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Register a new userThe dependence of relative dispersion on turbulence scales in Lagrangian Stochastic Models
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The aim of the article is to investigate the relative dispersion properties of the Well Mixed class of Lagrangian Stochastic Models. Dimensional analysis shows that given a model in the class, its properties depend solely on a non-dimensional parameter, which measures the relative weight of Lagrangian-to-Eulerian scales. This parameter is formulated in terms of Kolmogorov constants, and model properties are then studied by modifying its value in a range that contains the experimental variability. Large variations are found for the quantity $g^*=2gC_0^{-1}$, where $g$ is the Richardson constant, and for the duration of the $t^3$ regime. Asymptotic analysis of model behaviour clarifies some inconsistencies in the literature and excludes the Ornstein-Uhlenbeck process from being considered a reliable model for relative dispersion.
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This paper has been withdrawn by the author due to a crucial error in the formulation.
In this paper we describe the construction of an efficient probabilistic parameterization that could be used in a coarse-resolution numerical model in which the variation of moisture is not properly resolved. An Eulerian model using a coarse-grained field on a grid cannot properly resolve regions of saturation---in which condensation occurs---that are smaller than the grid boxes. Thus, in the absence of a parameterization scheme, either the grid box must become saturated or condensation will be underestimated. On the other hand, in a stochastic Lagrangian model of moisture transport, trajectories of parcels tagged with humidity variables are tracked and small-scale moisture variability can be retained; however, explicitly implementing such a scheme in a global model would be computationally prohibitive. One way to introduce subgrid-scale saturation into an Eulerian model is to assume the humidity within a grid box has a probability distribution. To close the problem, this distribution is conventionally determined by relating the required subgrid-scale properties of the flow to the grid-scale properties using a turbulence closure. Here, instead, we determine an assumed probability distribution by using the statistical moments from a stochastic Lagrangian version of the system. The stochastic system is governed by a Fokker--Planck equation and we use that, rather than explicitly following the moisture parcels, to determine the parameters of the assumed distribution. We are thus able to parameterize subgrid-scale condensation in an Eulerian model in a computationally efficient and theoretically well-founded way. In two idealized advection--condensation problems we show that a coarse Eulerian model with the subgrid parameterization is well able to mimic its Lagrangian counterpart.
Here we propose an optical method that use phase data of a laser beam obtained from Shack-Hartmann sensor to estimate both inner and outer scales of turbulence. The method is based on the sequential analysis of normalized correlation functions of Zernike coefficients. It allows excluding the value of refractive index structural constant from the analysis and reduces the solution of a two-parameter problem to sequential solution of two single-parameter problems. The method has been applied to analyze the results of measurements of the laser beam that propagated through a water cell with induced turbulence and yielded estimates for outer and inner scales.
The relative dispersion process in two-dimensional free convection turbulence is investigated by direct numerical simulation. In the inertial range, the growth of relative separation, $r$, is expected as $<r^2(t)>propto t^5$ according to the Bolgiano-Obukhov scaling. The result supporting the scaling is obtained with exit-time statistics. Detailed investigation of exit-time PDF shows that the PDF is divided into two regions, the Region-I and -II, reflecting two types of separating processes: persistent expansion and random transitions between expansion and compression of relative separation. This is consistent with the physical picture of the self-similar telegraph model. In addition, a method for estimating the parameters of the model are presented. Comparing two turbulence cases, two-dimensional free convection and inverse cascade turbulence, the relation between the drift term of the model and nature of coherent structures is discussed.
Any type of non-buoyant material in the ocean is transported horizontally by currents during its sinking journey. This lateral transport can be far from negligible for small sinking velocities. To estimate its magnitude and direction, the material is often modelled as a set of Lagrangian particles advected by current velocities that are obtained from Ocean General Circulation Models (OGCMs). State-of-the-art OGCMs are strongly eddying, similar to the real ocean, providing results with a spatial resolution on the order of 10 km on a daily frequency. While the importance of eddies in OGCMs is well-appreciated in the physical oceanographic community, other marine research communities may not. To demonstrate how much the absence of mesoscale features in low-resolution models influences the Lagrangian particle transport, we simulate the transport of sinking Lagrangian particles using low- and high-resolution global OGCMs, and assess the lateral transport differences resulting from the difference in spatial and temporal model resolution. We find major differences between the transport in the non-eddying OGCM and in the eddying OGCM. Addition of stochastic noise to the particle trajectories in the non-eddying OGCM parameterises the effect of eddies well in some cases. The effect of a coarser temporal resolution (5-daily) is smaller compared to a coarser spatial resolution (0.1$^{circ}$ versus 1$^{circ}$ horizontally). We recommend to use sinking Lagrangian particles, representing e.g. marine snow, microplankton or sinking plastic, only with velocity fields from eddying OGCMs, requiring high-resolution models in e.g. paleoceanographic studies. To increase the accessibility of our particle trace simulations, we launch planktondrift.science.uu.nl, an online tool to reconstruct the surface origin of sedimentary particles in a specific location.
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