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- Author or Editor: G. Arnason x
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Abstract
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Abstract
A 2-parameter forecasting model which includes the effects of vertical vorticity advection and turning of the vortex tubes is briefly described. Contributions of the above-mentioned terms are discussed and an example is presented.
The importance of consistent truncation over a large grid is pointed out.
Abstract
A 2-parameter forecasting model which includes the effects of vertical vorticity advection and turning of the vortex tubes is briefly described. Contributions of the above-mentioned terms are discussed and an example is presented.
The importance of consistent truncation over a large grid is pointed out.
Abstract
The effects of the state of the sea on the safety and economy of a ship's route are of considerable concern to the U. S. Navy and other organizations engaged in shipping. This article deals specifically with the problem of determining a ship's minimal-time route between two ports of call as reflecting an important aspect of desirable routing. This is a minimum value problem and the governing differential equations are derived by use of the Calculus of Variations. The basic theory is essentially the same for a ship on the sea as for an aircraft in horizontal flight, but in application the two problems differ in the manner in which the environment impedes the forward speed of the vehicle.
Direct solution of the governing differential equations by numerical methods appears feasible with the aid of an electronic computer and the results of a test case are presented. For this purpose it was convenient to replace a series of empirical equations relating ship's speed to wave height and direction by a single analytical expression.
Inspection of the basic differential equations and the empirical relation between ship's speed and the state of the sea indicates that in the case of moderate wave heights, the dependence on wave direction may be omitted as a good approximation. This is borne out in the test case which also shows a considerable saving in computing time because of the resulting simplification of the differential equation.
Abstract
The effects of the state of the sea on the safety and economy of a ship's route are of considerable concern to the U. S. Navy and other organizations engaged in shipping. This article deals specifically with the problem of determining a ship's minimal-time route between two ports of call as reflecting an important aspect of desirable routing. This is a minimum value problem and the governing differential equations are derived by use of the Calculus of Variations. The basic theory is essentially the same for a ship on the sea as for an aircraft in horizontal flight, but in application the two problems differ in the manner in which the environment impedes the forward speed of the vehicle.
Direct solution of the governing differential equations by numerical methods appears feasible with the aid of an electronic computer and the results of a test case are presented. For this purpose it was convenient to replace a series of empirical equations relating ship's speed to wave height and direction by a single analytical expression.
Inspection of the basic differential equations and the empirical relation between ship's speed and the state of the sea indicates that in the case of moderate wave heights, the dependence on wave direction may be omitted as a good approximation. This is borne out in the test case which also shows a considerable saving in computing time because of the resulting simplification of the differential equation.
Abstract
Two iterative methods are described for obtaining horizontal winds from the pressure-height field by means of higher-order geostrophic approximations for the purpose of improving upon the geostrophic wind. The convergence properties of the iterative methods are discussed; and in a simple theoretical case, one of the methods is found to diverge with strong cyclonic motion. Both iterative methods were applied to analyzed 500-mb. height charts and over most of the map converged in a few scans to wind values somewhere between the geostrophic wind and the wind obtained from the balance equation. However in a few locations continued iteration led to increasing differences between successively computed winds: i.e., the methods appeared to diverge. In fact, wind values in adjacent areas gradually tended to be corrupted. This lack of convergence, occurring mainly in areas of negative vorticity and additionally in the case of method II in areas of strong cyclonic vorticity, was associated with the development of excessive horizontal wind divergence, which after three or four iterations sometimes exceeded the relative vorticity. Stream functions were computed by relaxing the relative vorticity of the winds obtained by methods I and II, generally after one iteration. These were compared to the stream function obtained by solving the balance equation and no significant differences were noted. Barotropic forecasts prepared from the stream functions derived from the two methods are essentially the same as forecasts with the stream function obtained from the balance equation.
Abstract
Two iterative methods are described for obtaining horizontal winds from the pressure-height field by means of higher-order geostrophic approximations for the purpose of improving upon the geostrophic wind. The convergence properties of the iterative methods are discussed; and in a simple theoretical case, one of the methods is found to diverge with strong cyclonic motion. Both iterative methods were applied to analyzed 500-mb. height charts and over most of the map converged in a few scans to wind values somewhere between the geostrophic wind and the wind obtained from the balance equation. However in a few locations continued iteration led to increasing differences between successively computed winds: i.e., the methods appeared to diverge. In fact, wind values in adjacent areas gradually tended to be corrupted. This lack of convergence, occurring mainly in areas of negative vorticity and additionally in the case of method II in areas of strong cyclonic vorticity, was associated with the development of excessive horizontal wind divergence, which after three or four iterations sometimes exceeded the relative vorticity. Stream functions were computed by relaxing the relative vorticity of the winds obtained by methods I and II, generally after one iteration. These were compared to the stream function obtained by solving the balance equation and no significant differences were noted. Barotropic forecasts prepared from the stream functions derived from the two methods are essentially the same as forecasts with the stream function obtained from the balance equation.
