Journal ArticleDOI
On Burgers' model equations for turbulence
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In this paper, the authors considered the Burgers' model equations for turbulence and showed that small disturbances ultimately grow into a single large domain of relatively smooth flow, accompanied by a vortex sheet in which strong vorticity is concentrated.Abstract:
Burgers’ (1939) model equations for turbulence are considered analytically using a singular perturbation and nonlinear wave approach. The results indicate that there is an ultimate steady turbulent state. This is in agreement with the numerical results of Lee (1971) but not with Case & Chiu (1969): the last two papers start with a Fourier series approach.A consequence of this model is that small disturbances ultimately grow into a single large domain of relatively smooth flow, accompanied by a vortex sheet in which strong vorticity is concentrated. This makes the results from the model different from those usually expected for turbulent flow fields. The model, as a result of its simplicity, has retained a degree of regularity which is not found in most forms of turbulence.read more
Citations
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Journal ArticleDOI
A systematic literature review of Burgers’ equation with recent advances
TL;DR: The objectives of this paper are to discuss the recent developments in mathematical modelling of Burgers’ equation, and throw some light on the plethora of challenges which need to be overcome in the research areas and give motivation for the next breakthrough to take place in a numerical simulation of ordinary / partial differential equations.
Journal ArticleDOI
Generalized Burgers equations and Euler–Painlevé transcendents. II
TL;DR: In this paper, a connection problem for generalized Burgers equation (GBE) is solved for continuous and discontinuous initial data, where the solution is given analytically by the self-similar form.
Journal ArticleDOI
Universal scaling relations in scale-free structure formation
TL;DR: In this article, the authors show that all such systems produce a mass function proportional to M^(−2) and a column density distribution with a power-law tail of dA/dlnΣ ∝ Σ(−1).
Journal ArticleDOI
Mapping the core mass function to the initial mass function
TL;DR: In this article, the authors show that turbulent fragmentation robustly predicts two key features of the initial mass function (IMF), including a high-mass power-law scaling very close to the Salpeter slope, which is a generic consequence of the scale-free nature of turbulence and self-gravity.
Journal ArticleDOI
One-dimensional shock turbulence in a compressible fluid
TL;DR: In this paper, the interactions of weak nonlinear disturbances in a compressible fluid including shocks, expansion waves and contact surfaces are investigated by making use of the reductive perturbation method.
References
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Book ChapterDOI
A mathematical model illustrating the theory of turbulence
TL;DR: In this article, the application of statistical analysis and statistical mechanics to the problem of turbulent fluid motion has attracted much attention in recent years, and the authors investigated a complicated system of nonlinear equations, in order to find out enough about the properties of the solutions of these equations that insight can be obtained into the various patterns exhibited by the field and that data can be derived concerning the relative frequencies of these patterns in the hope that in this way a basis may be found for the calculation of important values.
Book
Mathematical Examples Illustrating Relations Occurring in the Theory of Turbulent Fluid Motion
TL;DR: In a series of papers on the resistance experienced by a fluid in turbulent motion and on the application of statistical mechanics to the theory of turbulent fluid motion, it was attempted to obtain a picture of the relative probabilities of the various possible patterns of the secondary motion, in order to arrive at a calculation of the magnitude of the turbulent shearing stress and of the resistances experienced by the primary motion in consequence of this stress as mentioned in this paper.
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Recent Advances in the Mechanics of Boundary Layer Flow
TL;DR: In this article, the boundary layer flow is derived from the Navier-Stokes equations to obtain solution for the special case of flow along a thin flat plate parallel to the direction of flow in an airstream of uniform speed.
Book ChapterDOI
Statistical Problems Connected with the Solution of a Nonlinear Partial Differential Equation
TL;DR: In this article, a nonlinear partial differential equation, somewhat resembling the equations of hydrodynamics, for a variable u is a function of the time and of a single coordinate.