### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Numerical Calculations
- 3. Measurements in the Strait of Kara Gates With a Towed CTD
- 4. Radar Imaging
- 5. Conclusions
- Acknowledgments
- References

[1] We analyze towed CTD measurements, numerical model calculations, and radar images in the Strait of Kara Gates. The measurements were made during an expedition in September 2007. Strong internal tides propagating from the Kara Strait to the Barents Sea were recorded. The internal waves are intensified by the opposite current from the Barents Sea. An internal bore followed by a packet of short-period internal waves is found southwest of the strait. Radar images show that short-period internal waves are generated after the internal bore. A hydraulic jump is found on the eastern side of the strait. Numerical modeling agrees with the experimental results.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Numerical Calculations
- 3. Measurements in the Strait of Kara Gates With a Towed CTD
- 4. Radar Imaging
- 5. Conclusions
- Acknowledgments
- References

[2] The Strait of Kara Gates (Figure 1) is located in northeastern part of Europe between the Barents and Kara Seas. The strait is also called Kara Strait or Karskiye Vorota. The Barents Sea is a relatively warm sea. In contrast, the Kara Sea is an ice-cold sea. The sea is not covered with ice only during two months in the summer. A warm flow exists from the Barents Sea to the Kara Sea due to the density difference.

[3] A shallow sill crosses the strait. The minimal depth of the sill is 30 m. It separates two basins, which are deeper than 100 m. *Pavlov and Pfirman* [1995] analyzed measurements of internal waves in the Kara Sea and indicated that internal waves with tidal frequencies are observed in the Kara Sea in summer. Their amplitudes are up to 12 m and the wavelength is several tens of kilometers. We do not possess any reliable historical oceanographic field measurements of short period internal waves in the Kara Gates because the region has been poorly investigated.

[4] In September–October 1997, researchers from the Shirshov Institute of Oceanology performed moored measurements of currents and temperature in the Strait of Kara Gates. Thus, we carried out the first study of internal waves in this region. Four moorings with currents and temperature meters were deployed for a few days in the strait. Internal tides in the Kara Gates were analyzed by *Morozov et al.* [2003] on the basis of moored measurements, numerical modeling, and satellite image.

[5] The analysis of measurements revealed that the flow is generally directed to the Kara Sea with velocities ranging from 6 to 25 cm/s. The maximum velocity reaches 50 cm/s. The core of the current is located at a depth of 50 m beyond the sill of the strait. A bottom reverse flow from the Kara Sea (mean velocity 11 cm/s, maximum velocity 43 cm/s) was recorded by a deep instrument.

[6] Temperature measurements demonstrated that the vertical displacement of isothermal surfaces from the mean position reaches 40 m, while the total depth at the measurement site is slightly greater than 100 m.

[7] The structure of internal tides in the Kara Gates is similar to that in the Strait of Gibraltar. Internal tides are generated due to a strong barotropic tide on slopes of the sill that crosses the strait [*Brandt et al.*, 1996; *Hibiya*, 1990; *Morozov et al.*, 2002]. A warm current from the Barents Sea to the Kara Sea generated by sea level difference intensifies the internal tide propagating to the southwest [*Morozov et al.*, 2003]. Superposition of the current and barotropic tide flow forms a complex dynamic situation in the Kara Gates.

[8] The field studies were continued in September 2007. The joint application of towed CTD measurements, radar imaging, and numerical modeling is a new approach in these studies. The results obtained are reported in this paper.

### 2. Numerical Calculations

- Top of page
- Abstract
- 1. Introduction
- 2. Numerical Calculations
- 3. Measurements in the Strait of Kara Gates With a Towed CTD
- 4. Radar Imaging
- 5. Conclusions
- Acknowledgments
- References

[9] The experiments were preceded by numerical calculations to plan the experiment and estimate the expected parameters of internal waves.

[10] Numerical modeling was performed to study the generation and propagation of the internal tide in the strait and the influence of the currents on the dynamics of internal motion. The model allows us to obtain a pattern of the internal wave motion generated over the slopes of the sill due to the barotropic tidal currents that induce vertical motion of the isopycnals. The numerical model also allows us to analyze the internal tide evolution during its propagation away from the generation region and to study the properties of the wave.

[11] We use a fully non-hydrostatic model developed by *Vlasenko and Hutter* [2002] with continuous stratification, which allows us to analyze the generation of internal waves over bottom topography and their propagation and evolution. We consider the flow in a continuously stratified rotating ocean of variable depth. The details of the model and governing equations are described by *Morozov et al.* [2002] and *Vlasenko and Hutter* [2002]. Although the model is two dimensional, we introduce an equation for the *V*-component of velocity normal to the *x*, *z* plane to account for the effects of rotation. The *V-*component is considered constant. The effects of refraction and radiation of waves are not considered in the model. The model is forced by specifying the stream function, which models the permanent flow from the Barents Sea to the Kara Sea superimposed on the tidal motion with M2 frequency.

[12] The wave perturbations of vorticity, stream function, and density are assumed zero at the lateral boundaries located far from bottom irregularities at the submarine ridge. We stop the calculations when the wave perturbations reach the lateral boundaries. Continuous stratification was specified in each of the 20 layers based on CTD measurements. The density assumed in the model corresponds to the measurements in the region. The bottom topography was specified on the basis of ETOPO2 digital dataset (available at http://www.ngdc.noaa.gov/mgg/global/global.html) and bottom echo sounding during passage of the strait.

[13] We have chosen a domain 80 km long with a horizontal step of 50 m and 20 vertical levels. The time step was approximately equal to 2.2 seconds. We specified the coefficients of horizontal eddy viscosity and density diffusivity as 6 m^{2}/s over the ridge and 2 m^{2}/s beyond the ridge over the flat bottom in the model. Coefficients of vertical turbulent viscosity and density diffusion were set at 0.0001 m^{2}/s. This choice of parameters allowed us to avoid numerical instability [*Richtmyer*, 1957]. A small horizontal step in these calculations allows us to increase the non-linearity, which suppresses the dispersion due to stronger rotation at high latitudes.

[14] Since the lower current from the Kara Sea occupies only a thin layer near the bottom in the deepest part of the strait, the model calculations took into consideration only the northeasterly flow from the Barents Sea, which occupies the entire depth. In the model (Figure 2), the flow direction is from left to right. Its mean velocity is 12 cm/s. A periodical barotropic tidal flow was superimposed on this current. The tidal current was estimated on the basis of TOPEX/POSEIDON satellite measurements. The amplitude of the tidal velocities was equal to 9 cm/s.

[15] Periodic changes in the tidal horizontal flow induce an internal wave propagating in both directions away from the sill. Perturbations of the density field induced by the internal tide are shown in the upper part of Figure 2 after four tidal periods of calculation.

[16] Owing to the existence of the permanent current, the density field fluctuations are asymmetric with respect to the sill. Due to the oppositely directed mean current the barotropic tide induces a stronger internal tide propagating to the southwest (opposite to the mean current) as compared to the NE-propagating one. The leading edge of the wave is flat and the trailing edge is steep. At a small distance from the ridge, the internal bore is formed at the trailing edge. The isopycnals sharply deepen almost by 10–15 m and form a bore. A packet of short-period waves follows the bore. Both the bore and short-period internal wave packets are propagating westward. The smaller scale waves and the bore induce vertically and horizontally non-uniform motions that influence surface waves. Manifestations of these motions are recognized in radar images [*Bakhanov and Ostrovsky*, 2002]. East of the sill, jumps in the depth of isotherms are almost as large as west of the sill, but no wave packets are formed after these jumps.

[17] A sharp deepening of isopycnals is observed on the Kara Sea side. This is a hydraulic jump that is trapped on the lee side of a flow beyond an obstacle. According to the calculations the isopycnal surface deepens from 50 to 110 m. The isopycnals deepen stepwise and follow the peaks of the bottom topography.

[18] Based on the numerical modeling, the wavelength of internal tide southwest of the sill (Barents Sea side) is estimated at 24 km. Introduction of the current from the Barents Sea intensifies the internal bore in the southwestern part of the strait.

[19] The amplitude of the wave oscillations over the slopes of the sill is nearly 30 m. An internal bore is formed at some distance from the sill on the Barents Sea side. It is manifested as a deepening of density contour lines by a jump greater than 10 m. A packet of short-period internal waves follows the internal bore.

[20] The model unites the results of towed measurements of internal tide (larger scale phenomenon) and radar imaging of a packet of high-frequency internal waves (smaller scale phenomenon).

[21] The wavelength can also be estimated from the dispersion relation. We should admit that the wave is generated over the sill in the strait and further propagates over a flat bottom. The latter is not true in reality. The calculation was performed by means of integrating the equation for vertical velocity (*w*) caused by an internal tide at zero boundary conditions at the surface and bottom:

where *N*^{2}(*z*) is the mean squared vertical profile of the Brunt-Vaisala frequency, *ω* is semidiurnal frequency, *f* is the Coriolis parameter, *k* is vertical wavenumber. The equation was integrated with a vertical step of 10 m.

[22] The wavelength calculated from the dispersion relation was equal to 28 km if the mean current is zero and 25 km if the vertically uniform current of 12 cm/s is directed opposite to the wave. This agrees with the results of calculations using the numerical model. Such a surprisingly long wavelength for the Kara Gates region is explained by proximity of the region to critical latitudes, where the M2 period becomes very close to the inertial period. Due to a small denominator the coefficient in the third term of (1) becomes large, which should be compensated by decreasing wavenumber *k*.

### 3. Measurements in the Strait of Kara Gates With a Towed CTD

- Top of page
- Abstract
- 1. Introduction
- 2. Numerical Calculations
- 3. Measurements in the Strait of Kara Gates With a Towed CTD
- 4. Radar Imaging
- 5. Conclusions
- Acknowledgments
- References

[23] The measurements were carried out in the strait with a towed CTD-profiler IDRONAUT 316 in scanning regime. The instrument was towed by the ship moving at a speed of 6 knots. During the ship motion, the instrument was periodically lowered and raised so that the records were made almost from the surface to the bottom. The cycle lasted for a few minutes (approximately 5 min) depending on the depth. The horizontal resolution of measurements was several hundred meters, and the distance between the lowest point of lowering and the bottom was approximately 2 meters. The same distance was maintained between the surface and the upper points of measurements.

[24] The scheme of the towing legs is shown in Figure 1. The towed measurements were carried out from September 8, 2007 (22:20) to September 9, 2007 (06:40). The section was made from the start point at 70°02′N, 57°55′E to a navigation turn at 70°23′N, 58°02′E and final point at 70°48′N, 58°47′E.

[25] The temperature section obtained by towed CTD-profiler IDRONAUT 316 in scanning regime is the most representative result from the point of view of internal tide generation, formation of internal bore and hydraulic jump. The field of isopycnals based on the numerical calculations and temperature section obtained by towed profiler are shown on the same scale in Figure 2.

[26] Figure 2 shows a snapshot of the displacements of isotherms along the cruise track. The measurements were made during a period shorter than the tidal cycle. However, no reverse flow was recorded because the estimated velocity of the mean flow was 12–15 cm/s, while the amplitude of the barotropic tide currents was 9 cm/s.

[27] According to the measurements, the internal bore is located at a distance of 18 km from the shallowest crest of the sill. One should keep in mind that the bore propagates westward. The 1°C isotherm sharply deepens by 15 m near the slope of the sill. The horizontal size of internal tide wave (the leading slope of the wave and the bore) allows us to estimate the wavelength at 21 km. According to the numerical calculation, the wavelength is equal to 24 km. The disagreement between the wavelength on the graphs based on numerical calculations and towed measurements is caused by the Doppler effect during the measurements when the ship was moving opposite to the wave propagation. The speed of the ship was U = 3 m/s (6 knots). According to the numerical calculations, the opposite phase velocity of tidal internal wave, was *c* = 0.4 m/s. According to the Doppler effect, when the ship moves in the opposite direction to the wave, the measured wave period *T*_{D} would be equal to

and the Doppler shifted wavelength would be equal to

which is close to the observed value. Here, we use only the plus sign in the denominator, which corresponds to the opposite directions of the ship and wave motions.

[28] A wave packet of short-period internal waves should appear after the internal bore. However, the spatial resolution of the towed instrument is approximately 900 m over the ocean depth close to 100 m. The speed of the ship is 6 knots, and the cycle of lowering and raising the instrument lasts approximately 5 minutes. During this time, the ship travels more than 900 m. Wavelengths of short internal waves in the wave packet after the bore estimated from the numerical model are of the order of several hundred meters. Thus, the spatial resolution during such measurements is not enough to resolve such short internal waves.

[29] Towed measurements demonstrate that a hydraulic jump is observed east of the sill. The 0°C isotherm deepens from 60 to 130 m. The hydraulic jump measured by the towed CTD-profiler is similar to that in the numerical modeling. It is a prominent feature and occupies a quasi-stationary location east of the sill.

[30] When an internal wave propagates opposite to the current its amplitude increases, and the wave length becomes shorter. If the effect is strong, an internal bore appears similar to the tidal bore when the tide propagates upstream in the river. On the other side of the sill, the wave propagates in the same direction as the current. This does not produce a strong bore. However, a bore is also seen in the numerical calculations on the Kara Sea side.

### 5. Conclusions

- Top of page
- Abstract
- 1. Introduction
- 2. Numerical Calculations
- 3. Measurements in the Strait of Kara Gates With a Towed CTD
- 4. Radar Imaging
- 5. Conclusions
- Acknowledgments
- References

[33] Analysis of the data of towed measurements in the Strait of Kara Gates shows that internal tides in the strait have large amplitude. The waves propagate along the strait axis in a stratified flow, which changes their properties. Internal tides in the strait are induced by the barotropic tide flowing over the sill. Due to the mean current flowing over the sill a hydraulic jump is formed, which is trapped east of the slope. The displacement of isopycnals in the jump exceeds 60 m.

[34] Internal tidal motion affects the entire water column. In the western part of the strait, the internal tide is intensified because its direction is opposite to the mean current. This interaction with the current shortens the wavelength and concentrates the wave energy at a smaller spatial scale and, hence, the wave amplitude increases. This process leads to a nonlinear transformation, breaking of the internal tide, formation of an internal bore on the trailing edge of the wave, and intense vertical motions that are manifested at the sea surface. The packets of short period internal waves, which follow the bore, are recorded at the surface by radar images.

[35] The numerical model used to calculate the generation and propagation of internal tides in the strait confirmed the observed properties of the internal tide. The wave parameters obtained in the model are in good agreement with the field observation.