# Lyapunov Exponent for a Stochastic Flow

## Speaker:

## Institution:

## Time:

## Location:

The following stochastic flow

\[

d\mathbf{r}=\mathbf{v}dt,\quad d\mathbf{v}=-(\mathbf{v/}\tau \mathbf{)}%

dt+d\mathbf w(t,\mathbf{r)},\quad \mathbf{r,v\in }R^{2}

\]

is considered which \ is used to describe tracer particles in turbulent

flow, drifters in the upper ocean, cloud formation, ultrasonic aggregation

of aerosols, mammal migration, iterating functions, and other phenomena. An

exact expression for the top Lyapunov exponent of the flow is given for

isotropic Brownian forcing $\mathbf w(t,\mathbf{r)}$ in terms of Airy functions.