Yu. I. Troitskaya

The viscous-diffusion nonlinear critical layer in a stratified shear flow

Stationary finite-amplitude wave disturbances in a stratified shear flow with Richardson number larger than 1/4 are investigated for large Reynolds numbers when viscosity and thermal conductivity, as well as nonlinearity, are essential factors in the critical layer. The jumps across the critical layer in average vorticity, reflection and transmission coefficients are calculated as functions of the local Reynolds number determined by the amplitude of the incident wave.

Satellite altimetry of inland water bodies

An algorithm is proposed for determining water level in inland water bodies and coastal zones of seas and oceans. The algorithm was tested for the water area of the Gorki Reservoir, for which radioaltimeter databases show considerable data losses. A model was constructed, describing the shape of a mean impulse reflected from a statistically heterogeneous piecewise-constant underlying surface (topographic model). The model was used to substantiate criteria for data choice for the Gorki Reservoir and to construct a regional algorithm for estimating water level using data from Jason-1 satellite and based on the analysis of the shape of telemetric impulses (retracking). Water level was calculated with the use of an algorithm of regional adaptive retracking Sensor Geophysical Data Record databases for the Gorki and Rybinsk reservoirs. Algorithm application has been shown to considerably increase the amount of actual data and significantly improve the accuracy of water level evaluation. The general principles of retracking of a complex domain (a coastal zone, an inland water body, etc.) are discussed. The principles are based on the calculation of signal with allowance made for the roughness of the reflecting surface and they can be applied to different geographic regions.

Theoretical Models of the Height of the Atmospheric Boundary Layer and Turbulent Entrainment at Its Upper Boundary

The planetary boundary layer (PBL), which directly interacts with the underlying surface, differs significantly in its nature from the low-turbulent stably stratified free atmosphere. Fluctuations of the Earth’s surface heat balance immediately affect the PBL and assimilate there owing to the effective mechanism of turbulent heat transfer. In this case the upper boundary of the PBL plays the role of a cover, preventing the direct penetration of thermal effects and contaminants into an overlying atmospheric layer. In view of this, air pollution is especially dangerous when associated with shallow PBL. In addition, local peculiarities of climate change are mainly determined by the PBL height due to the high sensitivity of thin stably stratified PBLs to the thermal effects. Deep convective PBLs are not very sensitive to weak thermal effects, but they significantly affect the formation of convective cloudiness and the climate system as a whole by means of the turbulent entrainment of the thermal energy, humidity, aerosols, and other admixtures through the upper boundary. The PBL height and turbulent entrainment must be calculated when simulating and forecasting air pollution, abnormal frosts and heat, and other hazardous phenomena. In this paper we discuss the state-of-the-art knowledge in the area of PBL height simulation and suggest a new model of turbulent entrainment for convective PBLs.

Quasi-linear model of interaction of surface waves with strong and hurricane winds

A quasi-linear model for determining the aerodynamic drag coefficient of the sea surface and the growth rate of surface waves under a hurricane wind is proposed. The model explains the reduction (stabilization) in the drag coefficient during hurricane winds. This model is based on the solution of the Reynolds equations in curvilinear coordinates with the use of the approximation of the eddy viscosity, which takes into account the presence of the viscous sublayer. The profile of the mean wind velocity is found with consideration for nonlinear wave stresses (wave momentum flux), whereas wave disturbances induced in air by waves on the water surface are determined in the context of linear equations. The model is verified by comparing the calculation results with experimental data for a wide range of wind velocities. The growth rate and drag coefficient for hurricane winds are calculated both with and without consideration for the shortwave portion of the windwave spectrum. On the basis of calculations with the quasi-linear model, a simple parametrization is proposed for the drag coefficient and the growth rate of surface waves during hurricane winds. This model is convenient for use in models of forecasting winds and waves.

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.

Modulation of the growth rate of short surface capillary–gravity wind waves by a long wave

Modulation of the growth rate of short capillary–gravity surface wind waves in the presence of a long wave with steepness much smaller than the maximum is studied theoretically. The Miles (1962) mechanism taking into account the viscous wave stresses in the air flow is considered to be the main process of short-wave generation. The short-wave growth rate is defined by the wind velocity gradient in the viscous sublayer of the logarithmic boundary layer. The long wave propagating on the wave surface induces an additional component of the wind velocity gradient oscillating with the length and time periods of the long wave, which results in modulation, with the same period, of the growth rate of the short wave riding on the long one. The growthrate modulation amplitude depends on the parameter M being of the order of the relation between the oscillating and the mean wind velocity gradients in the viscous sublayer \[M=\frac{2kac}{u^2_*}(ckv_{\alpha})^{1/2} \] (where c, k, a are the phase velocity, the wavenumber and the elevation amplitude of the long wave; v a is the viscosity coefficient in the air; u * is the wind friction velocity). When M = O (1) (weak winds and long waves) the oscillating component of the shortwave growth rate is of the same order as the mean one. If M is much smaller than unity, then the relative amplitude of the growth rate is of the same order as the steepness of the long wave.

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.

The analysis of results of remote sensing monitoring of the temperature profile in lower atmosphere in Bergen (Norway)

Considered is the application of MTP-5 meteorological temperature profiler used for the remote sensing of vertical profiles of the air temperature in the planetary boundary layer and the lower one-kilometer layer of the atmosphere. The measurements were carried out in Bergen (Norway) in 2011–2012. The obtained dataset of temperature profiles has temporal resolution of five minutes and vertical resolution of 50 m. The MTP-5 data are complemented with the measurements of the air temperature and the wind taken at two automatic weather stations and with the measurements of the rain intensity made with the rain radar. Studied is the impact of meteorological conditions and precipitation on the MTP-5 readings. It is revealed that formation of a thin water film (of ice or, to a smaller degree, of sleet) on the surface of the sensor cover of MTP-5 has a significant impact on the data of the temperature monitoring. The removal of intensive precipitation (the precipitation rate is >0.2 mm/hour) improved the reliability and quality of the temperature profile monitoring. In particular, it is demonstrated that significant air pollution and stably stratified atmospheric conditions which lead to low temperatures are reliably monitored with this instrument.

Quasi‐steady dissipative nonlinear critical layer in a stratified shear flow

When a wave with small but finite amplitude e propagates towards the CL, where the effects of nonlinearity and dissipation are essential, the jump of mean vorticity over the CL appears. For the dynamically stable stratified shear flow with the gradient Richardson number Ri≳1/4 the jump of vorticity has the same order as the undisturbed one [J. Fluid Mech. 233, 25 (1991)]. The process of formation of the flow with this substantial jump of vorticity (or ‘‘break’’ of the velocity profile) in the CL is studied at large time after beginning of the process. The transition region between the CL and the undisturbed flow, the dissipation boundary layer (DBL), is shown to be formed. Its thickness grows in time proportional to √t (t being time), and the CL moves towards the incident wave. When the jump of the wave momentum flux over the CL is constant in time, the flow characteristics can be found in the most simple way. The velocity profile in the DBL appears to be self‐similar, the displacement of the CL is propor...

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.