A mathematical model illustrating the theory of turbulence

By J. Burgers. 1948

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Citations in the corpus

Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems (2019, neutral): “5 [65].”
On the Regularity of the Composition of Diffeomorphisms (2011, background): “Later it was observed that other nonlinear evolution equations such as Burgers equation [6], KdV, or the Camassa Holm equation [7], [17] can be viewed in a similar way – see [22], [32], as well as [5], [19], and [23].”
Comparing the statistics of interstellar turbulence in simulations and observations - Solenoidal versus compressive turbulence forcing (2009, methodology): “However, compressive forcing yields significantly steeper scaling (also for ρ1/2v), which is close to Burgers (1948) turbulence (scaling proportional to k−2).”
On the universality of supersonic turbulence (2013, background): “…it is only recently that the spectral scaling of supersonic turbulence could be measured with improved precision (Kritsuk et al. 2007; Federrath et al. 2010), indicating P(v) ∝ k−2, which is much steeper than the Kolmogorov spectrum and closer to Burgers turbulence (Burgers 1948, , hereafter B48).”
On Lp-solutions of semilinear stochastic partial differential equations (2000, background): “A famous example in one space dimension is Burgers’ equation, when aij =1, =0, f=0; g(t; x; r)= 12 r 2 (see e.g. Burgers, 1948; Hopf, 1950; Liu and Yu, 1997), and the references therein).”
On the use of nonstandard finite difference methods† (2005, background): “Burgers equation [15,139,154]: ut þ uux 1⁄4 1uxx; where 1 is related to the reciprocal of the Reynolds number.”
Travelling Waves in Nonlinear Diffusion-Convection Reaction (2004, background): “The above class of explicit travelling wave solutions of the Burgers equation was documented by the person after whom the equation is named in [59,60].”
On the relationships between local vortex identification schemes (2005, background): “Isolated Burgers’ vortex Here we discuss the vortex core of the radially symmetric Burgers’ vortex (Burgers 1948).”
Existence and Smoothness of Navier-Stokes Equations (2018, methodology): “The Burgers equation can be used for modelling both travelling and standing nonlinear plane waves [1, 6, 7, 8, 10, 15].”
Shock wave simulations using Sinc Differential Quadrature Method (2011, unknown): “The equation is known as Burgers' equation because of the studies of Burger (1948)”
TOPICAL REVIEW: On the geometric approach to the motion of inertial mechanical systems (2002, background): “1) is the well-known inviscid Burgers equation [7].”
Numerical solution of one-dimensional Burgers' equation using reproducing kernel function (2008, unknown): “[13] R.C. Mittal, P. Singhal, Numerical solution of periodic Burgers’ equation, Indian J. Pure Appl.”