Rayleigh--Taylor turbulence in two dimensions

The first consistent phenomenological theory for two and three dimensional Rayleigh--Taylor (RT) turbulence has recently been presented by Chertkov [Phys. Rev. Lett. {\bf 91} 115001 (2003)]. By means of direct numerical simulations we confirm the spatio/temporal prediction of the theory in two dimensions and explore the breakdown of the phenomenological description due to intermittency effects. We show that small-scale statistics of velocity and temperature follow Bolgiano-Obukhov scaling. At the level of global observables we show that the time-dependent Nusselt and Reynolds numbers scale as the square root of the Rayleigh number. These results point to the conclusion that Rayleigh-Taylor turbulence in two and three dimensions, thanks to the absence of boundaries, provides a natural physical realization of the Kraichnan scaling regime hitherto associated with the elusive ``ultimate state of thermal convection''.Comment: 4 pages, 5 figure

Two-dimensional turbulent convection

We present an overview of the most relevant, and sometimes contrasting, theoretical approaches to Rayleigh-Taylor and mean-gradient-forced Rayleigh-Benard two-dimensional turbulence together with numerical and experimental evidences for their support. The main aim of this overview is to emphasize that, despite the different character of these two systems, especially in relation to their steadiness/unsteadiness, turbulent fluctuations are well described by the same scaling relationships originated from the Bolgiano balance. The latter states that inertial terms and buoyancy terms balance at small scales giving rise to an inverse kinetic energy cascade. The main difference with respect to the inverse energy cascade in hydrodynamic turbulence [R. H. Kraichnan,: "Inertial ranges in twodimensional turbulence," Phys. Fluids 10, 1417 (1967)] is that the rate of cascade of kinetic energy here is not constant along the inertial range of scales. Thanks to the absence of physical boundaries, the two systems here investigated turned out to be a natural physical realization of the Kraichnan scaling regime hitherto associated with the elusive "ultimate state of thermal convection" [R. H. Kraichnan,: "Turbulent thermal convection at arbitrary Prandtl number," Phys. Fluids 5, 1374-1389 (1962)]

Passive control of a falling sphere by elliptic-shaped appendages

The majority of investigations characterizing the motion of single or multiple particles in fluid flows consider canonical body shapes, such as spheres, cylinders, discs, etc. However, protrusions on bodies -- being either as surface imperfections or appendages that serve a function -- are ubiquitous in both nature and applications. In this work, we characterize how the dynamics of a sphere with an axis-symmetric wake is modified in the presence of thin three-dimensional elliptic-shaped protrusions. By investigating a wide range of three-dimensional appendages with different aspect ratios and lengths, we clearly show that the sphere with an appendage may robustly undergo an inverted-pendulum-like (IPL) instability. This means that the position of the appendage placed behind the sphere and aligned with the free-stream direction is unstable, in a similar way that an inverted pendulum is unstable under gravity. Due to this instability, non-trivial forces are generated on the body, leading to turn and drift, if the body is free to fall under gravity. Moreover, we identify the aspect ratio and length of the appendage that induces the largest side force on the sphere, and therefore also the largest drift for a freely falling body. Finally, we explain the physical mechanisms behind these observations in the context of the IPL instability, i.e., the balance between surface area of the appendage exposed to reversed flow in the wake and the surface area of the appendage exposed to fast free-stream flow.Comment: 16 pages, 13 figures, 2 tables, under consideration for publication in Phys. Rev. Fluids; revisio

Does multifractal theory of turbulence have logarithms in the scaling relations?

The multifractal theory of turbulence uses a saddle-point evaluation in determining the power-law behaviour of structure functions. Without suitable precautions, this could lead to the presence of logarithmic corrections, thereby violating known exact relations such as the four-fifths law. Using the theory of large deviations applied to the random multiplicative model of turbulence and calculating subdominant terms, we explain here why such corrections cannot be present.Comment: 7 pages, 1 figur

Problems in RMSE-based wave model validations

In order to evaluate the reliability of numerical simulations in geophysical applications it is necessary to pay attention when using the root mean square error (RMSE) and two other indicators derived from it (the normalized root mean square error (NRMSE), and the scatter index (SI)). In the present work, in fact, we show on a general basis that, in conditions of constant correlation coefficient, the RMSE index and its variants tend to be systematically smaller (hence identifying better performances of numerical models) for simulations affected by negative bias. Through a geometrical decomposition of RMSE in its components related to the average error and the scatter error it can be shown that the above mentioned behavior is triggered by a quasi-linear dependency between these components in the neighborhood of null bias. This result suggests that smaller values of RMSE, NRMSE and SI do not always identify the best performances of numerical simulations, and that these indicators are not always reliable to assess the accuracy of numerical models. In the present contribution we employ the corrected indicator proposed by Hanna and Heinold (1985) to develop a reliability analysis of wave generation and propagation in the Mediterranean Sea by means of the numerical model WAVEWATCH III®, showing that the best values of the indicator are obtained for simulations unaffected by bias. Evidences suggest that this indicator provides a more reliable information about the accuracy of the results of numerical models. © 2013 Elsevier Ltd

Point-source inertial particle dispersion

The dispersion of inertial particles continuously emitted from a point source is analytically investigated in the limit of small inertia. Our focus is on the evolution equation of the particle joint probability density function p(x,v,t), x and v being the particle position and velocity, respectively. For finite inertia, position and velocity variables are coupled, with the result that p(x,v,t) can be determined by solving a partial differential equation in a 2d-dimensional space, d being the physical-space dimensionality. For small inertia, (x,v)-variables decouple and the determination of p(x,v,t) is reduced to solve a system of two standard forced advection-diffusion equations in the space variable x. The latter equations are derived here from first principles, i.e. from the well-known Lagrangian evolution equations for position and particle velocity.Comment: 10 pages, submitted to JF

Rotating Rayleigh-Taylor turbulence

International audienceThe turbulent Rayleigh–Taylor system in a rotating reference frame is investigated by direct numerical simulations within the Oberbeck-Boussinesq approximation. On the basis of theoretical arguments, supported by our simulations, we show that the Rossby number decreases in time, and therefore the Coriolis force becomes more important as the system evolves and produces many effects on Rayleigh–Taylor turbulence. We find that rotation reduces the intensity of turbulent velocity fluctuations and therefore the growth rate of the temperature mixing layer. Moreover, in presence of rotation the conversion of potential energy into turbulent kinetic energy is found to be less effective and the efficiency of the heat transfer is reduced. Finally, during the evolution of the mixing layer we observe the development of a cyclone-anticyclone asymmetry

Galloping instability and control of a rigid pendulum in a flowing soap film

International audienceA pendulum suspended in a fast flowing soap film may show sustained oscillations. The conditions necessary for self excited motion to occur are outlined: a flow velocity above a threshold value along with geometrical constraints. The role of vortex shedding is discussed, and the observed instability is shown to be well described by the galloping instability. Experimental results are supported by numerical simulations. Furthermore, we observe that the instability may be suppressed by attaching a long enough filament to the rear of the pendulum