  We construct a Laplacian-level meta-generalized gradient approximation
(meta-GGA) for the non-interacting (Kohn-Sham orbital) positive kinetic energy
density $\tau$ of an electronic ground state of density $n$. This meta-GGA is
designed to recover the fourth-order gradient expansion $\tau^{GE4}$ in the
appropiate slowly-varying limit and the von Weizs\"{a}cker expression
$\tau^{W}=|\nabla n|^2/(8n)$ in the rapidly-varying limit. It is constrained to
satisfy the rigorous lower bound $\tau^{W}(\mathbf{r})\leq\tau(\mathbf{r})$.
Our meta-GGA is typically a strong improvement over the gradient expansion of
$\tau$ for atoms, spherical jellium clusters, jellium surfaces, the Airy gas,
Hooke's atom, one-electron Gaussian density, quasi-two dimensional electron
gas, and nonuniformly-scaled hydrogen atom. We also construct a Laplacian-level
meta-GGA for exchange and correlation by employing our approximate $\tau$ in
the Tao, Perdew, Staroverov and Scuseria (TPSS) meta-GGA density functional.
The Laplacian-level TPSS gives almost the same exchange-correlation enhancement
factors and energies as the full TPSS, suggesting that $\tau$ and $\nabla^2 n$
carry about the same information beyond that carried by $n$ and $\nabla n$. Our
kinetic energy density integrates to an orbital-free kinetic energy functional
that is about as accurate as the fourth-order gradient expansion for many real
densities (with noticeable improvement in molecular atomization energies), but
considerably more accurate for rapidly-varying ones.
