North Pacific decadal oceanic and atmospheric variability is examined from a 650-yr control integration of the Community Climate System Model version 2. The dominant pattern of winter sea surface temperature (SST) variability is similar to the observed “Pacific decadal oscillation,” with maximum amplitude along the Kuroshio Extension. SST anomalies in this region exhibit significant spectral pe...

We present tensor-product divergence-free and curl-free wavelets, and define associated projectors. These projectors permit the definition of an iterative algorithm to compute the Helmholtz decomposition in wavelet domain of any vector field. This decomposition is localized in space, in contrast to the Helmholtz decomposition calculated by Fourier transform. Then we prove the convergence of the...

In this paper, we present several results concerning vector potentials and scalar potentials with data in Sobolev spaces with negative exponents, in a not necessarily simply-connected, three-dimensional domain. We then apply these results to Poincaré’s theorem and to Korn’s inequality. 1 Weak versions of a classical theorem of Poincaré In this work, (the results of which were announced in [2]),...

This work develops optimal preconditioners for the discrete H(curl) and H(div) problems on two-dimensional surfaces by nodal auxiliary space preconditioning (Hiptmair Xu in SIAM J Numer Anal 45:2483–2509, 2007). In particular, unstructured triangulated surfaces, we develop fast user-friendly edge face element discretizations of curl–curl grad–div based inverting several surface Laplacians. The ...

2 Vector Analysis 6 2.1 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Scalar Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 The Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 The Divergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5 The Curl . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

We consider energy-minimizing divergence-free eigenfields of the curl operator in dimension three from the perspective of contact topology. We give a negative answer to a question of Etnyre and the first author by constructing curl eigenfields which minimize L energy on their co-adjoint orbit, yet are orthogonal to an OVERTWISTED contact structure. We conjecture that K-contact structures on S-b...