IWNET12
IWNET12
Fluctuations in laminar ow
José M. Ortiz de Zárate1, Jan V. Sengers2
1 Departamento de Física Aplicada I, Universidad Complutense, Madrid, Spain
2 Institute for Physical Science and Technology, University of Maryland, College Park, MD, USA
Abstract
One of the many physical dierences between equilibrium and nonequilibrium states is the existence of mode-
coupling phenomena at the linear level. Indeed, generically, dissipative uxes have deterministic (i.e. non-
random) components for systems outside equilibrium. For instance, and depending on the particular non-
equilibrium mechanism, the uid velocity or the heat ow do not average to zero. These non-vanishing averages
appear in the uctuating hydrodynamics equations, even when linearized over the uctuations of the thermo-
dynamic elds.
As extensively investigated in the past decades, this feature has important consequences on the theory of
hydrodynamic uctuations for systems that are not in equilibrium. In particular, equal-time eld uctuations are
enhanced and become spatially long-ranged. As a corollary, and opposed to equilibrium situations, incorporation
of boundary conditions is crucial for a correct description of the spatial spectrum of uctuations, especially at
large wavelengths.
In this presentation we review recent theoretical work on the intensity of thermal uctuations in uids under
laminar ow. We identify two dierent mode-coupling mechanisms leading to non-equilibrium enhancement
of the uctuations: self-coupling of similar modes with dierent wave number and cross-coupling between
wall-normal velocity and vorticity. We incorporate vanishing velocity uctuations at the walls, and discuss the
consequences for the intensity of uctuations. For the particular case of plane Couette ow, we compare the two
coupling mechanisms and conclude that cross-coupling is the most important one. The resulting enhancement is
highly anisotropic, wall-normal velocity uctuations are maximally enhanced in the streamwise direction, while
wall-normal vorticity uctuations are maximally enhanced in the spanwise direction. For the particular case
of wave vector in the spanwise direction (or, alternatively, streamwise-constant uctuations), we have obtained
a compact analytical expression for the spatial spectrum of the vorticity uctuations. These uctuations are
those maximally enhanced.
E-mail: jmortizz@fis.ucm.es

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