Kochen & Backen

Study Of Abrupt Transitions in Two-Dimensional Flows PDF

Aerodynamic force components for two points of sail. Left-hand boat: Down wind with stalled airfow— predominant drag component propels the boat with little heeling moment. Study Of Abrupt Transitions in Two-Dimensional Flows PDF on sails depend on wind speed and direction and the speed and direction of the craft.


Författare: Sergiy Kravchuk.
Swirling and stratified flows demonstrate a complex
behaviour with rich spectrum of possible regimes and
sudden changes in the pattern of flow. It is known
that these flows may become sensitive to small
perturbation in boundary conditions and form an
internal jump-like transition from one flow pattern
to a different one a hydraulic jump in stratified
and a vortex breakdown in swirling flows. Analysis of
the motion equations for such flows reveals
singularly perturbed nature of the problem; this
explains the abruptness and sensitivity of
transitions. The book reviews the model flows,
develops a theoretical framework for handling the
singularity at the point of transition, and provide a
procedure for finding the transition point. A
generalisation of the Tikhonov s boundary function
method is developed to study the problem. This
approach is illustrated by calculating of parameters
of an internal hydraulic jump for a model stratified
fluid flow. The book is aimed for graduate students
and professionals in fluid mechanics and applied
mathematics.

For apparent wind angles aligned with the entry point of the sail, the sail acts as an airfoil and lift is the predominant component of propulsion. For apparent wind angles behind the sail, lift diminishes and drag increases as the predominant component of propulsion. Various mathematical models address lift and drag by taking into account the density of air, coefficients of lift and drag that result from the shape and area of the sail, and the speed and direction of the apparent wind, among other factors. This knowledge is applied to the design of sails in such a manner that sailors can adjust sails to the strength and direction of the apparent wind in order to provide motive power to sailing craft. The combination of a sailing craft’s speed and direction with respect to the wind, together with wind strength, generate an apparent wind velocity. When the craft is aligned in a direction where the sail can be adjusted to align with its leading edge parallel to the apparent wind, the sail acts as an airfoil to generate lift in a direction perpendicular to the apparent wind. To understand forces and velocities, discussed here, one must understand what is meant by a „vector“ and a „scalar.

Driving force overcomes resistance to forward motion. Apparent wind and forces on a sailboat. As the iceboat sails further from the wind, the apparent wind increases slightly and the boat speed is highest on the broad reach. The sail is sheeted in for all three points of sail. Sailing craft B is on a beam reach. Sailing craft C is on a broad reach.