Surface thermal structure in a shallow-water, vertical discharge from a coastal power plant

Abstract

The surface temperature field induced by a turbulent buoyant jet, discharging upwards into shallow water and impinging on the water surface, is examined for the case of a power-plant cooling-water outfall off the southern California coast. The data, acquired using an airborne infrared camera, capture the evolution of turbulent-scale structure, as well as the advection of larger-scale patterns that can be used to infer the surface velocity. Some limited in-water measurements were also made. When the ambient, or receiving, water is relatively stagnant, the buoyant fluid moves nearly symmetrically outward from the impingement zone, and both the thermal and velocity fields decay over a radial distance of several tens of meters. Flow in this symmetric case appears to remain supercritical into the far-field, which differs from a recent numerical modeling study that predicts a near-field hydraulic jump. Within the plume, the data show an expanding set of thermal bands, similar to ring-like structures found in laboratory studies of a buoyant vertical jet having a stable near-field. In the presence of an alongshore current, both the plume and thermal bands become stretched out in the downstream direction; but this effect can be accounted for, and the thermal structure made symmetrical, by using an approximate two-dimensional model of the flow field. Characteristics of the observed thermal bands are compared against three ring-creation mechanisms proposed in the literature (jet vortex instability, horizontal shear instability, and internal bore formation), but the present dataset is insufficient to discriminate amongst them.

Appendix: Potential flow

For a two-dimensional flow that is both incompressible and irrotational, velocity components $u$ and $v$ can be expressed in terms of a stream function, $\varPsi$, and a velocity potential, $\phi$:

$$\begin{aligned} \begin{array}{l} u=\frac{\partial \psi }{\partial y},v=-\frac{\partial \psi }{\partial x}; \\ u=-\frac{\partial \phi }{\partial x},v=-\frac{\partial \phi }{\partial y}. \\ \end{array} \end{aligned}$$

(2)

For a uniform flow with velocity components $u=U$ and $v$ = 0, the stream function and velocity potential can be written as

$$\begin{aligned} \begin{array}{l} \psi =Uy, \\ \phi =-Ux. \\ \end{array} \end{aligned}$$

(3)

In case of a point source, velocities are given in polar coordinates with radial velocity $V_{r}=q/(2\pi r)$, where $q$ is volume flow rate per unit depth at the point source, and tangential velocity $V_{\theta } = 0$. The resulting stream function and velocity potential are given as

$$\begin{aligned} \begin{array}{l} \psi =\frac{q}{2\pi }\theta , \\ \phi =-\frac{q}{2\pi }\ln r. \\ \end{array} \end{aligned}$$

(4)

As the flow is incompressible and irrotational, both $\varPsi$ and $\phi$ satisfy Laplace’s equation. Therefore, solutions for multiple flow patterns can be linearly superposed. Thus the solution for a source in an ambient flow becomes

$$\begin{aligned} \begin{array}{l} \psi =\frac{q}{2\pi }\theta +Ur\sin \theta , \\ \phi =-\frac{q}{2\pi }\ln r+Ur\cos \theta . \\ \end{array} \end{aligned}$$

(5)