We experimentally demonstrate the first few-mode space division multiplexed (SDM) transmission of real-time 10Gb/s Ethernet (10GbE) traffic using commercial small form-factor pluggable SFP + transceivers without coherent detection or multiple input multiple output digital signal processing (MIMO-DSP) over 0.5km elliptical-core few-mode-fiber, achieving <-26dB crosstalk between LP(11e) and LP(11o) modes at 1.3μm.

We study the vortex-accelerated secondary baroclinic vorticity deposition ͑VAVD͒ at late-intermediate times, and dynamics of sinusoidal single-mode Richtmyer-Meshkov interfaces in two dimensions. Euler simulations using a piecewise parabolic method are conducted for three post-shock Atwood numbers (A*), 0.2, 0.635, and 0.9, with Mach number ͑M͒ of 1.3. We initialize the sinusoidal interface with a slightly ''diffuse'' or small-but-finite thickness interfacial transition layer to facilitate comparison with experiment and avoid ill-posed phenomena associated with evolutions of an inviscid vortex sheet. The thickness of the interface is chosen so that there are no secondary structures along the interface prior to the multivalue time t M , which is defined as the time when the extracted medial axis of an interfacial layer first becomes multivalued. For an interval of 11t M beyond t M , the simulations reveal nearly monotonic strong growth of both positive and negative baroclinic circulation in a vortex bilayer pattern inside the complex roll-up region. The circulations grow and secondary baroclinic circulation dominates at intermediate times, especially for higher A*. This vorticity deposition is due to misalignment of density gradient across the interface and vortex-centripetal acceleration ͑secondary baroclinic͒, and enhanced by the intensification of interfacial density gradient arising from the vortex-induced strain. Our simulation results for A*ϭ0.635 agree with the recent air-sulfur hexafluoride (SF 6 ) experiment of Jacobs and Krivets ͓Proceedings of the 23rd International Symposium on Shock Waves, Fort Worth, Texas, ͑2001͔͒, including several large-scale features of the evolving mushroom structure: The usual interface spike-bubble amplitude growth rate ȧ and the dimensions of the spike roll-up cavity. VAVD plays an important role in the intermediate time dynamics of the interfaces. Our amplitude growth rate ȧ disagrees with the O(t Ϫ1 ) result of Sadot et al. ͓Phys. Rev. Lett. 80, 1654 ͑1998͔͒.Instead, it approaches a constant which increases with A*(р0.9). An adjusting periodic single point vortex model which uses the calculated net circulation magnitude and its location, gives excellent results for the amplitude growth rates to late-intermediate times at low Atwood numbers (A* ϭ0.2,0.635). The evolution of enstrophy, vorticity skewness, and flatness are quantified for the entire run duration, and one-dimensional averaged kinetic-energy spectra are presented at several times.

We present numerical simulations of a planar shock interacting with a two-dimensional sulfur hexafluoride (SF6) cylinder. We have excellent agreement with experiments at two Mach numbers M=1.095 [Jacobs, Phys. Fluids A 5, 2239 (1993)] and M=1.2 [Zoldi, Ph.D. thesis, SUNY Stony Brook, 2002]. This includes intermediate scale features and quantities such as bounding box dimensions of coherent structures and velocity magnitude distribution function. Our simulations use a validated viscous FLASH [ASCI FLASH Center, “FLASH User’s Guide,” University of Chicago, 2002] environment initialized with a cylinder bounded by a finite-thickness interfacial transition layer of specific shape. The shape parameters are determined through iteration, beginning with the uncertain experimental images and optimizing to obtain maximal agreement with early to intermediate time evolving structures. The visiometric approach and the vortex paradigm [Hawley and Zabusky, Phys. Rev. Lett. 63, 1241 (1989)] are essential to obtain insight into this Richtmyer–Meshkov environment. We verify our recent discovery [Zabusky and Zhang, Phys. Fluids 14, 419 (2002)] that after the primary shock-deposition of vorticity by the incident shock, a vortex bilayer of large circulation magnitude grows significantly through intermediate times. The inclusion of physical viscosity allows us to examine some aspects of pre-turbulence at late–intermediate times.

The Richtmyer–Meshkov instability in an incompressible and compressible stratified two-dimensional ideal flow is studied analytically and numerically. For the incompressible problem, we initialize a single small-amplitude sinusoidal perturbation of wavelength λ, we compute a series expansion for the amplitude a in powers of t up to t(11) with the MuPAD computer algebra environment. This involves harmonics up to eleven. The simulations are performed with two codes: incompressible, a vortex-in- cell numerical technique which tracks a single discontinuous density interface; and compressible, PPM for a shock-accelerated case with a finite interfacial transition layer (ITL). We identify properties of the interface at time t = tM at which it first becomes ‘multivalued’. Here, we find the normalized width of the ‘spike’ is related to the Atwood number by (wm/λ)−0.5 = −0.33A. A high-order Pad approximation is applied to the analytical series during early time and gives excellent results for the interface growth rate a˙. However, at intermediate times, t > tM, the agreement between numerical results and different-order Padé approximants depends on the Atwood number. During this phase, our numerical solutions give a˙∝O(t−1) for small A and a˙∝O(t−0.4) for A = 0.9. Experimental data of Prasad et al. (2000) for SF6 (post shock Atwood number = 0.74) shows an exponent between −0.68 and −0.72 and we obtain −0.683 for the compressible simulation. For this case, we illustrate the important growth of vortex-accelerated (secondary) circulation deposition of both signs of vorticity and the complex nature of the roll-up region.

The spatial modes of a 1 km elliptical core few-mode optical fiber (6 spatial modes) are analyzed by using liquid crystal on silicon spatial light modulators to measure the fiber's mode crosstalk matrix in Hermite-Gaussian, Laguerre-Gaussian, and linearly polarized spatial mode bases. It is shown that the fiber's spatial modes can be described by Hermite-Gaussian modes, which can propagate 1 km over the optical fiber with <-20  dB (1%) average mode crosstalk even when the fiber has multiple 1 cm diameter bends. The use of elliptical core few-mode optical fibers for space division multiplexing in data centers is discussed.