An Introduction to Fluid Dynamics

By G. Batchelor. 1968

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations (2020, background): “From the theoretical standpoint, the governing equations of fluid mechanics have beenderived fromconservation laws (conservation of mass, momentum, and energy), leading to partial differential equations (PDEs) such as the well-known Navier-Stokes (NS) equations (4).”
Thin-Film Flows with Wall Slip: An Asymptotic Analysis of Higher Order Glacier Flow Models (2010, methodology): “With λ = O(1), we can expand the dependent variables in asymptotic expansions in powers of ε up to an error of O(ε(2)):”
Unsteady Motions in Combustion Chambers for Propulsion Systems (2006, background): “It is often convenient to introduce scalar and vector potentials © and A from which the velocity is found by di®erentiation (Bachelor, 1967): u = ¡r©+r£A With this representation, the dilatation and curl (rotation) of the velocity ̄eld are separated: r ¢ u0 = ¡r2© ; r£ u0 = r£r£A (5.”
Slip on Superhydrophobic Surfaces (2010, background): “It should be emphasized that the no-slip boundary condition is no more than a convenient approximation that has been found to hold under most normal ﬂow conditions (Batchelor 1985).”
Computational fluid dynamics of dispersed two-phase flows at high phase fractions (2003, methodology): “Therefore solving the Helmholtz equation [19] in order to evaluate the velocity perturbation and then the pressure is not a simple matter.”
Drop fragmentation on impact (2011, background): “owing to mass conservation u1A1 = u2A2 (Batchelor 1967).”
Wave capture and wave–vortex duality (2005, background): “For instance, in the passive advection case it is well known that |∇φ| grows exponentially in time, on average, in the Batchelor random-straining regime, in which isotropic statistics are assumed along with a scale separation between the length scales of U and φ. Haynes & Anglade (1997) find similar”
Do trout swim better than eels? Challenges for estimating performance based on the wake of self-propelled bodies (2007, methodology): “The standard expression for the impulse of an isolated, steadily traveling vortex loop ( Batchelor 1973 ) is then used to estimate forces.”
Learning to Control PDEs with Differentiable Physics (2020, methodology): “Next, we apply our algorithm to two-dimensional ﬂuid dynamics problems, which are challenging due to the complexities of the governing Navier-Stokes equations (Batchelor, 1967).”
Equatorial Circulation of a Global Ocean Climate Model with Anisotropic Horizontal Viscosity (2001, background): “Eddy viscosity arises from a parameterization of the deviatoric component, d, of the Reynolds stress, s, as proportional to the shear of the resolved flow, u, where d must have zero trace (Batchelor 1967; Miles 1994).”
Effects of thermal boundary conditions on natural convection flows within a square cavity (2006, background): “The relationships between stream function, w (Batchelor [23]) and velocity components for two dimensional flows are: U 1⁄4 ow oY and V 1⁄4 ow oX ; ð24Þ”