The weak temperature gradient (WTG) approximation is applied to simple shallow-water models of the Hadley circulation. While it is difficult to formally justify the use of the WTG approximation for this problem, the derived WTG solutions are shown to agree well with numerical solutions of the full equations and to converge to the traditional angular momentum conserving (AMC) solutions in the in...

Following Prandtl, a viscous-inviscid interaction (VII) method is presented, where the flow field is divided into a viscous shear layer and an inviscid outer region. Their coupling is performed with the quasi-simultaneous approach, making use of an appropriately chosen interaction law. Firstly, an engineering example of transonic airfoil flow is presented, in which the interaction law is based ...

Inviscid two-dimensional (2D) fluid phenomena like hurricanes, jet streams, Jupiter’s Red Spot, and protoplanetary disks are quite common in Nature. Unfortunately, 2D fluid phenomena are difficult to study in the laboratory because the finite size of laboratory apparati commonly introduces unwanted viscous and friction effects. Magnetized electron columns, however, behave like twodimensional fl...

This work describes a projection method for approximating incompressible viscous 1ows of nonuniform density. It is shown that unconditional stability in time is possible provided two projections are performed per time step. A 3nite element implementation and a 3nite volume one are described and compared. The performance of the two methods are tested on a Rayleigh–Taylor instability. We show tha...

We study the limiting behavior of systems of hyperbolic conservation laws with stii relaxation terms. Reduced systems, inviscid and viscous local conservation laws, and weakly nonlinear limits are derived through asymptotic expansions. An entropy condition is introduced for N N systems that ensures the hyperbolicity of the reduced inviscid system. The resulting characteristic speeds are shown t...

Steady, supersonic, dissipative, three-dimensional, axisymmetric flow is considered. A system of Burgers-type equations is shown to govern the flow field. In inviscid regions the Whitham theory gives the limiting form. Dissipative effects ultimately engulf the inviscid zone and at sufficiently large distances from the body the flow is governed by linear dissipative theory. The flow field is div...

At the core of this article is an improved, sharp dispersive estimate for the anisotropic linear semigroup e1 arising in both the study of the dispersive SQG equation and the inviscid Boussinesq system. We combine the decay estimate with a blow-up criterion to show how dispersion leads to long-time existence of solutions to the dispersive SQG equation, improving the results obtained using hyper...

An algorithm is described that calculates inviscid, laminar, and turbulent flows on triangular meshes with an upwind discretization. A brief description of the base solver and the multigrid implementation is given, followed by results that consist mainly of convergence rates for inviscid and viscous flows over a NACA four-digit airfoil section. The results show that multigrid does accelerate co...

We address the question of constructing simple inviscid vortex models that optimally approximate realistic flows as solutions of an inverse problem. Assuming the model to be incompressible, inviscid and stationary in the frame of reference moving with the vortex, the ‘structure’ of the vortex is uniquely characterized by the functional relation between the streamfunction and vorticity. It is de...