  We discuss the scaling exponents characterizing the power-law behavior of the
anisotropic components of correlation functions in turbulent systems with
pressure. The anisotropic components are conveniently labeled by the angular
momentum index $\ell$ of the irreducible representation of the SO(3) symmetry
group. Such exponents govern the rate of decay of anisotropy with decreasing
scales. It is a fundamental question whether they ever increase as $\ell$
increases, or they are bounded from above. The equations of motion in systems
with pressure contain nonlocal integrals over all space. One could argue that
the requirement of convergence of these integrals bounds the exponents from
above. It is shown here on the basis of a solvable model (the ``linear pressure
model"), that this is not necessarily the case. The model introduced here is of
a passive vector advection by a rapidly varying velocity field. The advected
vector field is divergent free and the equation contains a pressure term that
maintains this condition. The zero modes of the second-order correlation
function are found in all the sectors of the symmetry group. We show that the
spectrum of scaling exponents can increase with $\ell$ without bounds, while
preserving finite integrals. The conclusion is that contributions from higher
and higher anisotropic sectors can disappear faster and faster upon decreasing
the scales also in systems with pressure.
