Publications [#282445] of Lawrence N. Virgin
Papers Published
- Reynolds, RR; Virgin, LN; Dowell, EH, High-dimensional chaos can lead to weak turbulence,
Nonlinear Dynamics, vol. 4 no. 6
(December, 1993),
pp. 531-546, Springer Nature [doi]
(last updated on 2023/06/01)Abstract:
One of the outstanding unresolved questions of nonlinear dynamics is the relationship between chaos and turbulence. This is a deep and difficult question, not the least reason being that the definitions of "chaos" and "turbulence" are not universally agreed upon. Here we define chaos as the time history of a single descriptor of a deterministic dynamical system which undergoes a loss of temporal correlation with a change in some system parameter and that displays sensitivity to initial conditions. Turbulence is defined as the time history of the spatial distribution of a deterministic dynamical system which undergoes a loss of temporal and (subsequently) spatial correlation with a change in some system parameter(s). By analogy and numerical simulation it is argued that turbulence can be a consequence of multi-mode interaction of individually chaotic modes. The physical system used here is a fluttering panel in a supersonic airstream. am = modal amplitude coefficients D = panel stiffness (=Eh212(1-v2)) E = modulus of elasticity of panel material h = panel thickness k = dimensional foundation stiffness K = nondimensional foundation stiffness (=kL4/Dh) L = length of panel in direction of flow M = Mach number N = number of modes in series expansion of panel deflection Nfv/pa = dimensional applied inplane load Δp = dimensional static pressure differential across panel P = nondimensional static pressure differential across panel (=ΔpL4/Dh) q = dimensional dynamic pressure (=ρχU2/2) Rv = nondimensional inplane load (=Nfxpaa2/D) t = dimensional time T = period over which correlation is averaged U = dimensional flow velocity w = dimensional panel deflection W = nondimensional panel deflection (deflection/h) x = dimensional coordinate along panel α = inplane spring stiffness parameter λ = nondimensional dynamic pressure of flow over panel ( {Mathematical expression}) μ = mass ratio (ρχL/ρmh)) ν = Poisson's ratio ξ = nondimensional location along panel (x/L) Δξ = separation between points used in correlation function ξu = nondimensional correlation length ψ = correlation function © 1993 Kluwer Academic Publishers.Keywords:
Aerodynamics;Elasticity;Turbulence;Supersonic flow;