scholarly journals The Fefferman-Stein decomposition for the Constantin-Lax-Majda equation: Regularity criteria for inviscid fluid dynamics revisited

2012 ◽  
Vol 53 (11) ◽  
pp. 115607 ◽  
Author(s):  
Koji Ohkitani
Keyword(s):  
Fluid Dynamics ◽  
Regularity Criteria ◽  
Inviscid Fluid

On the computation of measure-valued solutions

Acta Numerica ◽  
2016 ◽  
Vol 25 ◽  
pp. 567-679 ◽  
Author(s):  
Ulrik S. Fjordholm ◽  
Siddhartha Mishra ◽  
Eitan Tadmor
Keyword(s):  
Fluid Dynamics ◽  
Materials Science ◽  
Numerical Algorithms ◽  
Approximate Solutions ◽  
Variational Problems ◽  
Convincing Evidence ◽  
Young Measures ◽  
Inviscid Fluid ◽  
New Paradigm ◽  
Uniqueness Of Solutions

A standard paradigm for the existence of solutions in fluid dynamics is based on the construction of sequences of approximate solutions or approximate minimizers. This approach faces serious obstacles, most notably in multi-dimensional problems, where the persistence of oscillations at ever finer scales prevents compactness. Indeed, these oscillations are an indication, consistent with recent theoretical results, of the possible lack of existence/uniqueness of solutions within the standard framework of integrable functions. It is in this context that Young measures – parametrized probability measures which can describe the limits of such oscillatory sequences – offer the more general paradigm of measure-valued solutions for these problems.We present viable numerical algorithms to compute approximate measure-valued solutions, based on the realization of approximate measures as laws of Monte Carlo sampled random fields. We prove convergence of these algorithms to measure-valued solutions for the equations of compressible and incompressible inviscid fluid dynamics, and present a large number of numerical experiments which provide convincing evidence for the viability of the new paradigm. We also discuss the use of these algorithms, and their extensions, in uncertainty quantification and contexts other than fluid dynamics, such as non-convex variational problems in materials science.

scholarly journals Numerical Simulations of Two-Layer Flow past Topography. Part I: The Leeside Hydraulic Jump

2018 ◽  
Vol 75 (4) ◽  
pp. 1231-1241 ◽  
Author(s):  
Richard Rotunno ◽  
George H. Bryan
Keyword(s):  
Fluid Dynamics ◽  
Hydraulic Jump ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Layer ◽  
Transition To Turbulence ◽  
Height Velocity ◽  
Inviscid Fluid ◽  
Initial Value ◽  
Density Interface

Abstract Laboratory observations of the leeside hydraulic jump indicate it consists of a statistically stationary turbulent motion in an overturning wave. From the point of view of the shallow-water equations (SWE), the hydraulic jump is a discontinuity in fluid-layer depth and velocity at which kinetic energy is dissipated. To provide a deeper understanding of the leeside hydraulic jump, three-dimensional numerical solutions of the Navier–Stokes equations (NSE) are carried out alongside SWE solutions for nearly identical physical initial-value problems. Starting from a constant-height layer flowing over a two-dimensional obstacle at constant speed, it is demonstrated that the SWE solutions form a leeside discontinuity owing to the collision of upstream-moving characteristic curves launched from the obstacle. Consistent with the SWE solution, the NSE solution indicates the leeside hydraulic jump begins as a steepening of the initially horizontal density interface. Subsequently, the NSE solution indicates overturning of the density interface and a transition to turbulence. Analysis of the initial-value problem in these solutions shows that the tendency to form either the leeside height–velocity discontinuity in the SWE or the overturning density interface in the exact NSE is a feature of the inviscid, nonturbulent fluid dynamics. Dissipative turbulent processes associated with the leeside hydraulic jump are a consequence of the inviscid fluid dynamics that initiate and maintain the locally unstable conditions.

Phase space density representation of inviscid fluid dynamics

1987 ◽  
Vol 30 (10) ◽  
pp. 2952 ◽  
Author(s):  
Henry D. I. Abarbanel ◽  
A. Rouhi
Keyword(s):  
Fluid Dynamics ◽  
Phase Space ◽  
Inviscid Fluid ◽  
Phase Space Density ◽  
Space Density

2-D Modeling of Nonlinear Dynamics of Forcespinning Jet Formation

2021 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Simon Padron ◽  
Karen Lozano
Keyword(s):  
Fluid Dynamics ◽  
Angular Velocity ◽  
Multiple Scales ◽  
Tangential Velocity ◽  
Production Method ◽  
Orifice Diameter ◽  
Inviscid Fluid ◽  
Exit Angle ◽  
Fluid Level ◽  
Jet Trajectory

Abstract Forcespinning is a novel method that makes use of centrifugal forces to produce nanofibers rapidly and at high yields. To improve and enhance the forcespinning production method, a 2D computational forcespinning inviscid fluid dynamics model is developed. Two models, namely time-independent and time-dependent, are obtained in order to investigate the influence of various parameters on fiber forcespinning formation (trajectory, jet diameter, tangential velocity). The fluid dynamics equations are solved using the method of multiple scales along with the finite difference method, and including slender-jet theory assumptions. It is important to produce jets with small diameters in the micro- and nano-range. The Weber (We) and Rossby (Rb) numbers were found to both expand the jet trajectory as they increased. Increasing We and/or decreasing Rb was found to decrease the jet diameter. Also, by varying forcespinning parameters, it has been found that the jet radius can be decreased by increasing the jet exit angle in the direction of rotation, reducing the spinneret fluid level, increasing the angular velocity of the spinneret, reducing spinneret length, and/or reducing the orifice diameter. Knowing the jet trajectories is important for designing and positioning of fiber collector. It has been found that the trajectories expand out with the increase of the jet exit angle in the direction of rotation, increase of fluid level, increase of angular velocity, and/or increase of the spinneret length. Production rates and jet radii for any predetermined radial collector distance were also determined.

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