Is a wind shear model for dynamic soaring always given by the velocity vector field:

F = < cy, 0 >,

where c is constant?

I've tried modeling c to introduce a decay in magnitude of the wind shear as it moves from left to right, but apparently this violates conservation of mass of the flow (assuming the flow is incompressible) and that the coefficient should be kept constant.


The shear layer is conventionally described as a "thin" transition above stationary air and below constant ambient wind. Within that layer,

The wind's gradient w.r.t the altitude between the shear boundaries can be modeled by any smooth (say, twice differentiable) monotonic function.

-- Section III, "Novel Approach to Dynamic Soaring Modeling and Simulation," Kai et al, J. Guidance, Control, and Dynamics 42(6), 2019, https://doi.org/10.2514/1.G003866.

This paper mentions nothing about wind velocity changing w.r.t. horizontal location. In fact it says

the wind blows horizontally by assumption

Because of incompressibility, and because the flow field is uniform both above and below the shear layer, any horizontal change within the shear layer would induce a vertical component of the wind vector. (Handwaving argument: imagine a brick wall downwind in the layer. That would force a downdraft along the wall.)

So today's models of wind shear ignore second-order effects like horizontal decay of magnitude of shear, perhaps because that suffices for the still interesting case of an albatros mid-ocean, as opposed to the turbulence immediately downwind of a mountain ridge. But this won't be the case forever, of course.


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