Fractal tracer distributions in turbulent field theories

We study the motion of passive tracers in a two-dimensional turbulent velocity field generated by the Kuramoto-Sivashinsky equation. By varying the direction of the velocity-vector with respect to the field-gradient we can continuously vary the two Lyapunov exponents for the particle motion and thereby find a regime in which the particle distribution is a strange attractor. We compare the Lyapunov dimension to the information dimension of actual particle distributions and show that there is good agreement with the Kaplan-Yorke conjecture. Similar phenomena have been observed experimentally.Comment: 17 pages, 7 figures, elsart.sty, psfig.sty, LaTe

Averaging theory for the structure of hydraulic jumps and separation in laminar free-surface flows

We present a simple viscous theory of free-surface flows in boundary layers, which can accommodate regions of separated flow. In particular this yields the structure of stationary hydraulic jumps, both in their circular and linear versions, as well as structures moving with a constant speed. Finally we show how the fundamental hydraulic concepts of subcritical and supercritical flow, originating from inviscid theory, emerge at intermediate length scales in our model.Comment: 6 EPSI figs included by psfig; 4 pages; to appear in PRL, vol.79, 1038 (Aug.11, 1997

Surface tension and the origin of the circular hydraulic jump in a thin liquid film

It was recently claimed by Bhagat et al. (J. Fluid Mech. vol. 851 (2018), R5) that the scientific literature on the circular hydraulic jump in a thin liquid film is flawed by improper treatment and severe underestimation of the influence of surface tension. Bhagat {\em et al.} use an energy equation with a new surface energy term that is introduced without reference, and they conclude that the location of the hydraulic jump is determined by surface tension alone. We show that this approach is incorrect and derive a corrected energy equation. Proper treatment of surface tension in thin film flows is of general interest beyond hydraulic jumps, and we show that the effect of surface tension is fully contained in the Laplace pressure due to the curvature of the surface. Following the same approach as Bhagat et al., i.e., keeping only the first derivative of the surface velocity, the influence of surface tension is, for thin films, much smaller than claimed by them. We further describe the influence of viscosity in thin film flows, and we conclude by discussing the distinction between time-dependent and stationary hydraulic jumps.Comment: 9 pages, 1 figur

Directed Percolation Universality in Asynchronous Evolution of Spatio-Temporal Intermittency

We present strong evidence that a coupled-map-lattice model for spatio-temporal intermittency belongs to the universality class of directed percolation when the updating rules are asynchronous, i.e. when only one randomly chosen site is evolved at each time step. In contrast, when the system is subjected to parallel updating, available numerical evidence suggests that it does not belong to this universality class and that it is not even universal. We argue that in the absence of periodic external forcing, the asynchronous rule is the more physical.Comment: 12 pages, RevTeX, includes 6 figures, submitted to Physical Review Letters; changed version includes a better physical motivation for asynchronous updates, extra references and minor change

Rotating Polygon Instability of a Swirling Free Surface Flow

We explain the rotating polygon instability on a swirling fluid surface [G. H. Vatistas, J. Fluid Mech. 217, 241 (1990) and Jansson et al., Phys. Rev. Lett. 96, 174502 (2006)] in terms of resonant interactions between gravity waves on the outer part of the surface and centrifugal waves on the inner part. Our model is based on potential flow theory, linearized around a potential vortex flow with a free surface for which we show that unstable resonant states appear. Limiting our attention to the lowest order mode of each type of wave and their interaction, we obtain an analytically soluble model, which, together with estimates of the circulation based on angular momentum balance, reproduces the main features of the experimental phase diagram. The generality of our arguments implies that the instability should not be limited to flows with a rotating bottom (implying singular behavior near the corners), and indeed we show that we can obtain the polygons transiently by violently stirring liquid nitrogen in a hot container

Shape and stability of a viscous thread

When a viscous fluid, like oil or syrup, streams from a small orifice and falls freely under gravity, it forms a long slender thread, which can be maintained in a stable, stationary state with lengths up to several meters. We discuss the shape of such liquid threads and their surprising stability. The stationary shapes are discussed within the long-wavelength approximation and compared to experiments. It turns out that the strong advection of the falling fluid can almost outrun the Rayleigh-Plateau instability. The asymptotic shape and stability are independent of viscosity and small perturbations grow with time as exp(Ct(1/4)), where the constant is independent of viscosity. The corresponding spatial growth has the form exp[(z/L)(1/8)], where z is the down stream distance and L similar to Q(2)sigma(-2)g and where sigma is the surface tension divided by density, g is the gravity, and Q is the flux. We also show that a slow spatial increase of the gravitational field can make the thread stable

Diffusion and bulk flow in phloem loading - a theoretical analysis of the polymer trap mechanism in plants

Plants create sugar in the mesophyll cells of their leaves by photosynthesis. This sugar, mostly sucrose, has to be loaded via the bundle sheath into the phloem vascular system (the sieve elements), where it is distributed to growing parts of the plant. We analyze the feasibility of a particular loading mechanism, active symplasmic loading, also called the polymer trap mechanism, where sucrose is transformed into heavier sugars, such as raffinose and stachyose, in the intermediary-type companion cells bordering the sieve elements in the minor veins of the phloem. Keeping the heavier sugars from diffusing back requires that the plasmodesmata connecting the bundle sheath with the intermediary cell act as extremely precise filters, which are able to distinguish between molecules that differ by less than 20% in size. In our modeling, we take into account the coupled water and sugar movement across the relevant interfaces, without explicitly considering the chemical reactions transforming the sucrose into the heavier sugars. Based on the available data for plasmodesmata geometry, sugar concentrations and flux rates, we conclude that this mechanism can in principle function. We find that the water flow through the plasmodesmata, which has not been quantified before, contributes only 10-20% to the sucrose flux into the intermediary cells, while the main part is transported by diffusion. On the other hand, the subsequent sugar translocation into the sieve elements would very likely be carried predominantly by bulk water flow through the plasmodesmata. Thus, in contrast to apoplasmic loaders, all the necessary water for phloem translocation would be supplied in this way with no need for additional water uptake across the plasma membranes of the phloem.Comment: 29 pages with 5 figure