E. V. Ezhova

Surface manifestations of internal waves investigated by a subsurface buoyant Jet: 1. The mechanism of internal-wave generation

In a large test reservoir with artificial temperature stratification at the Institute of Applied Physics, Russian Academy of Sciences, we have performed a major laboratory simulation of the nonstationary dynamics of buoyant turbulent jets generated by wastewater flows from underwater collector diffusers. The interaction of buoyant jets with the pycnocline leads to an active generation of internal waves. An analysis of the dependence of wave amplitude on the control parameter proportional to the rate of liquid flow from the collector diffuser has indicated that this dependence is adequately described by a function that is characteristic for the presence in the Hopf bifurcation system, which occurs for a soft actuation mode of self-oscillations of the globally instable mode. To check the conditions for the actuation of the globally instable mode, we have performed an auxiliary experiment in a small reservoir with a salt stratification formulated similar to the experiment in the big reservoir. Using the particle image velocimetry (PIV) method, we have measured the velocity field in the buoyant jet and constructed the profiles of transverse velocity in several sections. When the jet approaches the pycnocline, a counterflow is generated at the edges. A stability analysis for the resulting profiles of flow velocities performed by the method of normal modes has revealed that, for the jet portions with counterflow, the condition of absolute instability by the Briggs criterion for axisymmetric jet oscillations is satisfied, which testifies to the fact that the globally instable mode is actuated. The estimates for oscillation frequencies of the globally instable mode are well consistent quantitatively with the measured spectrum of jet oscillations.

Surface manifestations of internal waves investigated by a subsurface buoyant jet: 3. Surface manifestations of internal waves

In a large test reservoir at the Institute of Applied Physics, Russian Academy of Sciences, a series of experiments were performed to investigate the surface manifestations of internal waves radiated by a subsurface buoyant jet. The field of currents on the water surface of the reservoir was studied through the distribution of temperature with shallow thermocline. Using Particle Tracking Velocimetry (PTV), the velocity field of surface currents was measured. A theoretical model was developed to calculate the rates of disturbances on the surface. A comparison with experimental data indicated that the calculated data of the surface rate value are overestimated. This discrepancy was explained by the presence of a film of surface-active substances (SASs) with experimentally obtained parameters. Using scale modeling coefficients, we estimated the parameters of internal waves radiated by the subsurface wastewater system and the values of their surface manifestations in field conditions. We estimated the hydrodynamic contrasts in the field of surface waves, which can be caused by these inhomogeneous currents on the surface. For a wind velocity of 5 m/s, the magnitude of the contrast in the field of short waves can reach up to 10–25%, which is detected with confidence by remote-sensing methods.

Surface manifestations of internal waves investigated by a subsurface buoyant jet: Part 2. Internal wave field

In a large test reservoir with artificial temperature stratification at the Institute of Applied Physics, Russian Academy of Sciences, a major simulation of internal wave actuation by buoyant turbulent jets generated by wastewater flows from underwater collector diffusers in conditions of temperature stratification with deep and shallow thermocline has been performed. Using a modification of the particle tracing velocimetry (PTV) method in the stratification mode with shallow thermocline, the velocities of currents generated by internal waves at the surface of the water area are measured. A theoretical model is developed describing the fields of internal waves in the presence of jet stream. Dispersion relations and structures of lower (first and second) modes of internal waves in the stratified basin for different rates of liquid outflow from the collector model are obtained. The experimentally measured field of isothermal shifts with respect to the system of characteristic modes of internal waves is decomposed. A mixed regime of internal wave actuation with the simultaneous existence of the first and second modes is observed. The characteristics of perturbations in the liquid column and on its surface are compared. This analysis allows us to prove that the velocity fields on the surface are indeed surface manifestations of internal waves.

Nonstationary dynamics of turbulent axisymmetric jets in a stratified fluid: Part 2. Mechanism of excitation of axisymmetric oscillations in a submerged jet

It was shown based on laboratory experiments in a Large Thermally Stratified Tank (LTST) at the Institute of Applied Physics of the Russian Academy of Sciences that a turbulent axisymmetric jet in a stratified fluid with a sharp density drop (a pycnocline) intensively generates internal waves. An axisymmetric oscillation mode, for which a sufficient condition of stability in the parallel flow approximation is met, served as their source. This paper studies the stability of a nonparallel flow (with self-similar velocity profiles) that simulates a jet flow in the lower part of the pycnocline with respect to the axisymmetric mode. The estimates of the axisymmetric mode near the pycnocline are in agreement with the experimental data. The signs of the self-oscillating mode of the jet were experimentally revealed and the possibility of self-oscillations was theoretically proved: it was shown that the flow in the pycnocline vicinity is absolutely unstable.

Nonsteady dynamics of turbulent axisymmetric jets in stratified fluid: Part 1. Experimental study

The nonsteady dynamics of turbulent axially symmetrical jets in stratified fluid with a great density gradient (pycnocline) is studied in laboratory experiments in the large test reservoir with artificial temperature stratification at the Institute of Applied Physics, Russian Academy of Sciences (IAP RAS) simulating wastewater flows from underwater collectors in coastal cities. An underwater survey of jets in the pycnocline region has been carried out along with synchronous measurements of internal waves. It is shown that a jet quasiperiodically oscillates in a vertical plane, thus effectively generating internal waves when interacting with the pycnocline. It is ascertained that the axially symmetrical mode of jet oscillations is a source of internal waves.

On the application of a turbulence closure modified model to the description of the density jump evolution in a stably stratified medium

The self-similar turbulent density jump evolution has been studied in the scope of a turbulence closure modernized theory which takes into account the anisotropy and mutual transformation of the turbulent fluctuation kinetic and potential energy for a stably stratified fluid. The numerical calculation, performed using the equations for the average density and kinetic and potential energies of turbulent fluctuations, indicates that the vertical profiles of the buoyancy frequency, turbulence scale, and kinetic and potential energies drastically change when the turbulence anisotropy is strong. The vertical profiles of the corresponding energy and spatial discontinuity parameters, calculated at a weaker anisotropy, indicate that similar drastic changes are absent and a qualitative agreement exists with the known analytical solution, which describes the density jump evolution in a freshwater basin and was obtained previously [5, 8] in the scope of a turbulence local-similarity hypothesis applied in combination with the budget equation for the turbulent fluctuation kinetic energy.

On the structure of internal waves excited by buoyant plumes in stratified fluid

Laboratory scale models of sewage disposal from submerged diffusers of the wastewater outfalls was carried out in the Large Thermostratified Tank of IAP RAS. It is shown that intensive interaction of internal waves occurs due to the interaction of turbulent buoyant plumes and a region of temperature bound (thermocline) and a stream propagates under a thermocline. A theoretical model of the field of internal waves is constructed for experimentally obtained velocity and density fields. It is demonstrated that the bimodal regime of internal wave excitation takes place with the first mode localized in the thermocline region and the second one in the stream. The mode excitation coefficients can be described well in the framework of self-induced internalwave generation by buoyant plumes.