Abstract: In
the large, a correct prediction of a turbulent flow means getting the energy
balance and rotational structures correct. In 2d flows this means (in the large)
matching the energy and enstrophy statistics and in 3d it means matching the
energy and helicity statistics. In this report we consider the prediction of
energy and helicity of a family of approximate deconvolution large eddy
simulation models of turbulence. We derive the energy and helicity conservation
balance of the models and give a detailed analysis of helicity dissipation of
the (parameter free) model and an associated (one parameter) time relaxation
regularization.
As
an application of the model’s helicity balance and helicitydissipation,
we apply Kraichnan’s dynamic argument (a phenomenological argument)to the model.
Under the same conditions the true, underlying fluid velocity is expected to
exhibit an energy cascade (and using similar tools), this phenomenology predicts
that the model has a helicity cascade, linked to its energy cascade developed in
[30], satisfying
and
for
where
d is the filter width, k
is the wave number, are
the model’s energy and helicity dissipation rates, respectively. The analysis
is carried out for differential filters.
We conclude by describing how the results
are modified for other, general filters.
Keywords and phrases: helicity, turbulence, large eddy simulation, deconvolution, cascade.
