Showing papers on "Multiple-scale analysis published in 1981"
TL;DR: The linear instability of a non-zonal flow can be reduced to an eigenvalue-eigenfunction problem, governed by a nonseparable partial differential equation (Niehaus, 1980) as discussed by the authors.
Abstract: The linear instability of a non-zonal flow can be reduced to an eigenvalue-eigenfunction problem, governed by a nonseparable partial differential equation (Niehaus, 1980). Approximate solutions, found by the method of multiple scales, are derived here and compared with earlier results found using a spectral method. The amplitude maxima are correctly located. The zonal variations of local wavenumber and of amplitude are qualitatively correct, but not sufficiently extreme. Because the method is oversensitive to local conditions, and less sensitive to global constraints, this comparison provides theoretical limits to the possibility of parameterizing transient eddies in terms of the local time mean state of the atmosphere. The method can be extended easily to flows with more realistic vertical structure.
11 citations
TL;DR: In this article, the authors used the method of multiple scales to determine the response of a self-excited system having a single degree of freedom to multi-frequency harmonic excitations.
10 citations
TL;DR: In this article, it was shown that two different expansion procedures for hydrodynamical stability problems are equivalent, and the results were extended to calculate the stream function up to order ω 2.
Abstract: This paper shows that two different expansion procedures for hydrodynamical stability problems are equivalent. The method of multiple scales of Stewartson & Stuart (1971) is extended to calculate the stream function up to order $\epsilon^2$. Watson's (1960) rigorous amplitude expansion of the solution of the Navier-Stokes equations is also used to calculate the stream function up to the same order of magnitude, and a complete equivalence between the two results is found. An analysis of the Eckhaus model equations has been made and the results are equivalent.
9 citations
01 Jan 1981
TL;DR: In this paper, the angular motion of a symmetric, cruciform missile, having roll orientation-dependent aerodynamics, is studied, and an aerodynamic moment expansion, consistent with rotational and reflectional symmetry arguments, is incorporated into the equations of missile angular motion.
Abstract: : The angular motion of a symmetric, cruciform missile, having roll orientation-dependent aerodynamics, is studied An aerodynamic moment expansion, consistent with rotational and reflectional symmetry arguments, is incorporated into the equations of missile angular motion A generalized version of the method of multiple scales is incorporated to generate approximate solutions to the equations of angular motion for three specific cases: free-flight angular motion at constant roll rate, induced rolling motion with a priori yawing motion, and finally the combined problem of coupled yawing and rolling motion Critical roll rates are identified and solutions valid in the vicinity of these singular conditions are generated Approximate solutions used to derive stability criteria are compared with numerical solutions of exact, nonlinear equations of motion Results of the perturbation solutions show good agreement with the exact calculations for moderate angles of attack (Author)
3 citations
TL;DR: In this article, the problem of bending a thin plate under the action of in-plane forces is studied by using the method of multiple scales, and the bending of the thin plate is solved by using multiple scales.
Abstract: In this paper, problems of bending of a thin plate under the action of in-plane forces are studied by using the method of multiple scales.
1 citations