Wake Frequency Calculation: Tips, Tricks, and Tools

Wake frequency sits at the heart of many practical questions in wind engineering, offshore design, process instrumentation, and aerospace. A wake with a crisp, repeating pattern can excite a tower or a cable, rattle a thermowell, or show up as a narrow-band peak in wind-tunnel data. The good news: a simple relation does most of the heavy lifting, and with a few checks you can size risk quickly, then decide when to bring in tests or high‑fidelity simulation.

The core relation: Strouhal number

For bluff bodies that shed a Kármán street, the frequency f of vortex shedding scales with the incoming flow speed U and a characteristic length L of the body. The nondimensional Strouhal number St ties these together:

• St = f L / U
• f = St U / L

Pick L to match the shape and orientation that sets the wake width. For a circular cylinder in crossflow, L is the diameter D. For a rectangular deck, L is the width across the wind. For many practical cylinder problems in air or water at moderate Reynolds numbers, St hovers near 0.2. Rectangular sections often fall between 0.06 and 0.15, depending on aspect ratio and corner sharpness.

Two checks go along with this:

• Reynolds number Re = U L / ν should fall in a regime where a near-constant St is valid. Very low Re can suppress periodic shedding, while transitional regimes shift St modestly.
• If the structure can move, wake frequency can lock in to the structure’s natural frequency f_n over a band of flow speeds. During lock-in, the vortex street adjusts to the structure, not the other way around.

A companion relation helps estimate the wind or current that might produce lock-in:

• U_R = f_n L / St

Engineers use U_R to see whether common site conditions overlap the risk band and to tune damping or geometry early.

A quick calculation flow that works in practice

1. Identify the shedding scale
   • Circular cylinder: L = D
   • Prismatic building or deck: L = across-wind width
   • Thermowell or probe: L = outer diameter at the shedder, considering thermowell dimensions
2. Gather fluid and flow data
   • Mean speed U at the body location
   • Fluid kinematic viscosity ν, to check Re
   • Any turbulence intensity or roughness information if available
3. Pick St for the shape and regime
   • Cylinder: 0.18 to 0.22 in subcritical to supercritical ranges
   • Square or sharp-edged rectangle: 0.06 to 0.15
   • Blunt triangles, T‑bars, or complex sections: use data or conservative values
4. Compute f = St U / L and compare
   • Compare with structural modes f_n
   • Estimate lock-in speeds with U_R = f_n L / St
   • Check any code rules of thumb, for example f_shedding / f_n below about 0.8 for thermowells
5. Decide next steps
   • Clear separation from f_n and benign amplitudes: document and move on
   • Close calls: add damping, change geometry, or plan a test/CFD run

Typical Strouhal numbers by shape

These ranges are widely used in early-stage design and quick checks.

Shape and flow orientation	Characteristic length L	Typical St
Smooth circular cylinder, crossflow	Diameter D	0.18–0.22
Square prism, sharp corners	Across-wind width	0.12–0.15
Rectangular prism, sharp-edged	Across-wind width	0.06–0.15
Triangular prism, base to wind	Base width	0.12–0.20
Streamlined airfoil at small angle	Chord	weak, shape-dependent

When shapes depart from these categories, or when nearby bodies disturb the wake, plan on testing or simulation.

Worked examples across domains

Short, real-to-life calculations help calibrate intuition and set expectations.

• Bridge cable in a 12 m/s crosswind
  • D = 0.25 m, adopt St = 0.2
  • f = 0.2 × 12 / 0.25 = 9.6 Hz
  • If the cable’s first in-plane mode is around 8 to 12 Hz, expect a lock-in band near common winds. Helical strakes or added damping can push the response down dramatically.
• Thermowell in a gas line at 18 m/s
  • Outer diameter 25 mm, St = 0.2
  • f = 0.2 × 18 / 0.025 = 144 Hz
  • If a modal survey shows f_n = 180 Hz, the ratio is 0.8. That’s marginal by many company standards, so either stiffen the well, shorten insertion, or change shedding characteristics with a different stem profile.
• Offshore monopile in a 1.8 m/s current
  • D = 6 m, adopt St = 0.2
  • f = 0.2 × 1.8 / 6 = 0.06 Hz
  • Compare with global platform modes and local shell modes. If a low global sway mode sits near 0.05 to 0.1 Hz, apply a VIV fatigue check and consider strakes.

These numbers move linearly with speed. Doubling U doubles f.

When St is not constant, or not enough

Most bluff-body cases at moderate to high Re behave well with a near-constant St. Some situations deserve extra attention.

• Low-Re wake: below about Re ≈ 50 for cylinders, the wake can be steady or symmetric. Periodic shedding may not develop, so the simple St relation does not apply.
• Transitional cylinder regime: near the critical Re range for cylinders, boundary-layer state and roughness alter separation and shift St slightly. Roughness strips or natural roughness can move the critical range.
• Turbulent approach flow: high turbulence broadens the spectral peak and blunts coherence. Field spectra can show a wider bump rather than a razor-sharp line.
• Interference: nearby bodies change shear layers and can create new frequencies. Bundle effects on cables or piping racks often require dedicated tests or CFD.
• Streamlined bodies: airfoils near zero angle can show weak, intermittent shedding, or nearly none at all. For these, time-accurate CFD or measurement gives more reliable results than a borrowed St.

A basic Reynolds check helps guard against inappropriate assumptions. Re = U L / ν should be large enough for the selected St range and not deep in a transitional pocket where scatter grows.

Measuring wake frequency

Laboratory and field setups approach the same goal from different angles, yet share a common signal-processing toolbox.

• Wind or water tunnel
  • Hot-wire or hot-film probes placed in the wake record rapid velocity fluctuations and resolve the dominant line.
  • PIV or LDV provides time-resolved velocity fields, from which a space-time map reveals the shedding pattern and f.
  • Force balances, pressure taps, and surface pressure arrays capture unsteady loads.
• Field and full-scale
  • Accelerometers on cables, decks, or towers show lock-in bands and amplitudes, indicating the resonance frequencies. With a collocated anemometer, cross-spectral analysis links wind speed to response.
  • Strain gauges on critical details quantify fatigue cycles. Power spectral density plots often expose a narrow peak at f = St U / L.

Data acquisition needs enough bandwidth and signal-to-noise ratio. A rough rule is to sample at least 10 to 20 times the expected shedding frequency, with windows long enough to separate wind gust energy from a narrow-band wake line.

Predicting with CFD, responsibly

Unsteady CFD is a strong companion to tests. It can reveal flow physics, guide shape tweaks, and provide spectra where measurement is hard.

• Modeling approaches
  • URANS with k–ω SST or similar models captures periodic shedding for many engineering Reynolds numbers if the mesh and timestep resolve the shear layers.
  • LES or DES improves fidelity for vortex dynamics and unsteady lift but at higher cost, especially in 3D.
  • FSI coupling helps when structural motion feeds back into the wake.
• Practical workflow
  • Mesh refinement across the shear layers and several diameters downstream, with y+ and Δx tied to the turbulence model.
  • Time step small enough to give at least 50 to 100 points per shedding period.
  • Run past transients until periodic behavior stabilizes, then extract lift or pressure time histories and compute f with an FFT or zero-crossing method.
  • Validate against canonical cases, for example a smooth cylinder at a known Re with St near 0.2, before trusting new geometries.

CFD and tests complement each other. CFD supports parametric sweeps, while tests anchor results in real physics and capture surprises like surface contamination, small misalignments, or inlet turbulence that matter in practice.

Safety, fatigue, and design moves that work

Vortex-induced vibration is usually a serviceability and fatigue problem, and in rare cases a strength problem. Designers manage risk by separating likely wake frequencies from structural modes or by limiting response amplitude.

• Tuning the structure
  • Raise or lower a key natural frequency through stiffness changes, braces, or mass distribution, so f_n sits clear of expected f.
  • Add damping devices, for example tuned mass dampers in buildings or viscous dampers on cables, to manage resonance effectively. A higher Scruton number Sc = m ζ / (ρ L²) lowers response markedly.
• Shaping the flow
  • Helical strakes on chimneys or cables break coherence and cut lock-in amplitude.
  • Corner modifications on square towers, openings, or taper along height reduce crosswind excitation and smear out a single dominant f along the span.
  • Fairings or shrouds on process probes change St and reduce lift fluctuations.
• Managing exposure
  • Avoid grouping identical elements at equal spacing in crossflow without spacers or cross-ties. Cable clashing, wake galloping, and inter-array interference become less likely when spacing or phasing varies.
  • In offshore settings, strakes or fairings on risers and piles are standard tools to raise fatigue life.

Standards and company guidelines often wrap these ideas into simple criteria. Wind load standards include Strouhal values for common shapes, and specifications often include thermowell dimensions that are essential for accurate design assessments. Thermowell design practices cap the ratio of shedding frequency to natural frequency. Bridge and cable guidance documents provide damping targets and suppression hardware details.

Common pitfalls and how to avoid them

• Picking the wrong length scale L for a non-circular section. Always tie L to across‑wind width for the shedding direction of interest.
• Ignoring Reynolds number. A constant St only makes sense in the right Re window.
• Missing lock-in behavior. During lock-in, the street follows the structure, so f tracks f_n across a band of speeds. Look for plateau-like response in spectra.
• Using too short a time record. Narrow-band peaks need enough cycles to resolve. Windowing and overlap tapers reduce leakage.
• Sidewall and blockage in tunnels. High blockage alters base pressure and can shift f. Apply blockage corrections or enlarge the test section.
• Mesh too coarse in CFD. Under-resolved shear layers smear vortices and damp the lift signal, pushing St off target.

A compact cheat sheet

Short reference table: from inputs to actions

Input you know	What to compute or look up	What to do next
U, L, shape family	St range and Re	f = St U / L, compare to structural modes
f_n of critical mode	U_R = f_n L / St	Check if site winds or currents cross this speed
Turbulence intensity high	Expect broader peaks	Use longer data windows and consider added damping
Multiple bodies in proximity	Interference risk	Stagger spacing, add cross-ties, or test the array
Roughness or coatings present	Slight St shift	Use conservative St, confirm with small-scale tests

Short notes on tools and data handling

• Sensors: hot-wires for local velocity, PIV or LDV for field mapping, accelerometers for structural response, load cells for forces, pressure taps for unsteady surface loading.
• Software: ANSYS Fluent or CFX, OpenFOAM, STAR‑CCM+ for CFD, with a time-accurate setup; MATLAB or Python for FFT and PSD analysis.
• Data practice: sample at least an order of magnitude faster than the target f, use suitable windows, average spectra over multiple blocks, and verify peak stability against time.

Field-ready example with numbers and decisions