Estonian Scientists Uncover Dangerous Resonant Currents Threatening Ships in Varna Canal

Estonian scientists from Tallinn University of Technology (TalTech) have identified dangerous resonant water oscillations in the canal linking Lake Varna (Bulgaria) to the Black Sea.⁠

The findings come from a peer- reviewed study published in Ocean Science (17 August 2026) by Jüri Elken, Laura Piho, and Maarja Kruusmaa, with a related news release from the Estonian Research Council dated 21 October 2026.

Key details

Pilots had long noticed unusually strong currents in the ~2.4 km- long, 300 m-wide navigation canal (part of the Port of Varna complex, Bulgaria’s largest seaport). Researchers deployed three novel Hydromast stations (developed at TalTech’s Centre for Biorobotics) that recorded current speed, direction and water level at 1- minute intervals.

Analysis showed that moderate flows are occasionally interrupted by high-amplitude oscillations lasting tens of minutes. Dominant periods of 37 minutes (first mode of the channel- lake system) and 19 minutes (related to the channel’s quarter- wave mode and the system’s second mode) stood out. These arise from resonance in the sea- channel- lake system, which can amplify movements under certain atmospheric conditions.

Two strong events were recorded:

• One linked to a meteotsunami (abrupt onset under relatively moderate weather when a weather front moves at resonant speed over shallow coastal waters).
• Another more than 5 hours after a storm with landward/offshore winds up to 20 m/s.⁠

In the strongest cases, current velocity changed by up to 0.8 m/s and water level by up to 0.8 m within about 10 minutes. Such rapid changes pose hazards to ship navigation, harbor operations, and coastal management.

The work used high- resolution observations plus 1D barotropic analytical and numerical modeling of long waves in the system. It discusses approaches for better detecting and forecasting these sub- hourly oscillations, which standard hourly data often miss. The results have broader relevance for other canal–bay– lake systems and for improving port safety and environmental assessments.

Sources: Estonian Research Council / EurekAlert news release; full paper in Ocean Science (doi:10.5194/os-22-2471-2026).

Power Spectral Density (PSD) is a fundamental tool in signal processing and time-series analysis. It describes how the power (or variance) of a signal is distributed across different frequencies.

Simple explanation

Imagine a time series of measurements (e.g., water level or current speed recorded every minute).
PSD answers the question:
“At which frequencies (or periods) is most of the energy and variance concentrated?”

• High peaks in the PSD → strong, regular oscillations at those frequencies.
• A flat or slowly declining spectrum → more random or broadband variability.

Mathematical idea

For a continuous signal $x(t)$x(t), the PSD $S_{xx}(f)$Sxx​(f) is essentially the Fourier transform of the autocorrelation function of the signal (Wiener- Khinchin theorem).

In practice, with discrete data it is usually estimated using methods such as:

• Periodogram
• Welch’s method (averaging modified periodograms of overlapping segments- the method used in the Varna paper)
• Multitaper methods

Units are typically power per unit frequency (e.g., m²/Hz for water level, or (m/s)²/Hz for current velocity).

In the Varna- Black Sea paper

The authors computed the PSD of water- level time series at the four stations in the channel. Key results included:

• Clear spectral peaks at periods of ~37 minutes and ~19 minutes (among others).
• These peaks were identified as resonant modes of the channel- lake system.
• Spectrograms (time- varying PSDs) showed that these oscillations became strongly amplified during the two high- current- speed events.

They also used coherence analysis between stations together with the PSD to confirm that the oscillations were nearly synchronous along the channel.

Why PSD is useful here

Sub-hourly resonant oscillations would be almost invisible in hourly data. High- resolution (1- min) measurements and PSD analysis made it possible to:

1. Detect the natural frequencies of the system.
2. Link those frequencies to physical modes (first mode of the channel- lake system ≈ 37 min, quarter- wave mode ≈ 19 min).
3. Quantify when and how strongly the system resonated under atmospheric forcing (including a meteotsunami).

Welch’s method is one of the most widely used practical techniques for estimating the Power Spectral Density (PSD) of a signal.

It was introduced by Peter D. Welch in 1967 and remains the standard approach in many scientific fields (including oceanography, as used in the Varna paper).

Why do we need it?

A simple periodogram (the squared magnitude of the FFT of the entire record) is a very noisy and statistically inconsistent estimator of the true PSD. Welch’s method reduces this variance by averaging.

How Welch’s method works (step by step)

1. Divide the time series into overlapping segments
   • The full record of length $N$N is split into shorter segments of length $L$L.
   • Adjacent segments usually overlap by 50 % (or sometimes 75 %).
   • Example: a 3- month record of 1- minute data can be divided into many overlapping 1- day or 6- day segments.
2. Apply a window function to each segment
   • A tapering window (Hanning, Hamming, Blackman, etc.) is multiplied with each segment.
   • This reduces spectral leakage caused by the abrupt edges of the finite- length segments.
3. Compute the modified periodogram of each windowed segment
   • Take the FFT of the windowed segment and square its magnitude.
   • Normalize appropriately so the result has the correct physical units (power per frequency).
4. Average all the modified periodograms
   • The final PSD estimate is simply the average of all the individual periodograms.
   • Averaging dramatically reduces the variance of the estimate.

Mathematical summary

If $x_i(n)$xi​(n) is the $i$i-th windowed segment and $U$U is a normalization factor that accounts for the window’s energy, the Welch PSD estimate is:$$\widehat{S}(f)=\frac{1}{KU}\sum _{i=1}^K{\mid \sum _{n=0}^{L-1}{x}_i(n)e^{-j2\pi fn}\mid }^2$$where $K$K is the number of segments.

Trade-offs (important practical points)

Parameter	Effect of increasing it	Typical choice
Segment length $L$L	Better frequency resolution	Long enough to resolve the periods of interest
Number of segments $K$K	Lower variance (smoother spectrum)	As many as possible
Overlap	More segments → lower variance	50 % (most common)
Window type	Controls leakage vs. main- lobe width	Hanning is the default choice

In the Varna paper

The authors used Welch’s method with:

• Longer segments (e.g., 6 days) to examine the broader spectrum (periods from minutes to ~15 hours).
• Shorter segments (e.g., 1 day) to better resolve the higher- frequency sub-hourly peaks (the important 37 min and 19 min oscillations).

Advantages of Welch’s method

• Greatly reduced variance compared with a single periodogram.
• Relatively simple and computationally efficient.
• Works well with real- world (non- stationary, noisy) data.
• Easy to implement in MATLAB (pwelch), Python (scipy.signal.welch), R, etc.

Limitations

• Frequency resolution is limited by the chosen segment length.
• Over- smoothing can hide closely spaced peaks if segments are too short or too many averages are taken.
• Assumes the process is roughly stationary within each segment.

High current speed events in a harbor channel driven by resonant sub- hourly sea level dynamics: an example from Varna, Black Sea

Abstract

Current and sea-level observations in the 2.4 km-long, 300 m-wide channel between Varna Lake and the Black Sea, conducted by three novel Hydromast stations with a 1 min resolution, revealed that moderate sub-hourly dynamics were occasionally interrupted by high-amplitude oscillations with a period of a few tens of minutes. The resonant excitation of the events was studied using barotropic 1D analytical and numerical methods. Basic features of high-intensity sub-hourly variations can be interpreted as linear barotropic long waves in a sea-channel-lake system with resonant and damped forcing. The observed 37 min oscillations, identified from the power spectra, spectrogram, and wavelet analysis, can be explained as the first mode of the channel-lake system. Another period of 19 min resembles the zero, quarter-wave mode of the channel and the second mode of the channel-lake system. During the measurement period, two high-amplitude events were highlighted. One of the events is interpreted as having been caused by a meteotsunami; moderate meteorological conditions prevailed; strong channel oscillations began abruptly and lasted for a few cycles. The second event occurred more than 5 h after landward winds up to 20 m s⁻¹. The observed maximum changes in current and sea level – up to 0.8 m s⁻¹ and 0.8 m, respectively, over 10 min – are harmful to ship navigation, harbor operations, and coastal management. Building on these observations, approaches for detecting and forecasting strong sub-hourly oscillations are discussed.

Key points from the paper

• Study area: Navigation Channel 3 (the older, northern canal) connecting Lake Varna to Varna Bay and the Black Sea, part of Bulgaria’s largest port complex.
• Measurements: Three Hydromast stations recorded current velocity, direction, and water level at 1- minute resolution (mainly February- May 2025).
• Main findings:
  • Background sub- hourly variability is moderate.
  • Resonant oscillations (especially ~37 min and ~19 min periods) can be strongly amplified.
  • Rapid changes of ~0.8 m/s in current and ~0.8 m in water level within ~10 minutes pose real risks to shipping and port operations.
• The authors interpret the events using 1D shallow-water (barotropic long-wave) theory and discuss detection and forecasting methods useful for pilots and harbor authorities.

Downloads available on the page:

• Full PDF article (≈8.7 MB)
• Full- text XML
• BibTeX and EndNote citation files

How to cite:
Elken, J., Piho, L., and Kruusmaa, M.: High current speed events in a harbor channel driven by resonant sub-hourly sea level dynamics: an example from Varna, Black Sea, Ocean Sci., 22, 2471–2490, https://doi.org/10.5194/os-22-2471-2026, 2026.

This is the official open- access page for the peer- reviewed paper that underpins the recent news about dangerous water oscillations between Lake Varna and the Black Sea.

Journal: Ocean Science, Volume 22, pages 2471–2490, 2026

DOI: 10.5194/os-22-2471-2026,

https://doi.org/10.5194/os-22-2471-2026

Published: 17 August 2026

Provided: Estonian Research Council

Authors: Jüri Elken,
Laura Piho,
and Maarja Kruusmaa