Abstract
The purpose of the present note is to describe the details of a set of simulation tools which we developed in order to study the statistical properties of the solutions of the equation:
when \( \{ \vec{v}(t,x);t0,x \in {{\mathbb{R}}^{2}}\} \) is a stationary and homogeneous Gaussian field with a spectrum of Kolmogorov type. The study is motivated by problems of transport of passive tracer particles at the surface of a two dimensional medium. We are mostly concerned with mathematical modeling of problems from oceanography and we think of the surface of the ocean as a physical medium to which our modeling efforts could apply. For this reason we shall sometimes use the terminology drifters for the passive tracers. The programs have been written for the MASPAR II. We describe the different forms of the simulations and we give numerical results which illustrate the transport properties of such a random medium. These results lead to the formulation of several precise mathematical conjectures which we discuss in the last section.
Partially supported by ONR N00014-91-1010
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© 1996 Birkhäuser Boston
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Carmona, R.A., Grishin, S.A., Molchanov, S.A. (1996). Massively Parallel Simulations of Motions in a Gaussian Velocity Field. In: Adler, R.J., Müller, P., Rozovskii, B.L. (eds) Stochastic Modelling in Physical Oceanography. Progress in Probability, vol 39. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2430-3_2
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DOI: https://doi.org/10.1007/978-1-4612-2430-3_2
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