Abstract The incompressible Toner–Tu (ITT) partial differential equations (PDEs) are an
important example of a set of active-fluid PDEs. While they share certain properties with the …

Shell models have found wide application in the study of hydrodynamic turbulence because
they are easily solved numerically even at very large Reynolds numbers. Although bereft of …

Shell models allow much greater scale separations than those presently achievable with
direct numerical simulations of the Navier-Stokes equations. Consequently, they are an …

We consider the three-dimensional (3D) Cahn-Hilliard equations coupled to, and driven by,
the forced, incompressible 3D Navier-Stokes equations. The combination, known as the …

The practical results gained from statistical theories of turbulence usually appear in the form
of an inertial range energy spectrum E (k)∼ kq and a cutoff wavenumber kc. For example …

We consider solenoidal space-periodic space-analytic solutions to the equations of
magnetohydrodynamics. An elementary bound shows that due to the special structure of the …

We study the three-dimensional, incompressible, non-hydrostatic Boussinesq fluid
equations, which are applicable to the dynamics of the oceans and atmosphere. These …

We revisit the scaling properties of the energy spectra in fully developed incompressible
homogeneous turbulence in forced magnetofluids (MHD) in three dimensions (3D), which …

The old idea that an infinite-dimensional dynamical system may have its high modes or
frequencies slaved to low modes or frequencies is revisited in the context of the 3D Navier …

It is shown that appearance of inertial range of scales, adjacent to distributed chaos range,
results in adiabatic invariance of an energy correlation integral for isotropic homogeneous …