34 citations · 63 across the 20 of their papers we have counts for
20 papers
Dimensional scaling of flame propagation in discrete particulate clouds
Fredric Y. K. Lam, XiaoCheng Mi, Andrew J. Higgins
The critical dimension necessary for a flame to propagate in suspensions of fuel particles in oxidizer is studied analytically and numerically. Two types of models are considered:…
On regularity of the Euler equations in fluid dynamics
F. Lam
We assert that the solutions to the Cauchy problem of the inviscid vorticity equation remain regular and unique for any smooth initial data of finite energy. However, the primitive…
The Navier-Stokes equations in primitive variables
F. Lam
The Navier-Stokes equations in the primitive formulation for incompressible flow describe the evolution of velocity and pressure, without recourse to vorticity. We show that, beyon…
Leray self-similarity equations in fluid dynamics
F. Lam
In the present note, we show that, as a priori bounds, the vorticity dynamics derived from Leray's backward self-similarity hypothesis admits only trivial solution in viscous as we…
Remarks on singular solutions of the Euler equations
F. Lam
We examine the blow-up claims of the incompressible Euler equations for several specific flow-fields, (1) the columnar eddies in the vicinity of stagnation; (2) a quasi-three-dimen…
The Navier-Stokes equations in periodic domains
F. Lam
In the present technical note, we establish that the setting of the primitive variables of the unsteady incompressible fluid dynamics is ill-formulated in spatially periodic domain…
Viscous flow regimes in unit square: Part 4. Vorticity dynamics from monopoles to multipoles
F. Lam
The initial-boundary value problem of the vorticity equation has been solved numerically by an iterative method. A variety of initial vorticity distributions is specified. All of t…
Viscous flow regimes in unit square: Part 3. Phenomena of leapfrogging and approaching among multiple vortex pairs
F. Lam
In the present note, we solved numerically the viscous vorticity equation of the initial-boundary value problem describing the classic Helmholtz phenomena of vortex interaction. In…
Viscous flow regimes in a square. Part 1. Lid-driven cavity
F. Lam
In the present paper, we examine the viscous flow evolution in a square cavity. Coupled with the stream function, the initial-boundary value problem of the vorticity is numerically…
Viscous flow regimes in a square. Part 2. Impact and rebound process of vortex dipole-wall interaction
F. Lam
In this technical note, we demonstrate the robustness of our numerical scheme of vorticity iteration in dealing with the dipole-wall interaction at small viscosity, with emphasis o…
On flow-field decomposition in fluid dynamics
F. Lam
In the theory of hydrodynamic stability, the procedure to decompose an incompressible flow field into its basic motion and disturbances is imprecise and problematic because the dis…
Front Roughening of Flames in Discrete Media
Fredric Lam, XiaoCheng Mi, Andrew J. Higgins
The morphology of flame fronts propagating in reactive systems comprised of randomly positioned, point-like sources is studied. The solution of the temperature field and the initia…
Non-linear vorticity upsurge in Burgers' flow
F. Lam
We demonstrate that numerical solutions of Burgers' equation can be obtained by a scale-totality algorithm for fluids of small viscosity (down to one billionth). Two sets of initia…
Remarks on backward uniqueness of parabolic equations and incompressible Navier-Stokes well-posedness
F. Lam
We explain why the theory of Escauriaza, Seregin, and Sverak (Russian Math. Surveys, 2003) on potential finite time singularity in Navier-Stokes solutions must be largely misappreh…
Vorticity evolution in a rigid pipe of circular cross-section
F. Lam
In this paper, we show that the spatio-temporal evolution of incompressible flows in a long circular pipe can be described by vorticity dynamics. The principal techniques to obtain…
On Exact Solutions of the Navier-Stokes Equations for Uni-directional Flows
F. Lam
In the present note, we show that the uni-directional flows in a rectangular channel and in a circular pipe are exact spatio-temporal solutions of the Navier-Stokes equations over…
Short-time evolution of pipe Poiseuille flow
F. Lam
In the present paper we prove that the pipe Poiseuille flow of parabolic velocity profile attenuates exponentially in time with respect to three dimensional infinitesimal disturban…
On the Well-posedness of Magnetohydrodynamics Equations for Incompressible Electrically-Conducting Fluids
F. Lam
It is shown that the Cauchy problem of the equations in magnetohydrodynamics in the whole space is globally well-posed for any initial smooth and localized data. In general, the ma…
Integral Invariance and Non-linearity Reduction for Proliferating Vorticity Scales in Fluid Dynamics
F. Lam
An effort has been made to solve the Cauchy problem of the Navier-Stokes equations in the whole space by two methods. It is proved that the sum of the three vorticity components is…
Stability of the Couette-Poiseuille flow by the Reynolds-Orr energy equation
F. Lam
The normal-mode analysis of the Reynolds-Orr energy equation governing the stability of viscous motion for general three-dimensional disturbances has been revisited. The energy equ…