Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From limited observations to the state of turbulence: Fundamental
  difficulties of flow reconstruction   Numerical simulations of turbulence provide non-intrusive access to all the
resolved scales, although they often invoke idealizations that can compromise
realism. In contrast, experimental measurements probe the true flow with lesser
idealizations, but they continually contend with spatio-temporal sensor
resolution. Assimilating observations directly in simulations can combine the
benefits of both approaches. The problem is expressed in variational form,
where we seek a Navier-Stokes solution that minimizes a cost function defined
in terms of the deviation of numerical predictions and observations. In this
framework, measurements are no longer a mere record of the instantaneous, local
quantity, but rather an encoding of the antecedent flow events that we aim to
decode using the governing equations. We examine three state estimation
problems: In circular Couette flow, starting from wall stress data, we
accurately reconstruct the nonlinear saturated wavy Taylor vortices. Through a
discussion of transition to chaos in a Lorenz system, we highlight the
challenge of navigating the landscape of the cost function, and how the
landscape can be modified by sensor placement. In turbulent channel flow, the
Taylor microscale and Lyapunov timescale place restrictions on the resolution
of observations that ensure an accurate reconstruction of all the scales. The
notion of domain of dependence of an observation is introduced and related to
the Hessian of the cost function. For measurements of wall stress, the
eigenspectrum of the Hessian demonstrates the sensitivity of short-time
observations to the near-wall turbulent scales and to outer large scales. At
long times, backward chaos obfuscates the interpretation of the data:
observations that are infinitesimally close may be traced back to entirely
different earlier flow states--a dual to the more common butterfly effect for
forward trajectories.

36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
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The categories of this paper are: stat
6
The categories of this paper are: astro-ph