A Gaussian measure \(\mu\) on the vector space M(d) of real \(d\times d\) matrices is called isotropic if it is invariant under all automorphisms \(\tau_ u: M(d)\to M(d)\), \(A\mapsto U^{-1}AU\), where \(U\in O(d)\), the group of orthogonal matrices. \(\mu\) is characterized by its covariance C. Let W(t) be an M(d) valued (''additive'') Brownian motion with covariance C(t\(\wedge s)\). The solution of the Stratonovich SDE \(dX(t)=X(t)\circ dW(t)\) is a (right multiplicative) Brownian motion in Gl(d), whose law is isotropic again. The Lyapunov exponents of X(t) can be calculated in terms of the covariance C, using elementary Itô calculus. Consider now a stationary Gaussian (vector) field V(x) on \({\mathbb{R}}^ d\). There is an associated family of white noises W(x,dt), which can be integrated into a stochastic flow \(\phi_ t\) of diffeomorphisms. If V(x) is isotropic (i.e., V(Ux) and UV(x) have the same distribution for any \(U\in O(d))\) \(\phi_ t\) is called Brownian flow, its derivative flow is a multiplicative Brownian motion. The Lyapunov exponents \(\alpha_ 1\geq...\geq \alpha_ d\) can be expressed in terms of the covariance of V(x), they are equidistant and \(\alpha_ 10\) if \(d\geq 5\). For \(d=2,3\) the sign of \(\alpha_ 1\) depends on V(x). Finally, assuming instability (i.e., \(\alpha_ 1>0)\), weak convergence of \(\phi_ t^{-1}(dx)\) to a (random) distribution on \({\mathbb{R}}^ d\) is proved, where dx is Lebesgue measure on \({\mathbb{R}}^ d\). This stationary distribution, the statistical equilibrium, is singular with respect to dx iff the flow does not preserve dx. The paper is not self contained.