Timothy W. Kao’s research while affiliated with Catholic University of America and other places

The complex moisture and heat exchange process over the ocean was studied as a strongly coupled system of momentum, heat, moisture, and microwater droplets. Many unusual temperature profiles observed over the ocean can be naturally explained through the latent heat of evaporation of microwater droplets produced by the breaking waves. It is hoped that this preliminary analysis will lead to a better understanding of the complex sea-air interface and provide a more accurate means for estimating the rate of evaporation and heat transfer over large bodies of water.

Experiments were conducted in a long channel in which a mixed region was allowed to collapse in the thermocline region of a stratified fluid. Two solitary wave-like disturbances were generated travelling to the right and left of the mixed region. The mixed region fluid was partly entrained in these waves. The waves were allowed to reflect from the end walls and to collide after the reflexions. The velocity structure of the wave was studied before, during and after a collision by means of hot-film anemometry and streak pictures. Wave speeds were accurately determined by two hot-film probes. Permanence of form and amplitude decay of the waves were observed over long distances and through successive collisions and reflexions. An analytical result for the structure of the solitary wave in an ambient stratification of the hyperbolic tangent type, but of finite total water depth, was obtained using Benney's method. Excellent agreement between the experimental and theoretical results was obtained. The results showed that the generated waves were indeed solitary waves.

The inflow of a fluid of different density into an ambient fluid of uniform density and finite depth is studied numerically using the full Navier–Stokes and diffusion equations. The problem is posed as an initial-boundary-value problem. In both the overflow (lighter buoyant inflow) and underflow (heavier inflow) cases, a gravity current is established with a pronounced headwave. A significant feature of the flows is the presence of strong downwelling (overflow case) and upwelling (underflow case) activity near the front. The overflow case has been applied by Kao, Park, and Pao to the study of small-scale oceanic fronts formed by the river discharge into the coastal region. The present paper deals with the fluid mechanical and numerical aspects of the overall problem in addition to presenting the results of the underflow case. It is found that the characteristics of the flow in the near field of the inflow are mainly governed by an inflow densimetric Froude number, Fe. In particular, the flow regime in the near field gradually changes from a plume-like to a jet-like behavior as Fe changes from less than to greater than unity. For the overflow case the local densimetric Froude number Fd of the current is shown to be a constant and a similarity solution is found in the far field behind the headwave giving a universal result for the density and velocity structure in the vertical for the range of parameters explored.

Buoyant surface discharge into an ambient body of water is studied two-dimensionally by using the full Navier-Stokes and diffusion equations. The study extends an earlier paper by the authors to include the effects of the earth's rotation and ambient stratification. It is found that for low Rossby numbers, quasigeostrophic balance is achieved in time ≈10/ƒ. The deflection, due to the Coriolis effect, of the forward motion of the buoyancy-driven current to the along-front direction decreases the forward speed of the front during the passage toward steady state. When the steady state is achieved, the front becomes stationary in relation to the ambient fluid ahead of it, The structure of the front in the steady state now includes a strong baroclinic along-front jet and surface convergence and downwelling at the front. The vorticity in the frontal region is shown to be in thermal wind balance except near the free surface where the diffusional effect becomes dominant. A comparison with field data is given. It is also found that front progression, when it occurs, is an efficient mechanism for the generation of internal waves at the thermocline. The effect of wind is also briefly explored.

A new method is introduced to produce a uniform stratified flow over a stationary obstacle in an open channel. The flow is achieved by discharging the flow from the channel through a sink. The details of the sink are unimportant. The flow speed is limited only by the sink capacity. Selective withdrawal at lower densimetric Froude numbers is effectively eliminated through the use of a contraction. The standing, free-surface, long wave arising from the initiation of the flow is also eliminated by the contraction. Experiments are conducted for flow over a sphere for a range of Reynolds numbers from O(102) to O(103) and a range of Richardson numbers from O(10−1) to O(10). Dye and neutrally buoyant droplets are used for quantitative analysis of the wake structure. The wake is also probed by a hot-film anemometer. The frequency of vortex shedding is obtained. Comparison with data from towed experiments is also presented.

The velocity of propagation of a variety of gravity motivated density currents is given. Several stratification configurations of the ambient fluid environment are considered. Applications are given to surface warm discharge in lakes or reservoirs, the spreading of a slug of sewage sludge at the thermocline level of the sea or lake, and the spreading of oil slick on water. Extension of the result to axisymmetric spreading is also given. (A)

A study is made of the two-dimensional buoyant surface discharge into an ambient body of water. The numerical study is based on an initial boundary value problem using the full Navier-Stokes and diffusion equations. A turbulence model using the Munk-Anderson parameterization formula for density stratification effect is also incorporated. The results show the establishment of a surface density current with strong surface convergence and downwelling near the front. Comparison is made with the field experiments of Garvine and Monk on a small-scale oceanic front in Long Island Sound. Excellent agreement is obtained.

Results showing the three‐dimensional vortex shedding structure when a sphere is towed at a constant velocity through a stratified fluid are presented. It is found that for small Richardson numbers (weak stratification) and Reynolds numbers in the range from 4×103 to 2×104 the vortex is shed three‐dimensionally. However, stratification quickly and effectively inhibits the vertical motion and the initially turbulent wake collapses and reveals the vertically oriented portion of the vortex structure, reminiscent of a two‐dimensional vortex street behind a circular cylinder when viewed from above. The structure is, however, distinctly three‐dimensional. It is also found that the estimated vortex shedding frequency is in reasonable agreement with previously published results for a sphere in a homogeneous fluid. It is suggested that a weak stratification is an excellent means for revealing the vortex structure of a three‐dimensional body in a homogeneous fluid, and that the vortex tube in the wake of a sphere in a homogeneous fluid has a closed‐end double helical structure. Two branches of the double helix are continuously unwinding in an opposite sense from the formation region. Moreover, the present double helical model satisfies Thompson’s circulation theorem in contrast to previously proposed helical models.

A complete theory of the collapse of a wake in the form of a two-dimensional circular mixed region of uniform density in a linearly stratified fluid is given. The initial stage is based on existing theories and the principal stage is based on the concept of a quasi-steady density current in a stratified environment. The two stages are properly matched. The dimensionless time at the initiation of the principal stage is determined theoretically. The theoretical result is in excellent agreement with previous numerical and experimental results.

A general criterion for the presence or absence of selective withdrawal in a fluid or arbitrary stratification due to a line sink in a channel is presented. Several examples are given. The criterion is based on whether the speed of upstream propagating columnar disturbances is greater or less than the initial uniform velocity induced by the line sink. The result is then extended to topographical influence in the form of a lateral contraction of the channel walls. Experiments were conducted and they verified the conclusions for the lateral contraction. The use of lateral contractions to insure uniform flow in a stratified channel or reservoir is indicated.