131 citations · 329 across the 16 of their papers we have counts for
15 papers · 1 filter
On persistence of spatial analyticity in the hyper-dissipative Navier-Stokes models
Aseel Farhat, Zoran Grujic
The goal of this note is to demonstrate that as soon as the hyper-diffusion exponent is greater than one, a class of finite time blow-up scenarios consistent with the analytic stru…
Local near-Beltrami structure and depletion of the nonlinearity in the 3D Navier-Stokes flows
Aseel Farhat, Zoran Grujic
Computational simulations of turbulent flows indicate that the regions of low dissipation/enstrophy production feature high degree of local alignment between the velocity and the v…
Oscillations and integrability of the vorticity in the 3D NS flows
Y. Do, A. Farhat, Z. Grujic +1
In the studies of the Navier-Stokes (NS) regularity problem, it has become increasingly clear that a more realistic path to improved a priori bounds is to try to break away from th…
Assimilation of nearly turbulent Rayleigh-Bénard flow through vorticity or local circulation measurements: a computational study
Aseel Farhat, Hans Johnston, Michael S. Jolly +1
We introduce a continuous (downscaling) data assimilation algorithm for the 2D Bénard convection problem using vorticity or local circulation measurements only. In this algorithm,…
An algebraic reduction of the `scaling gap' in the Navier-Stokes regularity problem
Zachary Bradshaw, Aseel Farhat, Z. Grujic
It is shown--within a mathematical framework based on the suitably defined scale of sparseness of the super-level sets of the positive and negative parts of the vorticity component…
A data assimilation algorithm: the paradigm of the 3D Leray-alpha model of turbulence
Aseel Farhat, Evelyn Lunasin, Edriss S. Titi
In this paper we survey the various implementations of a new data assimilation (downscaling) algorithm based on spatial coarse mesh measurements. As a paradigm, we demonstrate the…
On the Charney Conjecture of Data Assimilation Employing Temperature Measurements Alone: The Paradigm of 3D Planetary Geostrophic Model
Aseel Farhat, Evelyn Lunasin, Edriss S. Titi
Analyzing the validity and success of a data assimilation algorithm when some state variable observations are not available is an important problem in meteorology and engineering.…
The space , volumetric sparseness, and 3D NSE
Aseel Farhat, Zoran Grujic, Keith Leitmeyer
In the context of the -theory of the 3D NSE, it is shown that suitable smallness of a solution in Besov space suffices to prevent a possible blo…
Continuous Data Assimilation for a 2D Bénard Convection System through Horizontal Velocity Measurements Alone
Aseel Farhat, Evelyn Lunasin, Edriss S. Titi
In this paper we propose a continuous data assimilation (downscaling) algorithm for a two-dimensional Bénard convection problem. Specifically we consider the two-dimensional Boussi…
Data Assimilation algorithm for 3D Bénard convection in porous media employing only temperature measurements
Aseel Farhat, Evelyn Lunasin, Edriss S. Titi
In this paper we propose a continuous data assimilation (downscaling) algorithm for the Bénard convection in porous media using only coarse mesh measurements of the temperature. In…
Abridged continuous data assimilation for the 2D Navier-Stokes equations utilizing measurements of only one component of the velocity field
Aseel Farhat, Evelyn Lunasin, Edriss S. Titi
We introduce a continuous data assimilation (downscaling) algorithm for the two-dimensional Navier-Stokes equations employing coarse mesh measurements of only one component of the…
Continuous Data Assimilation for the 2D Bénard Convection through Velocity Measurements Alone
Aseel Farhat, Michael S. Jolly, Edriss S. Titi
An algorithm for continuous data assimilation for the two- dimensional Bénard convection problem is introduced and analyzed. It is inspired by the data assimilation algorithm devel…
Global Regularity for an Inviscid Three-dimensional Slow Limiting Ocean Dynamics Model
Chongsheng Cao, Aseel Farhat, Edriss S. Titi
We establish, for smooth enough initial data, the global well-posedness (existence, uniqueness and continuous dependence on initial data) of solutions, for an inviscid three-dimens…
Long-time Behavior of a Two-layer Model of Baroclinic Quasi-geostrophic Turbulence
Aseel Farhat, R. Lee Panetta, Edriss S. Titi +1
We study a viscous two-layer quasi-geostrophic beta-plane model that is forced by imposition of a spatially uniform vertical shear in the eastward (zonal) component of the layer fl…
Global Well-posedness of an Inviscid Three-dimensional Pseudo-Hasegawa-Mima Model
Chongsheng Cao, Aseel Farhat, Edriss S. Titi
The three-dimensional inviscid Hasegawa-Mima model is one of the fundamental models that describe plasma turbulence. The model also appears as a simplified reduced Rayleigh-Bénard…