of numerical simulations and our estimates reported here suggest that it is proportional to Up
4 , where Up is the jet velocity at the inflow to the thermocline. This
might provide a better approximation of the experimental data by [10].
Surface Manifestations of Internal Waves
Surface manifestations of internal waves were investigated both experimentally and
theoretically by [13]. The experimental part consists of two series of experiments in
the LTST with different arrangement of the measuring equipment. The experiments
were performed at the stratification with a shallow thermocline in order to make the
surface currents caused by internal waves detectable. The horizontal velocities at
the water surface were measured by a modified Particle Tracking Velocimetry
technique (PTV), see [13] for details. The measured velocities are shown in Fig. 12.
As a first step, the time before the signal detected by the PTV at a sufficient
distance from the source (a collector model) was compared to the theoretically
estimated time of the signal arriving to the measurement area. The latter time was
derived from the theoretical group velocity of internal waves at the generation
frequency. The velocity has been obtained, as described in section “Generation of
Internal Waves by Turbulent Buoyant Plumes”, from the dispersion relation following from the solution of the eigenvalue problem for the Taylor-Goldstein
equation (with measured profiles of buoyancy and mean horizontal velocity in the
thermocline). Theoretically predicted times for different outflow velocities correspond to the experimentally measured times, thus confirming that a signal detected
at the surface could have been related to internal waves.
As a second step, theoretically predicted amplitudes of the horizontal velocity at
the surface were compared to the experimentally measured velocities. Theoretical
estimates were as before based on the solution of the eigenvalue problem for the
Taylor-Goldstein equation. The authors used the vertical profile of the stream
function to calculate the displacements of the liquid particles from the equilibrium
due to IW at the frequency of generation [3]. The theoretical estimates of surface
velocities were calculated on the basis of these considerations:
uðz, tÞ = ðc − U 0 Þ
∂ξ
∂z
− ξ
∂U 0
∂z
.
ð5Þ
The theoretically predicted velocities significantly exceeded the experimentally
measured data. This discrepancy was explained by the presence of surfactant film in
the LTST. The films were taken into account in the theoretical analysis, and an
agreement between the measured and theoretical velocities was obtained for the
experimentally measured elasticity coefficients.
The third step of the analysis included a theoretical estimate of the hydrodynamic contrasts, which surface currents can induce in the spectra of surface wind
Surface Manifestations of Internal Waves Induced …
81
4 , where Up is the jet velocity at the inflow to the thermocline. This
might provide a better approximation of the experimental data by [10].
Surface Manifestations of Internal Waves
Surface manifestations of internal waves were investigated both experimentally and
theoretically by [13]. The experimental part consists of two series of experiments in
the LTST with different arrangement of the measuring equipment. The experiments
were performed at the stratification with a shallow thermocline in order to make the
surface currents caused by internal waves detectable. The horizontal velocities at
the water surface were measured by a modified Particle Tracking Velocimetry
technique (PTV), see [13] for details. The measured velocities are shown in Fig. 12.
As a first step, the time before the signal detected by the PTV at a sufficient
distance from the source (a collector model) was compared to the theoretically
estimated time of the signal arriving to the measurement area. The latter time was
derived from the theoretical group velocity of internal waves at the generation
frequency. The velocity has been obtained, as described in section “Generation of
Internal Waves by Turbulent Buoyant Plumes”, from the dispersion relation following from the solution of the eigenvalue problem for the Taylor-Goldstein
equation (with measured profiles of buoyancy and mean horizontal velocity in the
thermocline). Theoretically predicted times for different outflow velocities correspond to the experimentally measured times, thus confirming that a signal detected
at the surface could have been related to internal waves.
As a second step, theoretically predicted amplitudes of the horizontal velocity at
the surface were compared to the experimentally measured velocities. Theoretical
estimates were as before based on the solution of the eigenvalue problem for the
Taylor-Goldstein equation. The authors used the vertical profile of the stream
function to calculate the displacements of the liquid particles from the equilibrium
due to IW at the frequency of generation [3]. The theoretical estimates of surface
velocities were calculated on the basis of these considerations:
uðz, tÞ = ðc − U 0 Þ
∂ξ
∂z
− ξ
∂U 0
∂z
.
ð5Þ
The theoretically predicted velocities significantly exceeded the experimentally
measured data. This discrepancy was explained by the presence of surfactant film in
the LTST. The films were taken into account in the theoretical analysis, and an
agreement between the measured and theoretical velocities was obtained for the
experimentally measured elasticity coefficients.
The third step of the analysis included a theoretical estimate of the hydrodynamic contrasts, which surface currents can induce in the spectra of surface wind
Surface Manifestations of Internal Waves Induced …
81