, and the difference between the external and internal pressures was satisfied at the poles and the equator. He showed that since there is no stationary value for V as the elongation a/b increases, the only stable condition is when the drop is stable and V(π R 0 T)−½ < 4. Taylor's spheroidal assumption has been applied to the problem of the deformation and disintegration of pairs of drops raised to equal and opposite potentials. In this case directionality is imposed upon the problem by the attractive forces between the drops which provide a contribution, increasing with decreasing separation, to the outwardly-directed stresses in their surfaces. Stationary values of V were found to exist at values of a/b > 1, and the corresponding values of V(π R 0 T)−½ were less than 4.0 by a factor which increased rapidly as the initial separation was decreased. These critical values of V(π R 0 T)−½ at the disintegration point ranged from Rayleigh's value of 4.0 at infinite separations to 3.117, 6.842 × 10−1, 2.880 × 10−2 and 8.654 × 10−4 for initial separations of 10, 1, 0.1 and 0.01 radii, respectively. These values of V(π R 0 T)−½ are slightly reduced for larger drops owing to the influence of the hydrostatic pressure difference between their vertical extremities.

These calculations were tested experimentally on suspended drops of water, aniline and benzene, and good agreement was obtained in all cases. High speed photographs indicated that the process of disintegration was similar to that observed by Taylor, with an extremely rapid transformation (<10−8 sec) from an approximately spheroidal shape to a conical profile. Measurements taken from the photographs demonstrated that the radius of curvature and the elongation of a drop at the moment of disintegration agreed quite closely with the predicted values.

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Alfred J. Kalyanapu
,
A. K. M. Azad Hossain
,
Jinwoo Kim
,
Wondmagegn Yigzaw
,
Faisal Hossain
, and
C. K. Shum

Abstract

Recent research in mesoscale hydrology suggests that the size of the reservoirs and the land-use/land-cover (LULC) patterns near them impact the extreme weather [e.g., probable maximum flood (PMF)]. A key question was addressed by W. Yigzaw et al.: How do reservoir size and/or LULC modify extreme flood patterns, specifically PMF via modification of probable maximum precipitation (PMP)? Using the American River watershed (ARW) as a representative example of an impounded watershed with Folsom Dam as the flood control structure, they applied the distributed Variable Infiltration Capacity (VIC) model to simulate the PMF from the atmospheric feedbacks simulated for various LULC scenarios. The current study presents a methodology to extend the impacts of these modified extreme flood patterns on the downstream Sacramento County, California. The research question addressed is, what are the relative effects of downstream flood hazards to population on the American River system under various PMF scenarios for the Folsom Dam? To address this goal, a two-dimensional flood model, the Flood in Two Dimensions–Graphics Processing Unit (Flood2D-GPU), is calibrated using synthetic aperture radar (SAR) and Landsat satellite observations and observed flood stage data. The calibration process emphasized challenges associated with using National Elevation Dataset (NED) digital elevation model (DEM) and topographic light detection and ranging (lidar)–derived DEMs to achieve realistic flood inundation. Following this calibration exercise, the flood model was used to simulate four land-use scenarios (control, predam, reservoir double, and nonirrigation). The flood hazards are quantified as downstream flood hazard zones by estimating flood depths and velocities and its impacts on risk to population using depth–velocity hazard relationships provided by U.S. Bureau of Reclamation (USBR). From the preliminary application of methodology in this study, it is evident from comparing downstream flood hazard that similar trends in PMF comparisons reported by W. Yigzaw et al. were observed. Between the control and nonirrigation, the downstream flood hazard is pronounced by −3.90% for the judgment zone and −2.40% for high hazard zones. Comparing the control and predam scenarios, these differences are amplified, ranging between 0.17% and −1.34%. While there was no change detected in the peak PMF discharges between the control and reservoir-double scenarios, it still yielded an increase in high hazard areas for the latter. Based on this preliminary bottom-up vulnerability assessment study, it is evident that what was observed in PMF comparisons by W. Yigzaw et al. is confirmed in comparisons between control versus predam and control versus nonirrigation. While there was no change detected in the peak PMF discharges between the control and reservoir-double scenarios, it still yielded a noticeable change in the total areal extents: specifically, an increase in high hazard areas for the latter. Continued studies in bottom-up vulnerability assessment of flood hazards will aid in developing suitable mitigation and adaptation options for a much needed resilient urban infrastructure.

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