8 research outputs found
Nonlinear Hamiltonian dynamics of Lagrangian transport and mixing in the ocean
Methods of dynamical system's theory are used for numerical study of
transport and mixing of passive particles (water masses, temperature, salinity,
pollutants, etc.) in simple kinematic ocean models composed with the main
Eulerian coherent structures in a randomly fluctuating ocean -- a jet-like
current and an eddy. Advection of passive tracers in a periodically-driven flow
consisting of a background stream and an eddy (the model inspired by the
phenomenon of topographic eddies over mountains in the ocean and atmosphere) is
analyzed as an example of chaotic particle's scattering and transport. A
numerical analysis reveals a nonattracting chaotic invariant set that
determines scattering and trapping of particles from the incoming flow. It is
shown that both the trapping time for particles in the mixing region and the
number of times their trajectories wind around the vortex have hierarchical
fractal structure as functions of the initial particle's coordinates.
Scattering functions are singular on a Cantor set of initial conditions, and
this property should manifest itself by strong fluctuations of quantities
measured in experiments. The Lagrangian structures in our numerical experiments
are shown to be similar to those found in a recent laboratory dye experiment at
Woods Hole. Transport and mixing of passive particles is studied in the
kinematic model inspired by the interaction of a jet current (like the Gulf
Stream or the Kuroshio) with an eddy in a noisy environment. We demonstrate a
non-trivial phenomenon of noise-induced clustering of passive particles and
propose a method to find such clusters in numerical experiments. These clusters
are patches of advected particles which can move together in a random velocity
field for comparatively long time
New capabilities of Chetaev’s model
This paper considers anomalies in the magnetotelluric field in the Pc3 range of geomagnetic pulsations. We report experimental data on Pc3 field recordings which show negative (from Earth’s surface to air) energy fluxes Sz1. Using the model of inhomogeneous plane wave (Chetaev’s model), we try to analytically interpret anomalies of energy fluxes. We present two three-layer models with both electric and magnetic modes satisfying the condition |Qh|>1. Here we discuss a possibility of explaining observable effects by the resonance interaction between inhomogeneous plane waves and layered media
Optimal Harvest Problem for Fish Population—Structural Stabilization
The influence of environmental conditions and fishery on a typical pelagic or semi-pelagic fish population is studied. A mathematical model of population dynamics with a size structure is constructed. The problem of the optimal harvest of a population in unstable environment conditions is investigated and an optimality system to the problem research is constructed. The solutions properties in various cases have also been investigated. Environmental conditions influence the fish population through recruitment. Modelling of recruitment rate is made by using a stochastic imitation of environmental conditions. In the case of stationary environment, a population model admits nontrivial equilibrium state. The parameters of fish population are obtained from this equilibrium condition. The variability of environment leads to large oscillations of generation size. The fluctuations of the fish population density follow the dynamics of recruitment rate fluctuations but have smaller gradients than recruitment. The dynamics of the optimal fishing effort is characterized by high variability. The population and the average size of individuals decrease under the influence of fishery. In general, the results of computer calculations indicate the stabilization of the population dynamics under influence of size structure. Optimal harvesting also contributes to stabilization