The quadratic convection term in the incompressible Navier-Stokes equations is considered as a nonlinear forcing to the linear resolvent operator, and it is studied in the Fourier domain through the analysis of intera...
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We describe a recent evolution of Harmonic Analysis to generate analytic tools for the joint organization of the geometry of subsets of Rn and the analysis of functions and operators on the subsets. In this analysis w...
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The problem of propagation of turbulent premixed flame is analyzed using the field equation introduced recently by Kerstein, Ashurst and Williams (1987). The dynamic renormalization group method is applied to this equ...
The problem of propagation of turbulent premixed flame is analyzed using the field equation introduced recently by Kerstein, Ashurst and Williams (1987). The dynamic renormalization group method is applied to this equation and the formula for the turbulent flame velocity is derived in the lowest order in the ε-expansion. The formula, which does not include adjustable parameters, agrees well with experimental (Abdel-Gayed et al., 1984) and numerical (Ashurst & Barr 1983) results on flame propagation in high-Reynolds number turbulent media. Ways to design transport and large-eddy (sub-grid) models for simulation of combustion processes, based on the ideas developed in the present paper, are discussed.
Risk-driven behaviour provides a feedback mechanism through which individuals both shape and are collectively affected by an epidemic. We introduce a general and flexible compartmental model to study the effect of het...
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The equations of motion describing inviscid fluid flow are solved numerically in two dimensions for the case where the flow can be described by patches of constant vorticity. The case where the vorticity is described ...
The equations of motion describing inviscid fluid flow are solved numerically in two dimensions for the case where the flow can be described by patches of constant vorticity. The case where the vorticity is described initially by two circular patches is studied in detail. The numerical evidence indicates that when the minimum distance between the two patches is initially less than the radius of the patches a singularity forms in finite time on the boundary curves of the patches. The singularity appears to be a jump discontinuity in the tangent vector of the boundary curve.
Deviations from classical scaling behavior are shown to result in flattened energy and dissipation–fluctuation inertial‐range spectra in fully developed turbulence.
Deviations from classical scaling behavior are shown to result in flattened energy and dissipation–fluctuation inertial‐range spectra in fully developed turbulence.
The correspondence principle postulated for the description of hydrodynamic turbulence [Phys. Rev. Lett. 57, 1722 (1986)] combined with the theory of thermal boundary layer [B. Castaing et al. (private communication)]...
The correspondence principle postulated for the description of hydrodynamic turbulence [Phys. Rev. Lett. 57, 1722 (1986)] combined with the theory of thermal boundary layer [B. Castaing et al. (private communication)] is applied to high Rayleigh number convection in a Bénard cell. Quantitative interpretation of recent experimental data [B. Castaing et al. (private communication)] is presented. The predicted intermittency exponent following from comparison of the theory with experiment is 0.175<μ<0.275. A crucial experimental test of the renormalization group theory of turbulence is proposed.
A new dimensional analysis for high Rayleigh number thermal convection is proposed to give an alternative interpretation of the scaling laws observed recently by Castaing et al. [J. Fluid Mech. (in press)]. The key as...
A new dimensional analysis for high Rayleigh number thermal convection is proposed to give an alternative interpretation of the scaling laws observed recently by Castaing et al. [J. Fluid Mech. (in press)]. The key assumption in the present approach is that the central fluctuating temperature field actively interacts with the turbulent velocity field, and this interaction leads to a velocity inertial subrange that deviates significantly from Kolmogorov’s freely cascading inertial range.
Hamiltonian integration schemes for the Nonlinear Schroedinger Equation are examined. The efficiency with respect to accuracy and integration time of an integrable scheme, a standard conservative scheme, and a symplec...
Hamiltonian integration schemes for the Nonlinear Schroedinger Equation are examined. The efficiency with respect to accuracy and integration time of an integrable scheme, a standard conservative scheme, and a symplectic method is compared.
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