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In meteorological applications, a zonal wavenumber or hemispheric wavenumber is the dimensionless number of wavelengths fitting within a full circle around the globe at a given latitude: [1] k = 2 π r cos φ λ , {\displaystyle k={\frac {2\pi r\cos \varphi }{\lambda }},}
The zonal and tesseral terms for n = 1 are left out in . The coefficients for the n=1 with both m=0 and m=1 term correspond to an arbitrarily oriented dipole term in the multi-pole expansion. The coefficients for the n=1 with both m=0 and m=1 term correspond to an arbitrarily oriented dipole term in the multi-pole expansion.
Zonal, sectoral, and tesseral harmonics are depicted along the left-most column, the main diagonal, and elsewhere, respectively. (The negative order harmonics Y ℓ ( − m ) {\displaystyle Y_{\ell (-m)}} would be shown rotated about the z axis by 90 ∘ / m {\displaystyle 90^{\circ }/m} with respect to the positive order ones.)
Zonal and meridional flow are directions and regions of fluid flow on a globe. Zonal flow follows a pattern along latitudinal lines, latitudinal circles or in the west–east direction. [ 1 ] Meridional flow follows a pattern from north to south, or from south to north, along the Earth's longitude lines, longitudinal circles ( meridian ) or in ...
The zonal spherical harmonics are rotationally invariant, meaning that () = () for every orthogonal transformation R.Conversely, any function f(x,y) on S n−1 ×S n−1 that is a spherical harmonic in y for each fixed x, and that satisfies this invariance property, is a constant multiple of the degree ℓ zonal harmonic.
The perturbation is assumed to be much smaller than the mean zonal flow. U ≫ u ′ , v ′ {\displaystyle U\gg u',v'\!} The relative vorticity η {\displaystyle \eta } and the perturbations u ′ {\displaystyle u'} and v ′ {\displaystyle v'} can be written in terms of the stream function ψ {\displaystyle \psi } (assuming non-divergent flow ...
Typical values for the wind stress are about 0.1Pa and, in general, the zonal wind stress is stronger than the meridional wind stress as can be seen in figures 2.1 and 2.2. It can also be seen that the largest values of the wind stress occur in the Southern Ocean for the zonal direction with values of about 0.3Pa.
Note that the practical value of trips on the diagonal, e.g. from zone 1 to zone 1, is zero since no intra-zonal trip occurs. Work trip distribution is the way that travel demand models understand how people take jobs.